PROCEEDINGS OF A SYMPO - IAEA Nuclear Data Services

PROCEEDINGS OF A SYMPO 

■ i 

INTERNATIONAL ATOMIC ENERGY AGENCY, VIENNA, 1 973

NUCLEAR DATA 

IN SCIENCE AND TECHNOLOGY 

VOL. I

The follow in g States are M em bers o f the International A to m ic Energy A g en cy : 

A F G H A N IS T A N G U A T E M A L A P A N A M A 

ALB A N IA H A IT I P A R A G U A Y 

ALGERIA H O LY SEE PERU 

A R G E N TIN A H U N G A R Y PHILIPPINES 

A U S TR A L IA ICELAND POLAND 

A U S T R IA IN D IA POR TU G AL 

BANGLADESH INDONESIA R O M A N IA 

BELGIUM IRAN SA U D I ARA BIA 

BOLIVIA IRAQ SENEGAL 

BRAZIL IRELAND SIERRA LEONE 

BULGARIA ISRAEL SINGAPORE 

BURMA IT A L Y S O U T H AFRIC A 

BYELORUSSIAN S O V IE T IV O R Y C O A S T SPAIN 

S O C IA L IS T REPUBLIC J A M A IC A SRI L A N K A 

C A M E R O O N JAPAN SU D A N 

C A N A D A JORDAN SWEDEN 

CHILE K E N Y A SW ITZE R LAN D 

C H IN A KHMER REPUBLIC SYR IA N ARAB REPUBLIC 

CO LOM B IA K O R E A , REPUBLIC OF TH A IL A N D 

C O S T A RICA K U W A IT TU N ISIA 

CU BA LEBANON TURK EY 

CYPRUS LIBERIA U G A N D A 

C Z E C H O S L O V A K S O C IA L IS T LIB YAN ARAB REPUBLIC UK R A IN IA N S O V IE T S O C IA L IS T 

REPUBLIC LIECH TEN STEIN REPUBLIC 

D EN M ARK LUXEM BOURG UNION OF S O V IE T S O C IA L IS T 

D O M IN IC A N REPUBLIC M A D A G A S C A R REPUBLICS 

ECU AD O R M A L A Y S IA UNITED K IN G D O M OF G REAT 

E G Y P T , ARAB REPUBLIC OF M A L I BRITAIN A N D NORTHERN 

EL S A L V A D O R M E X IC O IRELAND 

E TH IO PIA M O N A C O UN ITE D S T A T E S O F A M ERICA 

FIN LAND M O R O C C O U R U G U A Y 

FRANCE NETHERLANDS VENEZUELA 

G ABO N NEW ZE A LA N D V IE T -N A M 

G E R M A N Y , FEDERAL REPUBLIC OF NIGER Y U G O S L A V IA 

G H A N A NIGERIA ZA IR E , REPUBLIC OF 

GREECE N O R W A Y Z A M B IA 

P A K IS T A N 

T h e A g e n cy * s S ta tu te w as a p p r o v e d o n 2 3 O c t o b e r 1 9 5 6 b y th e C o n fe r e n c e o n th e S ta tu te o f th e IA E A 

h e ld at U n ited N a tion s H ea d q u a rters, N ew Y o r k ; it e n te re d in to f o r c e on 29 July 1 9 5 7 . T h e H eadquarters o f 

th e A g e n c y a re situ ated in V ie n n a . Its p r in c ip a l o b je c t iv e is " t o a c c e le r a t e and e n la r g e th e c o n tr ib u tio n o f 

a t o m ic e n e r g y to p e a c e , h e a lth and prosp erity th rou gh ou t th e w o r ld " . 

Prin ted by th e IA E A in A u stria 

S e p te m b e r 1973

PROCEEDINGS SERIES 

NUCLEAR DATA 


PROCEEDINGS OF THE SYMPOSIUM ON 

APPLICATIONS OF NUCLEAR DATA 


HELD BY THE 

INTERNATIONAL ATOMIC ENERGY AGENCY 

IN PARIS, 12 - 16 MARCH 1973 

In two volumes 

VOL. I 

INTERNATIONAL ATOMIC ENERGY AGENCY 

VIENNA, 1973

N U C L E A R D A T A IN S C IE N C E A N D T E C H N O L O G Y 

IA E A , V IE N N A , 19 7 3 

S T I / P U B / 3 4 3

FOREWORD 

The IAEA Sym posium on "A pplication s o f N uclear Data in Science and 

T ech n ology" was convened by the International A tom ic E nergy A gency on 

12-16 M arch 1973 in P a ris at the invitation o f the F ren ch G overnm ent. 

The m eeting was held on the recom m endation of the International N uclear 

Data C om m ittee (INDC) and the International W orking Group on N uclear 

Structure and R eaction Data (IWGNSRD). The main purpose o f the Symposium 

was to illum inate the needs fo r nuclear data in the tech n ologica l and s cie n 

tific com m unity. O ver 200 delegates attended, represen tin g 30 countries 

and five international organ izations. A total o f 74 papers was presented, 

including the Keynote A ddress and the Sym posium Sum m ary. 

F o r many yea rs the m echanism s fo r satisfying the nuclear data needs 

related to neutron-induced reaction s have been fa irly w ell organized by those 

con cern ed with n eu tron -rea ctor tech n ology, which is a m ajor field o f ap p lication 

fo r this kind o f data. H ow ever, fo r sev era l y ea rs it has becom e increa 

sin g ly evident that there is a strong need fo r better, u p -to-d ate c o m 

pilations o f n uclear data fo r a large num ber o f other application s. The IAEA 

was th erefore requested to convene a sym posium in o rd e r to review the 

status o f and needs fo r new nuclear data evaluation activ ities. During the 

p rep aration , it becam e evident that the sym posium should em phasize data 

needs in the variou s applications rather than existing data com pilation 

activ ities. 

The p rogra m com m ittee attempted to achieve a balance betw een rea ctor 

and n o n -re a cto r applications as w ell as a balance between the needs fo r 

variou s applications and the needs for com pilation w ork. As a resu lt, four 

o f the sixteen regular session s w ere devoted to applications related to 

nuclear energy, seven to other applications and five to top ics related to 

data com p ilation s. In con trast to the International C onferences on N uclear 

Data fo r R ea ctors (P a ris , 17 - 21 O ctober 1966, and H elsinki, 15-19 June 

1970), this Sym posium was not meant to be a forum fo r the presentation o f 

experim en tal data. 

The Sym posium dem onstrated that the com pilation o f structure and 

d ecay data would benefit from con sid erably in creased support. These data 

are b a sic to m ost other d ata-application -orien ted com pilations. The long 

delay in bringing com pilations o f this type up to date cau ses unacceptable 

h old-u ps in the p rocess o f bringing such data from p rod u cers to u sers. 

Under the heading 'Sym posium Sum m ary' , D r. W .B. L ew is, at the end o f 

the m eeting, d iscu ssed the m ost im portant con clu sion s to be drawn from 

the sym posium with regard to data needs and the status of com pilations. 

A further sum m ary o f the m eeting, by L. H järne, appears in A tom ic Energy 

R eview , 1973, V o l.11, N o.2, 395. 

The P roceed in g s are divided into two volu m es, the first o f which con 

tains, besid es the Keynote A d d ress, th irty-tw o papers in the field s o f 

Future T echn ology R equirem ents, R eactor T echnology, Safeguards, L ife 

S cien ces, R adioisotopes in C hem istry, F issio n -P ro d u ct N uclear Data and

A cce le ra to r and Space Shielding. The second volum e - with forty con tribu 

tions, in addition to the Sym posium Sum m ary - co v e rs the field s o f Fusion 

R esea rch , Evaluated Neutron Data F ile s, A ctivation A nalysis (G eneral and 

N eutrons), C om pilation and Evaluation - Data C entres, L arge-V olu m e 

C om pilations, V arious A pplications, A ctivation A nalysis: Charged P a rticles 

and Photons, and A pplication-O riented Computations and Evaluations. 

The A gency w ishes to thank the French authorities fo r their hospitality 

and active support of the Sym posium , and the authors and participants for 

their valuable contributions. S pecial thanks are due to the Chairmen o f the 

individual session s fo r their su ccessfu l efforts in guiding the d iscu ssion s. 

E D I T O R I A L N O T E 

The p a p ers and d iscu ssion s in corp ora ted in the p roceed in g s published 

by the International A tom ic E n ergy A g en cy a re edited by the A g en cy 's ed itorial 

sta ff to the exten t con sid ered n e c e s s a r y fo r the r e a d e r 's a ssista n ce. 

The view s exp r e s s e d and the gen era l s ty le adopted rem ain, h ow ever, the 

resp o n sib ility o f the named authors o r particip an ts. 

F o r the sake o f sp eed o f publication the p resen t P roceed in gs have been 

printed by com position typing and p h o to -o ffset lithography. Within the lim itations 

im p osed by this m ethod, e v e r y effo rt has been m ade to maintain a 

high ed itorial standard; in particular, the units and sym b ols em ployed a re 

to the fu llest p ra ctica b le exten t th ose standardized o r recom m ended by the 

com peten t international scien tific bodies. 

The a ffilia tion s o f authors a r e th ose given at the tim e o f nom ination. 

The u se in th ese P roceed in g s o f p a rticu la r designations o f cou n tries o r 

te r r ito r ie s d oes not im ply any judgem ent by the A g en cy as to the legal status 

o f such cou n tries o r te r r ito r ie s , o f th eir au th orities and institutions o r o f 

the delim itation o f th eir bou n d a ries. 

The m ention o f sp e c ific com panies o r o f th eir products o r brand-nam es 

d oes not im ply any en d orsem en t o r recom m endation on the part o f the 

International A tom ic E n ergy A g en cy.

CONTENTS OF VOL. I 

KEYNOTE ADDRESS - OPENING OF THE SYMPOSIUM 

C riteria o f ch oice for com pilations o f nuclear data .............................. . 3 

D.J. Horen and A.M. Weinberg 

FUTURE TECHNOLOGY REQUIREMENTS (Section I) 

F ission in g uranium plasm as (IA E A -S M -1 7 0 /5 3 ).......................................... 15 

K. Thom and R. T. Schneider 

D iscu ssion .............................................................................................................. 37 

N uclear data requirem ents for fu sion -fission (hybrid) re a cto rs 

(IA E A -S M -170/56) .............................................................................................. 39 

W.C. Wolkenhauer and B. R. Leonard, Jr. 

D iscu ssion .............................................................................................................. 50 

N uclear data requ irem en ts in the design o f the BIFOLD N uclear 

P ow er Source (IA E A -S M -170/39) ................................................................ 51 

W. F. Stubbins and R. A. Wolfe 

A study o f lon g -term heat generation in nuclear by-products 

from LWR and LM FBR system s (IA E A -S M -170/58) ......................... 71 

J. A. Angelo, Jr., R. G. Post, F. Haskin and 

C. Lewis 

D iscu ssion .............................................................................................................. 87 

Sections e ffica ce s de creation de dom m ages (IA E A -S M -170/65) . . . 89 

M. Lott, J.P. Genthon, F. Gervaise, P. Mas, 

J. C. Mougniot et Nguyen Van Doan 

D iscu ssion .............................................................................................................. 126 

REACTOR TECHNOLOGY (Section II) 

Точность ядерных данных и ее влияние на разработку быстрых 

реакторов. Подход к выработке требований 

на точность ядерных данных 

(IA E A -S M -170 / 91 ) .............................................................................................. 129 

J I .H . Усачев,В.Н. Манохин иЮ.Г. Бобков 

D iscu ssion .............................................................................................................. 142 

R ôles re sp e ctifs des évaluations et des exp érien ces in tégrales pour 

la physique des réacteu rs rapides (IA E A -S M -170/69) ....................... 143 

J.Y. Barré et J.P. Chaudat 

D iscu ssion .............................................................................................................. 154

C r o s s -s e ctio n uncertainty effects on the ratio o f the high-energy 

neutron flux to the pow er and resulting estim ation o f the 

irradiation lim it e r r o r s in a fast pow er rea ctor 

(IA E A -S M -1 7 0 /7) ................................................................................................ 155 

A. Boioli, G. P. Cecchini, M. Cosimi and 

M. Salvatores 

E l uso de parám etros neutrónicos de reson an cia y seccion es 

e fica ce s neutrónicas de captura radiativa para la evaluación 

de la in tegral de reson an cia de activación resu elta y no 

resu elta (IA E A -S M -170/2) ............................................................................ 163 

G .H . Ricabarra, R. Turjanski y M .D . Ricabarra 

A ssessm en t o f m ethods and data fo r predicting integral 

p rop erties fo r u ranium -fuelled th e rm a l-re a cto r physics 

experim ents (IA E A -S M -170/18) .................................................................. 175 

R. C h a w la 

U tilisation de résultats de m esu res intégrales pour 

p r é cis e r le s valeurs des constantes n u cléaires neutroniques 

(IA E A -S M -170/67) .............................................................................................. 189 

P. R e u s s 

D iscu ssion .............................................................................................................. 194 

SAFEGUARDS (Section III) 

The role o f nuclear data in nuclear m aterial safeguards 

(IA E A -S M -170/78) .............................................................................................. 197 

C. Weitkamp, A. v. Baeckmann, K. Bohnel, 

M. Küchle and L. Koch 

D iscu ssion .............................................................................................................. 215 

The role o f nuclear data in the practical application of 

n on-destru ctive nuclear assay m ethods (IA E A -SM -170/54) ............ 217 

M. M. Thorpe 

Influence of uncertainties in fission -p rod u ct nuclear data on 

the interpretation of gam m a-sp ectrom etric m easurem ents 

on burnt fuel elem ents (IA E A -S M -1 7 0 /1 2 )................................................ 233 

O. J. Eder and M. Lammer 

D iscu ssion .............................................................................................................. 267 

An analysis o f claim s and available radioactive data for 

safeguards (IA E A -S M -170/1) ....................................................................... 269 

D. Berényi 

D iscu ssion .............................................................................................................. 282 

U F E SCIENCES (Section IV) 

Le role des données n u cléaires dans l'u tilisation des 

indicateurs rad ioactifs en m édecine (1 A E A -S M -1 7 0 /9 7 )..................... 287 

C. Kellershohn et D. Comar 

D iscu ssion .............................................................................................................. 311 

N uclear data requirem ents in ra d iological protection and 

radiotherapy (IA E A -S M -170/59) .................................................................. 313 

J. A. Dennis 

D iscu ssion .............................................................................................................. 326

P rob lèm es p osés par la fabrication de plutonium -238 de qualité 

biom éd icale (IA E A -S M -170/64) ................................................................... 329 

R. Berger, C. Devillers, F. Gervaise et G. Le Coq 

D iscu ssion .............................................................................................................. 334 

N uclear data and neutron activation analysis o f b iologica l sam ples 

(IA E A -S M -170/3) ................................................................................................ 335 

N. M. S p y r о u 

L es constantes n u cléaires dans le s p h arm acopées; leu r utilité 

pour la norm alisation des substances pharm aceutiques 

(IA E A -S M -170/70) .............................................................................................. 351 

Y. Cohen 

D iscu ssion .............................................................................................................. 356 

A pplication of nuclear data in the preparation o f radion u clides 

for use in m edicine and biology (IA E A -S M -170/92) ............................ 359 

R. B. R . P e r s s о n 

D iscu ssion .............................................................................................................. 372 

RADIOISOTOPES IN CHEMISTRY (Section V) 

R adioisotope applications in ch em istry — a review 

(IA E A -S M -17 0 /9 6 ) .............................................................................................. 377 

L. G ó r s k i 

D iscu ssion .............................................................................................................. 381 

N uclear data requ ired fo r the interpretation o f hot-atom 

ch em istry (IA E A -S M -170/28) ....................................................................... 383 

A. H. W. Áten 

D iscu ssion .............................................................................................................. 389 

FISSION-PRODUCT NUCLEAR DATA (Section VI) 

F ission -p rodu ct chain yields from experim ents in therm al 

re a cto rs (IA E A -S M -1 7 0 /9 4 )............................................................................ 393 

E.A.C. Crouch 

D iscu ssion .............................................................................................................. 457 

Cum ulative yields of therm al neutron fission products: som e 

resu lts and recom m endations based on a recen t evaluation 

(IA E A -S M -170 /3 4 ) .............................................................................................. 459 

W .H . Walker 

D iscu ssion .............................................................................................................. 476 

Bibliothèque de données relatives aux produits de fission 

(IA E A -S M -170/63) .............................................................................................. 477 

C. Devillers, J. Blachot, M. Lott, B. Nimal, 

Nguyen Van Dat, J .P . Noel et R. De Tourreil 

D iscu ssion o f fission -p rod u ct yield evaluation m ethods and a 

new evaluation (IA E A -S M -170/13) .............................................................. 505 

M. Lammer and O. J. Eder 

D iscu ssion .............................................................................................................. 551 

Need o f nuclear le v e l sch em es fo r calculated c r o s s -s e c tio n s 

o f fission -p rod u ct nuclei (IA E A -S M -170/74) .......................................... 553 

H. Gruppelaar 

D iscu ssion .............................................................................................................. 558

Evaluation of the ranges of fission products (IA E A -S M -1 7 0 /1 6 )......... 559 

F. Rustichelli 

D iscu ssion .............................................................................................................. 573 

A CCELERATO R AND SPACE SHIELDING (Section VII) 

Use o f nuclear data in designing sp a ce -scie n ce experim ents 

(IA E A -S M -170/42) .............................................................................................. 577 

B .C . Clark, P. G. Kase, J.P. Martin and 

J. G. Morse 

D iscu ssion .............................................................................................................. 593 

N uclear data fo r shielding and activation estim ates for 

TRIUMF (IA E A -S M -170/35) .......................................................................... 595 

I. M. Thorson and W. J. Wiesehahn 

T ransport o f neutrons induced by 8 0 0 -MeV protons 

(IA E A -S M -17 0 /4 5) .............................................................................................. 607 

R. G. Fluharty , P.A. Seeger, D. R. Harris, 

J.J. Koelling and O. L. Deutsch 

D iscu ssion .............................................................................................................. 617 

Chairm en o f S ession s and S ecretariat o f the Sym posium ..................... 621

KEYNOTE ADDRESS 

OPENING OF THE SYMPOSIUM

CRITERIA OF CHOICE 

FOR COMPILATIONS OF NUCLEAR DATA* 

D .J . HOREN, A .M . WEINBERG 

Oak Ridge N ational Laboratory, Oak Ridge, T e n n ., 

U nited States o f A m erica 

About twelve years ago, when the scientific community began to realize 

that priorities in science w ere inevitable, one of us (AMW) proposed what 

are now called "criteria for scientific choice" [ 1 ]. These amounted to a 

set of principles — admittedly much easier to formulate in the abstract than 

to apply in specific cases — that could help one decide the relative m erit 

of, and therefore priority to be assigned to, different scientific activities. 

The criteria of choice w ere divided into two categories: internal and 

external. Internal criteria arose out of the logic and structure of a field: 

they w ere concerned with such questions as, "is the field ripe for exploitation 

— i.e . are there pressing scientific issues in which knowledgeable 

practitioners see ways of making progress? O r does the field itself attract 

v ery able people? " These internal criteria address themselves to the 

solvability of scientific problem s. (Peter Medawar describes science — 

in a clever paraphrase of D israeli — as the Art of the Soluble [ 2 ]. ) Internal 

criteria m easure a scientific activity by the extent to which it yields results 

that are worthwhile as judged by the standards of the field in which the 

results are obtained. 

External criteria m easure a scientific activity from the standpoint of 

the universe outside the activity. They address themselves to the usefulness 

(as contrasted to the solvability) of scientific research: its usefulness to 

other scien ces, to engineering and technology, to society at large. In a 

general sort of way, it was argued that where large sums of public money 

w ere required to support a scientific activity, external criteria must loom 

prominently in judging relative priorities. 

About the time of the publications on criteria for scientific choice, 

one of us (AMW) chaired a panel of the President's Science Advisory 

Com mittee (PSAC) concerned with scientific information. That report, 

entitled "Science, Government, and Information" [3 ], is probably fam iliar 

to many in this audience. Its main emphasis was on the specialized information 

centre. The report viewed such secondary handlers of scientific 

information as a key to restoring order to what seem ed like a chaotic 

expansion of scientific knowledge. In retrospect, it seem s that the panel 

was graced with good luck in stressing the role of the specialized information 

centre. Such centres have proliferated even beyond what we enthusiasts 

anticipated when writing the report. In nuclear structure and 

reactions alone, there are now at least 28 such centres throughout the 

world according to the studies of the International Working Group on Nuclear 

Structure and Reaction Data (IWGNSRD) [4] . 

It therefore seem ed appropriate, in talking to an audience that includes 

both com pilers of nuclear data and users of nuclear data, to try to synthesize 

* P resen ted b y A . M . W e in b e r g . 

3

4 HOREN and WEINBERG 

these two separate threads from earlier works: Scientific Information, in 

this instance, Nuclear Information, and Criteria for Scientific Choice. 

F o r just as science itself, and certainly nuclear science, must adjust to 

limited resou rces, so scientific compilation, and in particular compilation 

of nuclear data, is sim ilarly constrained. Thus the problem of priorities — 

what to do first, where to allocate resou rces in science — also faces the 

community of com pilers. They too must decide what to com pile and what 

to leave for later. Can we establish a-p riori criteria of choice for scientific 

compilation? Can such criteria be regarded as m ore than a philosophic 

exercise? 

THE NECESSITY FOR CHOICE 

The com pilers of scientific data have in recent years lagged behind 

the producers of scientific data, and have had to establish p rio ritie s. In 

nuclear science, technical developments have greatly magnified this discrepancy 

between the m ass of data and the com p iler's capacity to handle it. 

The use of high-resolution solid-state detectors, as well as other 

im proved techniques, has multiplied the number of recorded bound states 

per nucleus five- to ten-fold during the past decade; and the widespread 

utilization of automatic processing has created a heavy glut of undigested 

nuclear data. There are now som e 3000-4000 nuclear-structure scientists 

who publish about 3500 papers annually. The data contained in each paper 

varies anywhere from a single number — e .g . the reporting of a half-life 

measurem ent, or spin, etc. — to thousands of numbers. F o r example, 

Mühlbauer has observed m ore than 2000 gam m a-ray transitions below 

1. 4 MeV following neutron capture in 152Eu [ 5] ! Ignoring the quantities — 

level energies and properties — that can be deduced from this particular 

data, but, considering only the energies, intensities, and uncertainties 

on each quantity, one has to deal with 4 X 2000 or 8000 numbers! 

The history of the Nuclear Data P roject from 1959-1972 illustrates 

how this increase in data has com plicated the life of the com piler of m a ss- 

chain data. P rior to 1963 the number of compilations per m an-year was 

3. 5-5, with each compilation having 100 times the quantity of data reported 

in an average research paper; today this number has fallen to about 1. 8 

compilations per m an-year. Since 1959 the number of research papers 

per m an-year (at least in the United States) has remained relatively constant 

at about one. The average quantity of-reported data, however, has increased 

by a factor of ten, and the ratio of data per compilation versus that per 

average research paper has remained about constant at 100/1. Thus the 

com piler has increased his ability to handle data by a factor of four to 

five — i. e. (1. 8/5) X 10 — but this has not been sufficient to cope with the 

ten-fold increased production of data.1 Thus one can make a serious 

argument for relatively m ore, rather than less, money going into secondary 

treatment of data. 

1 W e h a v e trie d to e s tim a te th e c o s t o f g a th e r in g and c o m p ilin g n u c le a r d a ta . T h e a v e r a g e research 

p a p e r rep orts a p p r o x im a te ly 30 m e a su re d n u m bers (in c lu d in g u n c e r ta in tie s ), w h ic h is e q u iv a le n t to a b ou t 

$ 15 00 p er n u m b e r; in th e U n ite d S tates an a v e r a g e re s e a r ch p a p e r co s ts a p p r o x im a te ly $ 45 0 0 0 . D ata p rod u cers 

a re g e n e r a tin g s o m e 110 0 00 n u m b ers a n n u a lly . A n a v e r a g e D a ta P r o je c t c o m p ila t io n c o n ta in s a p p r o x im a te ly 

3 00 0 n u m b ers a t a c o s t o f a p p r o x im a te ly $10 p er n u m b e r, o r o n e p e r c e n t o f th e p r o d u c tio n c o s t. 

In this c o n n e c t io n th e authors w o u ld li k e to p o in t to th e im p o r ta n c e o f e s ta b lis h in g a u n ifo rm and in te r n a tio n a l 

sy stem o f k e y w ord s and in d e x in g as a m ea n s o f a m p lify in g th e c o m p ile r s ' in c r e a s in g ly d iffic u lt jo b o f k e e p in g 

up w ith th e d a ta .

SYMPOSIUM KEYNOTE 5 

INTERNAL CRITERIA: NUCLEAR COMPILATION AS PART OF 

NUCLEAR SCIENCE 

Scientific compilation is, of coarse, part of science. One could 

therefore argue that criteria of choice that are appropriate for science 

ought to be applicable to scientific compilation. M oreover, the motivations 

for scientific compilation in a way parallel the motivations for science itself. 

We say we do science, on the one hand, to find order in nature where none 

had hitherto been perceived (the Newtonian view) or, on the other hand, 

to enable man, through application of science, to control nature for m an's 

benefit (Baconian view). In a parallel sense, the scientific com piler is 

motivated, on the one hand, by his desire to find scientific regularities 

and new insights where none have been found before, or to help scientists 

in his own field find such regularities; and, on the other hand, his desire 

to make the results of his compilations useful to scientists in other fields, 

and to those who apply science to the useful arts. We would call the first 

motivation for scientific compilation internal, the second external. 

Within the field of nuclear science one can find both internally and 

externally motivated compilation groups. The approach as to what they 

com pile, as well as their methods, is usually reflected to som e degree 

by their histories. M ost of the internally motivated groups w ere established 

by active research ers, mainly as an aid to cope with the data or to detect 

system atic trends. 

M ost of the com pilers in this audience are fam iliar with instances in 

which compilations have proved of som e significance in the creation of 

new nuclear scien ce. To mention a few examples, we would cite the nuclear 

shell m odel which stem m ed mainly from a combination of com piled data and 

the injection of a new idea, strong spin-orbit coupling.2 The highly successful 

description of nuclear properties in the rare-earth and actinide regions in 

term s of a non-spherical model has been refined through an intermingling 

of experiments, compilations, and theoretical ideas. Compilations played 

an important role also in the evolving description of the vibrations of near- 

spherical nuclei, or the development of the optical-m odel description for 

nuclear reactions. Other examples in which compilations have played a 

significant part in the discovery of new nuclear science can of course, 

be given. 

The com piler, in pursuing his aims that are part of nuclear science — 

i.e . finding regularities, discrepancies, and lacunae — must be guided by 

som e internal criteria. He must decide what data are m ost likely to yield 

s uch nuggets, are m ost worth spending his time on. It would be our im pression 

that the com p iler's sensitivity to what is important, and therefore his 

ordering of priorities, is established in much the sam e way as are the 

sensitivities toward priorities of nuclear science itself. M oreover, since 

the com pilers, at least in those centres serving basic nuclear science, 

2 A lth o u g h a n u m b e r o f w ork ers, s o m e b e fo r e 1 9 3 0 , h a d su g g ested th e p o s s ib ility o f n u c le a r s h e ll 

stru ctu re b a s e d o n t h e o r e t ic a l and s k e tc h y e x p e r im e n t a l grounds [ s e e , e . g . ELSÄSSER, W . , J. Phys. R adiu m £ 

(1 9 3 4 ) 6 2 5 ] , it r e m a in e d u n til e a r ly 1949 fo r M a r ia M A Y E R [ P hys. R e v . 7 5 (1 9 4 9 ) 1 9 6 9 ] and in d e p e n d e n tly 

th e te a m o f H A X E L , O . , JENSEN, J . H . D . , SUESS, H .E . [P h y s . R e v . 7 5 ( 1 9 4 9 ) 1 7 6 6 ] to p resen t a t o t a lly 

c o n v in c in g c a s e fo r th e e x is t e n c e o f m a g ic n u m b ers, as w e ll as a r a tio n a le fo r th e m in term s o f stron g s p in -o r b it 

c o u p lin g (s u g g e s te d to M a y e r b y F e r m i),

T A B L E I. A R E A S OF A P P L IC A T IO N O F N U C L E A R D A T A AND TECHNIQUES 

A p p lie d a rea U s a g e M a in d a ta re q u ire m e n ts 

E le c t r ic a l p o w e r 

B io lo g y and 

m e d ic in e 

A g ricu ltu re 

G e o lo g y 

A r c h e o lo g y 

F o re n sic 

In d u stria l 

P h y s ic a l s c ie n c e s 

F ission rea ctors 

D esign 

R a d io a c t iv e w a s te d isp osa l 

R e g u la tio n 

E n v iro n m e n ta l 

F u e l e le m e n t co n tr o l 

( i . e . safeguards) 

R a d io is o to p e b a tteries 

C o n tr o lle d th e rm a l fu sion 

D ia g n o s tic studies 

T h era p y 

R esearch 

F o o d p r e se rv a tio n 

G e n e tic studies 

P lant studies 

A c t iv a t io n a n alysis 

L eak d e t e c t io n ^ 

G au ges (th ic k n e s s , d en sity) 

C o n tro ls 

F ire d e t e c t io n d e v ic e s 

F ilters 

M a te r ia ls tre a tm e n t 

S o lid - s t a te d e v ic e s 

M a te ria ls analysis 

R a d iography 

N u c le a r p h ysics 

A stroph ysics 

S o lid state 

C h em istry 

N eu tron d a ta , fissio n d a ta , d e c a y d a ta , 

n u c le a r stru ctu re 

D e c a y data 

C h a r g e d - p a r t ic le r e a c tio n s , n eu tron r e a c tio n s 

D e c a y d ata (s o m e r e a c t io n data) 

D e c a y d a ta , n eu tron and c h a r g e d -p a r t ic le 

r e a c tio n s (p ro to n s , тг-m e s o n s , h e a v y ion s) 

D e c a y data 

D e c a y d a ta , n eu tron c a p tu r e , X - r a y flu o r e s c e n c e 

b y m e a n s o f c h a r g e d p a r tic le s o r 7 Ч 

V a riou s ty p e s n o te d a b o v e d e p e n d in g u p on 

a p p lic a t io n 

L e v e l o f k n o w le d g e o f n u c le a r 

p h y s ics r e q u ire d b y user 

H igh 

Low 

H igh 

M e d iu m to low 

M e d iu m to h igh 

Low 

Low to m e d iu m 

Low to m e d iu m 

Low to h igh 

d e p e n d in g o n s p e c i f ic a rea 

HOREN and WEINBERG


are them selves an integral part of the nuclear science community, there 

is little problem of what to com pile next: at least, it is not m ore difficult 

than the problem of what to m easure next. This is determined by the state 

of knowledge of the science and is largely a personal judgment. 

A second, and perhaps m ore important, question of priority is the 

depth and com plexity of a compilation. F o r som e purposes, only a broad, 

but not deep, compilation is necessary (the initial stages of the optical model, 

for example). However, where one is interested in a m icroscop ic test of 

a theoretical model, an in-depth compilation is required. Again, however, 

since these are so integral a part of nuclear science, it is hard for us to 

p rescribe criteria that are different from the intrinsic criteria of choice 

appropriate for nuclear science itself. After all, nuclear science, like 

all science, the A rt of the Soluble: one goes where one's instincts, 

sharpened by the scientific am bience in which one operates, lead. The 

main point is that as long as nuclear compilation is supported at a level 

sufficient for the com piler to be au courant with the data, and the com piler 

maintains his contacts with the nuclear community, significant new nuclear 

science w ill com e from nuclear compilations. 

EXTERNAL CRITERIA: NUCLEAR COMPILATION AS AN AID TO 

APPLICATION 

In Table I we sum m arize som e of the areas in which nuclear data or 

techniques are being applied. As one sees, these range from power 

generation to nuclear m edicine, from agriculture to forensic science, and, 

of course, include the basic physical sciences — nuclear physics, astrophysics, 

solid state, chem istry, etc. Most striking is the wide variation 

in sophistication both in the use of the data and in the user's knowledge of 

nuclear science. In view of this, one easily surm ises that the need for 

critical evaluation of the data will be somewhat dependent upon the specific 

application for which it is intended. 

Papers to be presented at this symposium suggest that these points 

will be aptly demonstrated in the respective sessions. Hence we confine 

ourselves to two specific examples of the use of nuclear data: as it applies 

to em ergency core-coolin g system s (ECCS) and its present and possible 

future role in biological applications. 

(1) ECCS: Perhaps an apt example of heavily applied use for com piled 

non-neutron nuclear data is the estimate o f the afterheat in a light-water 

reactor. This is one of the factors needed to asses the perform ance of the 

ECCS, and som e 22 000 pages of testimony pertaining to this topic have 

been am assed during the past year. Among the important technical 

questions involved is whether or not the fuel elements heat up too much 

during the first few seconds after blow-down. To obtain this information 

from in-situ m easurem ents would be extrem ely difficult. T herefore, to 

estimate the heat build-up, two calculational approaches have been considered 

— one based upon experimental m easurem ents of the gamm a and 

beta power associated with the therm al fission of 235U, the other on a detailed 

knowledge of the yields and decays of the fission products. The latter 

inform ation has been com piled since the beginning of the Manhattan P roject, 

particularly, through the active work of Katharine Way, who is generally 

recognized as one of the founders of m odern nuclear data compilation.

8 HOREN and WEINBERG 

Partly because of the work of T .R . England [6 ], questions were recently 

raised concerning the validity of accepted procedures for handling the fission 

product after-heat. This has led to a re-exam ination of the problem , and 

once again exemplifies a fundamental contribution that can be made to applied 

program s by the nuclear scientist in his role as com piler/evaluator. 

Given a choice, the reactor engineer or scientist would certainly prefer 

to have available all the evaluated nuclear data required to calculate the 

heat release after blow-down. An engineer is unlikely to have had sufficient 

training and experience to evaluate the experimental data, whereas a nuclear 

scientist would probably find it difficult were he too long rem oved from the 

experimental details. Furtherm ore, to perform the calculation by going 

back to the fission product yields and decays would be almost im possible 

if he w ere forced to start at the beginning and com pile and evaluate all the 

data himself. 

A look at data on direct m easurem ent of the gamma and beta powers 

illustrates the engineer's difficulty. In Fig. 1 we show the results of four 

independent measurem ents of the beta power. It takes little imagination 

to visualize the bewilderm ent which the nuclear engineer will experience 

when confronted with such data. Should he, or can he, examine the detailed 

m easurem ents to try to determine the sources of the apparent discrepancies? 

Should he treat the data as four equal and independent sets? Should he accept 

the uncertainties quoted by the authors? Here is a place where the experience 

of the compilation community could well be brought to bear on an important 

technical m atter. 

(2) Biological applications: The use of nuclear data and techniques for 

biological purposes continues to grow. At present 20 to 30 radioisotopes 

are in routine clinical use, mainly as diagnostic tools. Approximately 

120 others are being used in research studies. Recently, there has been 

a resurgence in the use of neutrons in cancer therapy. With the new high- 

energy proton accelerators coming on-line, as well as heavy-ion accelerators, 

F IG . 1 . C o m p a r is o n o f d iffe r e n t ia l b e ta e x p e r im e n ts . T h e in te g r a te d b é ta p o w e r fr o m fou r d iffe r e n tia l 

m ea su re m e n ts is p lo t t e d r e la t iv e to a w e ig h te d a v e r a g e (th is fig u r e w as k in d ly p r o v id e d by A . M . P erry o f O R N L).


new techniques in m edical radiology that exploit the interactions of such 

projectiles (and also 7r-mesons) with tissue w ill m ost likely be developed. 

This w ill entail detailed knowledge of many nuclear interactions as well as 

phenomena associated with atomic physics, such as charged-particle 

stopping pow ers. 

In this area alone one can find examples for which the quality of the 

data is relatively unimportant and others for which it is critical. The 

typical role of the com piler, as a supplier of evaluated data, probably 

will not suffice in all cases. The m edical user, in the application of 

7r-mesons, will need assistance that goes far beyond that historically 

provided by a com piler; undoubtedly, he will often have to communicate 

directly with the com piler/evaluator. 

In general, though, the needs of the applied scientist are for evaluated 

nuclear data and, in particular, data that have been evaluated with his 

needs in mind. To be sure, there now are many nuclear compilation centres, 

such as the Brookhaven National Neutron C ross Section Center, which 

com pile and evaluate data for special classes of users. Of the centres 

listed by IWGNSRD, about two-thirds are externally motivated and are part 

of the applied community; one-third are internally motivated — i .e . consider 

them selves part of nuclear science rather than of nuclear applications. 

Obviously, insofar as barriers exist between the internally and externally 

motivated data com pilers, these barriers ought to be rem oved. This has 

happened in the case of evaluated neutron cro ss-se ctio n data — through the 

operation of the Neutron C ross-S ection Advisory Com m ittees, both national 

and international. And the creation of the U .S. Nuclear Data Committee 

to cover broader nuclear data (including that for nuclear science itself) 

is an experiment well worth serious attention. 

THE PROBLEM IN PERSPECTIVE 

By the year 2000 we anticipate that in the United States alone there 

will be 500 operating reactors. The rest of the world will not be far behind. 

It w ill be a world in which the existence of radioactive nuclei will not be a 

scientific curiosity but an ever present factor in our daily lives. All kinds 

of people will have to know about radioactive nuclei; chem ical engineers, 

geologists, geochem ists, atmospheric scientists, oceanographers, 

paleographers, ecologists, anthropologists, veterinarians, agricultural 

scientists, soil scientists, econom ists, and political scientists. Each 

group w ill want information in a format that is easy to use, easy to transmit, 

and easy to rem em ber. It w ill be the task of the com pilers to be responsive 

to the needs o f many sectors of our society and to provide nuclear data in 

specific formats for each sector. 

We see therefore a strong and growing need for externally motivated 

nuclear compilations. It is unlikely that potential users w ill com e uninvited 

to the com pilers and ask for particularly useful kinds of compilations. The 

com piler must seek out potential users continuously and energetically. 

Several m echanism s might make this task a little less than im possible. 

(1) There are conferences such as this one where users and com pilers 

m eet to exchange views on m ajor problem s and to w ork out together useful 

courses of action.

1 0 HOREN and WEINBERG 

(2) It is possible to embed nuclear data centres in large multidisciplinary 

organizations. This is currently the case in the nuclear laboratories of 

many countries, and leads to reasonably good communication channels 

between com pilers and obvious potential users who are connected with the 

nuclear energy enterprise. 

(3) Com m ittees which we mentioned earlier, such as the US Nuclear 

Data Com mittee, may be very useful in helping to establish priorities for 

compilation of nuclear data. Certainly the various Neutron C ross-Section 

A dvisory Com m ittees have been helpful both in the m easurem ent and evaluation 

of data for reactor design. However, the m ore general fields of 

nuclear science and application do not have the sam e unifying theme or, 

for that matter, the centralized m anagerial structure as does reactor design 

and engineering. This will make it harder for committees to sense accurately 

the needs of this larger community. M oreover, com m ittees are cum bersom e: 

w ill they im pose further delays on the transfer of information from experimenter 

to user — which after all is what we are trying to expedite? 

(4) Finally, the m ost important ingredient is the intelligence, the energy, 

and vision of the individual com piler or of com piler organizations. One 

important issue here is how one can make the centres that have a tradition 

of internal motivation, a commitment to basic nuclear science, m ore useful 

to the community of applied science. One obvious, and quite sim ple, answer 

is to urge that these com pilers of nuclear data becom e m ore fam iliar with 

the needs of users. After all, when a com piler establishes a priority 

according to the internal logic of nuclear science, it is necessary to fam iliarize 

him self with that logic — to decide what is needed to strengthen the edifice 

of nuclear scien ce. Is one being unrealistic to urge that nuclear com pilers 

themselves accept som e responsibility for the needs of the applied com 

munity that their data may serve so that, though their prim ary commitment 

remains to their science, and their prim ary criteria of choice remain 

internal, they use som e cues from the applied world in setting their p r io r ities? 

As a practical matter, this means that at least a few com pilers in 

each of the basic compilation groups would acquire knowledge of and sen sitivity 

to the applied scie n ce s. 

Establishing priorities in nuclear compilation is hardly any easier than 

is establishing priorities in nuclear science itselt. And indeed, rather than 

proposing specific priorities, we have alluded to mechanism s for establishing 

priorities — in particular, the steering or guiding committee, and the inform 

ed individual com piler, especially the one who works in a broad, 

interdisciplinary setting. The two mechanism s, of course, do not exclude 

each other. We would only hope that this present-day tendency to centralize 

decisions in science by setting up central com m ittees does not work to lessen 

the individual com p iler's own responsibility to becom e acquainted with, and 

sensitive to, the needs of the basic and applied communities his compilations 

serve. 

R E F E R E N C E S 

[ 1 ] " C r it e r ia fo r S c ie n t if ic C h o i c e ” , M in e r v a I . p p . 1 5 9 -1 7 1 (W in te r 1 9 6 3 ); "C r ite r ia fo r S c ie n t if ic 

C h o ic e II: T h e T w o C u ltu r e s ", M in e r v a III, p p . 3 - 1 4 (A u tu m n 1 9 6 4 ). 

[ 2 ] M E D A W A R , P .B ., T h e A rt o f th e S o lu b le , M e th u e n and C o m p a n y L t d ., L on d on (1 9 6 7 ). 

[ 3 ] A rep ort o f th e P resid en t's S c ie n c e A d visory C o m m itte e , U .S . G o v e r n m e n t P rin tin g O f f i c e , W a sh in gton 

(January 1 0 , 1 9 6 3 ).

SYMPOSIUM KEYNOTE 1 1 

[ 4 ] I n te r n a tio n a l W o rk in g G rou p o n N u c le a r S tru ctu re and R e a c tio n D a ta , M in u tes o f First M e e t in g , 

I N D C (S E C )-2 9 /G (a n d m in u tes o f su b seq u en t m e e tin g s ), IA E A N u c le a r D ata S e c t io n , V ie n n a (O c t o b e r 1 9 7 2 ). 

[ 5 ] M Ü H LBAU ER, K . , Z . Phys. 2 3 0 (1 9 7 0 ) 1 8. 

[ 6 ] E N G L A N D , T . R ., "A n In v e s tig a tio n o f F ission P rod u ct B e h a v io r and D e c a y H e a tin g in N u c le a r R e a c to r s ", 

P h .D . T h e s is , U n iv e rsity o f W isco n s in (A u g u s t 1 9 6 9 ).

Section I 

FUTURE TECHNOLOGY REQUIREMENTS

C hairm an 

KOLSTAD (USA)

FISSIONING URANIUM PLASMAS 

K . THOM 

A EC/NASA Space N uclear System s O ffice, 

W ashington, D. C. 

and 

R .T . SCHNEIDER 

University o f Florida, G ain esville, F la ., 

United States o f A m erica 

Abstract 

F ISSIO N IN G U R A N IU M P L A SM A S. 

IA E A -S M -170 /5 3 

S e v e ra l c o n c e p t s fo r c a v it y r e a c to r s h a v e b e e n p ro p o s e d in w h ic h th e n u c le a r fu e l is in th e p la sm a 

s ta te . M o tiv e s for c o n d u c tin g r e s e a r ch re la te d to su ch h ig h -te m p e r a tu r e r e a cto r s a re th e p o s s ib le a p p lic a t io n 

o f th e se r e a c to r s fo r h i g h - s p e c if ic - im p u ls e p r o p u lsio n in s p a c e , m a g n e to h y d r o d y n a m ic e le c t r i c a l p ow er 

g e n e r a tio n a t h ig h e f f ic i e n c y , d ir e c t n u c le a r p u m p in g o f la sers, and as a s o u r ce for p r o ce s s h e a t. 

T h e c o n f in e m e n t o f th e fissio n in g u ra n iu m p la s m a w ith in th e c a v it y is sou ght by m e a n s o f flu id m e c h a n ic s . 

T h e e x t r a c t io n o f p ow er is a c c o m p lis h e d by r a d ia tiv e tra n sfer. T h e s e r e q u ire m e n ts im p o s e s p e c i f ic p r o b le m s 

u p o n c r it ic a lit y c a lc u la t io n s . 

A s ig n ific a n t d iff e r e n c e e x is ts b e tw e e n th e n eu tron te m p e r a tu r e (th e r m a l) and th e u ra n iu m p la sm a 

te m p e r a tu r e . For this re a so n , m o r e a c c u r a t e n eu tron s c a tte r in g and ca p tu r e c r o s s - s e c t io n d a ta in th e 

s e v e r a l- e V -r e g io n a re n e e d e d . T e m p o r a l flu c tu a tio n o f th e fu e l d en sity and v a r ia tio n o f th e s p a tia l fu e l 

d istr ib u tio n d u rin g o p e r a tio n and sta rt-u p r e q u ir e n ew c o d e s . R e a c tiv ity p ertu rb ation s d u e to p o s s ib le u raniu m 

in flu x v a r ia tio n s h a v e to b e c a r e fu lly an aly sed for p o w e r e x cu r s io n s and su bsequen t d istu rb a n ce s o f th e b a la n c e d 

sy stem o f flo w c o n f in e m e n t and r a d ia tiv e p o w e r tra n sm ission . 

In c o n n e c t io n w ith s o m e o f th e c o n c e p t s under c o n s id e r a tio n , re s e a r ch o n n u c le a r r a d ia tio n d a m a g e o f 

o p t i c a l transp arent m a te r ia l is n e e d e d . 

T h e US N a tio n a l A e r o n a u tic s and S p a c e A d m in istra tio n has c o n d u c te d an in te n s iv e r e s e a r ch p ro g ra m 

o n v a r io u s a sp e c ts o f fissio n in g p la sm a s , a n a ly tic a lly and in s im u la tio n , p a r tic u la r ly r e g a rd in g th e fe a s ib ilit y 

o f tw o m a jo r c o n c e p t s o f c a v it y r e a c to r s . S u ch w o rk is d e s c r ib e d . T h e n e e d s fo r fu rth er re s e a r ch , e s p e c ia lly 

in v ie w o f re q u ire d n u c le a r d a ta , is d iscu ssed . 

A s ig n ific a n t ste p forw a rd w ill b e th e r e a liz a t io n o f a p r o p o s e d h y b rid re s e a r ch f a c i lit y co n s is tin g o f a 

s o l id - f u e l d riv er s e c t io n e n c lo s in g th e fis s io n in g p la s m a . T h is f a c i lit y w o u ld a llo w b a s ic r e s e a r c h o n fissio n in g 

p la s m a s . T h e re q u ire m e n ts for c o d e s for d e s ig n o f su ch a t w o -c o m p o n e n t f u e l-r e a c t o r sy stem a re d iscu ssed . 

INTRODUCTION 

A fissioning plasma is a reacting fissionable fuel that by its own 

fission power is sufficiently energized to exist in a gaseous partially ionized 

state. Fissioning plasmas have so far only been produced 1n nuclear explosions. 

Steady-state fissioning plasmas are expected to be useful because 

of the high temperature at which they exist. However, theoretical investigations 

have shown that the realization of a pi asma-core reactor represents 

a major development effort. With the exception of space propulsion at a high 

specific Impulse and at a high level of thrust, no technological needs for 

the high-temperature capabilities of fissioning plasmas in the past were 

pressing enough to warrant the cost of such a development. However, for the 

purpose of space propulsion, the U.S. National Aeronautics and Space Administration 

has conducted research on fissioning plasmas [1, 2]. More 

recently, problems such as power shortages and thermal pollution have 

developed that make plasma-core reactors desirable for more applications than 

space propulsion. Advanced propulsion remains, however, a principal 

motivation for plasma-core reactor research. 

15

16 THOM and SCHNEIDER 

A frequently used term In rocket propulsion is "specific impulse". It 

is the ratio of thrust and mass flow rate and is proportional to the propellant 

exhaust velocity. At low specific impulse, such as in chemical 

propulsion, the propellant and fuel weights are much larger than the weight 

of structures. In this case the payload fraction depends exponentially on 

the ratio of the final speed of the rocket and the exhaust velocity; during 

low specific impulse propulsion, lunar-return missions and particularly 

planetary missions, diminishing payload fractions result. 

High exhaust velocities can be achieved in ion propulsion or by electromagnetic 

plasma acceleration. However, the jet power is the product of 

thrust and exhaust velocity and thus increases with the cube of the latter. 

At high specific impulse, power requirements can become so large that the 

dead weight of the power plant offsets gains in payload fraction, such that 

the ratio of the power plant weight and jet power becomes the dominant 

characteristic of propulsion. This ratio is called the specific mass. It 

is determined by dividing the kilograms of power plant mass by the kilowatts 

of jet power and is obviously an expression for power density. A fissioning 

plasma, burning nuclear fuel at very high temperatures and densities, is a 

very high power density energy source. In prospective plasma core rockets, 

shielding, neutron moderation and reflection impose a large dead weight. 

After analysis it turns out, however, that such minimum weight is not incompatible 

with more ambitious space missions, because the inherently low 

specific mass of fissioning plasma rockets will lead to significant gains 

in payload fraction and in reductions of trip times. Such advantages are 

compared with the capabilities of other propulsion methods for a manned 

round trip to Mars (fig. 1). For plasma core propulsion, the initial mass 

in earth orbit is an order of magnitude smaller than for chemical propulsion. 

It has been estimated that the resulting reduction of cost for such a mission 

could compensate for the cost of the development of plasma core reactors in 

one or two such flights, but that may remain questionable because advances 

in other propulsion modes may alter such present comparisons. In this 

treatise of fissioning plasmas a broader view of technological usefulness 

than space propulsion is taken as to lead to various detailed scientific and 

engineering problems, of which, nuclear data are a significant part. 

FISSIONING PLASMA REACTOR CONCEPTS 

Major concepts of plasma core reactors are the coaxial flow system, the 

nuclear light bulb engine, the nuclear pumped laser system, and the nuclear 

piston engine. These concepts, particularly the first two, have motivated 

a program of specific research aimed at demonstrating their feasibility. The 

magnitude of this research effort, extending over the past 15 years, is about 

200 professional manyears [3]. Accordingly, the present schemes of plasma 

core reactors should be regarded as mature in the sense of careful probing in 

theory and experiment, short mainly of fission tests at larger power. 

The coaxial flow scheme, originally conceived for advanced space propulsion, 

is based on fluid mechanics confinement of the fissioning plasma 

(fig. 2), and is analyzed in [4, 5, 6]. Enriched “ by -¡s introduced into the 

cavity in the form of a fast moving wire. The fissioning plasma is held in a 

central position by a rapid flow of hydrogen injected through porous cavity 

walls or through an array of slots. This propellant flow separates the hot 

plasma from the walls and also intercepts the powerful thermal radiation from 

the plasma. Thereby it is heated up for expansion through a nozzle. Some 

uranium plasma is entrained in the propellant flow and subsequently lost. 

The cavity is surrounded by a beryllium oxide moderator-reflector, and all 1s 

contained in a pressure vessel.

IA E A -S M -1 70/53 

MISSION TIM E, DAYS 

F I G . l , P r in c ip a l m o d e s o f p r o p u ls io n . 

F IG .2 . O p e n - c y c l e g a s - c o r e c o n c e p t .

18 TH OM and SCHNEIDER 

Three requirements determine the characteristics of the system: fuel 

mass and density to achieve criticallty, sufficiently high temperatures to 

achieve a high specific impulse, and a low rate of fuel loss through the 

exhaust nozzle, for economic operation. These requirements result in rather 

rigid boundaries for power and weight. A "best" configuration can, however, 

not be determined because of trade-offs among the variables. Typically, a 

coaxial flow plasma reactor for space propulsion operates at 6000 MW power, 

producing thrust at 4000 sec specific impulse. The cavity diameter is about 

4 meters, the pressure ranges from 400 to 600 atm., and the total weight of 

the system is of the order of 500000 kg figuring present radiator technology. 

The fissioning plasma temperature is up to 50000°K in the center of the 

fuel region, decreasing to less than 25000°K at the edge of the fuel. The 

critical mass is about 40 to 80 kg 235ц depending on poison. 

The nuclear light bulb engine concept consists of seven modules, such 

as shown in Fig. 3, contained 1n a pressure vessel together with a BeO and 

graphite moderator reflector [7]. In contrast to the coaxial flow system, 

the nuclear light bulb scheme provides for full containment of the fuel 

within a transparent Internally cooled wall configuration, thereby circumventing 

the problem of fuel losses through the exhaust. The fissioning 

plasma is kept away from the transparent walls by a tangentially injected 

swirl flow of buffer gas, which is recirculated. Some uranium plasma that 

is entrained in the buffer gas flow Is separated out during the recirculation 

process and Is fed back to the fuel region. Thermal radiation from 

the fissioning plasma penetrates the buffer gas flow and the transparent 

walls and is Intercepted by a flow of seeded hydrogen propellant. Typical 

data for the nuclear light bulb engine are power: 4600 MW; specific 

Impulse: 1870 sec; weight: 35000 kg; edge-of-the-fuel temperature: 5000°K; 

and pressure: 500 atm. 

Both of these fissioning plasma reactor concepts represent machines of 

enormous power and stresses. It is not apparent that these schemes can be 

scaled down significantly because of critlcality requirements combined with 

the need of high temperature operation. However, at significantly decreased 

temperature, the pressure decreases accordingly as does the power. In such 

a case, the plasma core reactor operates in a nonequllibrium mode, in which 

U R A N IU M P L A S M A 

INTERNALLY COOLED 

TRANSPAREN T WALL 

F I G .3 . N u cle a r lig h t -b u lb g a s - c o r e c o n c e p t .

IA E A -S M -1 70/5 3 19 

the plasma is optically thin. Extraction of power would most efficiently be 

effected by laser radiation [8]. In such a self-critical nuclear powered 

laser system, nuclear energy is directly converted into coherent light by 

elastic and inelastic collisions of fission fragments with the uranium atoms 

(and possibly other gas admixtures), Fig. 4. Population Inversion is 

expected to result from the vastly different energies of the fission fragments 

over most of the lengths of their stopping distances as compared to 

the energy level of the plasma. In order to maintain the fissionable fuel 

in a partially ionized gaseous state, one may have to resort to UFg. 

Another fissioning plasma reactor concept is the nuclear piston engine 

[9]. This engine resembles an Otto-motor as indicated in Fig. 5. During 

the intake stroke a mixture of enriched UFß and helium is drawn into a 

cylinder that is surrounded by a moderator-reflector. During the compression 

stroke the density of the gas is increased until criticality is 

reached. The chain reaction is initiated by an external neutron source. 

Because of the buildup of power, temperature and pressure are increased in 

the cylinder and can be extracted as shaft horsepower in the following power 

stroke. An exhaust stroke ejects the now again subcritical UFg and He 

mixture into a cooling and reprocessing loop. 

In Fig. 5 an auxiliary precompressi on piston is shown which follows 

the working piston at high compression to provide time for buildup of power 

and to assure that maximum power is released as the piston passes dead 

center. Preliminary calculations [10] show that a one cylinder engine 

requires a minimum volume of 0.23 m3 and a compression ratio of 1:10. 

Crankshaft speed of 100 to 500 rev/min and a critical mass of about 3 kq 

235u seem to be feasible. Power outputs of several megawatts per cylinder 

at an efficiency up to 60% seem to be realizable. The main problem to be 

solved seems to be the handling of the chemically aggressive UFg. A comprehensive 

knowledge of thermodynamic properties of ÜFg and UFg-He mixtures 

at high temperatures is required. This includes dissociation temperatures 

and interaction of fission fragments with UFg. 

FIG*4. N uclear pumped laser.

2 0 TH OM and SCHNEIDER 

POTENTIAL APPLICATIONS 

F I G .5 . N u c le a r p iston e n g in e . 

The aforementioned plasma core reactor concepts involve the fissioning 

plasma as a source of radiation. In contrast to the conditions in a solid 

nuclear fuel, fission fragments and photons in a plasma have relatively 

large mean free paths such that the fission energy is not thermal1 zed 

locally, i.e., in a close proximity of the locus of the fission event. 

Fission fragments traversing the plasma undergo up to 105 collisions with the 

plasma uranium atoms. As a result of deexcitation and recombination processes 

and in combination with bremsstrahlung, a broad spectrum of optical 

radiation is generated, which, depending on density and temperature, can 

escape from the plasma. A model of possible radiation is depicted in Fig. 6 . 

In the process of energy loss resulting from collisions, the fission fragment 

energy decays from an original level of 100 MeV to that of the average plasma 

temperature. A scheme of possible radiation levels is illustrated in the 

form of a tower with radiative power outlets at various energies. The fissioning 

plasma is seen as a source of photons at ranges of energy and intensity 

by orders of magnitude greater than those of any other terrestrial 

steady state energy source. Possible technological applications of fissioning 

plasmas more general than are apparent in the previous discussion of 

plasma core reactor concepts are envisioned by figuring direct uses of such 

photon fluxes. The complex of desirable relevant investigations may, in a 

provocative manner, be called "photonics" research. 

Radiation in the range of 0.1 to 10 eV is expected to be useful in 

photochemistry, because molecular bond energies range up to 4 eV In organic 

matter and up to more than 10 eV for very stable inorganic solids. Intense

IA E A -S M -1 70/53 2 1 

Energy range 

0.1-10 MeV Nuclear 

transitions 

100-5000eV Inner shell 

transitions 

0.1 -1 eV Degraded 

energy 

2 2 

THOM and SCHNEIDER 

4 -ST flG E COM PRESSION 

WITH INTERCOOLING 

F IG .7 . B lo c k d e s ig n o f p la s m a - c o r e M H D p ow er p la n t. 

Because of its high specific impulse, however, the plasma core rocket is 

superior to other propulsion systems for manned missions to the nearby 

planets. For missions deep into space, beyond perhaps Jupiter or Saturn, 

the projected thermonuclear fusion rocket becomes superior because of its 

higher specific impulse. In lunar ferry and space tug service, the plasma 

core propulsion unit would be employed in a reusable fashion, to result in 

greatly improved economy of cargo transport between earth orbit and the 

lunar surface. It is presently not contemplated to use plasma core rockets 

for launch from the earth surface into orbit. 

The needs for crew shielding from radiation of fission products present 

in the reactor cavity and in the exhaust have been investigated [11]. 

Shielding requirements, depending on fission fragment retention times, have 

been derived. Only qualitative consideration has been given so far to the 

effect of fission products deposition in near earth space. This problem 

warrants more investigation because in the state of Ionization such fission 

products will be trapped by the geomagnetic field and can be deflected back 

to the atmosphere. 

MHD power generation using a plasma core reactor is investigated in [12]. 

Both the plasma core reactor exhaust and the MHD channel flow are at very 

high temperatures to yield a large overall efficiency. In addition, at such 

high temperatures the working gas stream is sufficiently ionized in equilibrium 

to circumvent nonequilibrium ionization problems that have impeded the 

development of MHO power generation from solid fuel nuclear reactor energy 

sources. A schematic of a projected plasma core reactor MHD terrestrial 

power plant is shown in Fig. 7. Computations show an efficiency of 70%, a 

reduction of thermal pollution per unit power by factor of 3 to 5 compared 

with that of contemporary power plants, and a high fuel economy. In 

addition, such a system appears to be essentially safe because no excess 

reactivity is in the plasma cavity. The fissile fuel is in continuous 

recirculation and allows for continuous removal of fission products. 

RESEARCH 

Confinement 

т5 

PRE- STEAM 

HEftTER P0WER- 

*2 '3 PLftNT 

The objective of plasma core reactor fluid mechanics confinement is to 

isolate the hot gaseous fuel from the cavity walls and, simultaneously, to 

intercept the thermal radiation from the fissioning plasma in a propellant 

flow for heating and subsequent expansion. In present plasma core reactor 

concepts, the nuclear fuel and propellant are injected into the cavity at 

different locations and are exhausted together from the reactor through a 

nozzle. For criticality it is necessary that the fuel volume be not less 

,T4

IA E A -S M -1 7 0/5 3 23 

than 20% of the cavity volume, and for economy it is required that the ratio 

of the fuel mass flow rate to the propellant mass flow rate, mp/mp, be as 

small as possible. For rocket application, an acceptable level of mp/mp 

depends on the cost to lift the weight into earth orbit. At present this is 

figured at mp/mp = 1:100 to 1:200. For other applications involving closed 

loop configurations, mp/mp does not appear to be a critical parameter. 

A series of experimental studies has been conducted [13] to demonstrate 

the feasibility of fluid mechanics confinement. Air/freon and air/air combinations 

were used to simulate propellant and fuel flows and were injected 

into a cavity at greatly different velocities. In earlier experiments, the 

gas injection was spatially sharply discontinuous at the cavity inlet region, 

resulting in turbulent boundary layer mixing. Supported by theoretical 

analysis a method was devised for producing a wide shear layer between the 

flows with a gradual transition from high to low velocity streaming. As a 

result, in cold flow simulation, a fuel-to cavity-volume ratio greater than 

0.2 was achieved, at mp/mp = 70. Hot flow simulation is conducted in 

relatively small volumes by radiofrequency induction heating, with the 

indication that the temperature gradient across the boundary layer tends to 

suppress the formation of eddies and, consequently, results in a better confinement. 

Increasing size, temperature and density, in order to approach 

plasma core reactor conditions, requires low frequencies and large power. A 

10 to 100 kHz tunable 4 megawatt hot flow research apparatus is under 

construction. 

Radiative Heat Transfer 

Most of the power generated by the fissioning plasma inside the cavity 

of a plasma core reactor is transmitted to the propellant, or working fluid, 

by optical radiation. Relevant research is consequently concerned with the 

spectral distribution of radiated power and with the absorption of such 

radiative power in the propellant. Simultaneously, one has to consider the. 

deposition of energy in structures from all the energy fluxes from the 

fissioning plasma. In the nuclear light bulb engine concept, the fissioning 

plasma 1s confined by a swirl flow buffer gas within transparent fused 

silica tubing. Because of this additional structural element, radiative heat 

transfer has been studied with particular care for the nuclear light bulb 

system. 

The total power of the conceptual full scale nuclear light bulb engine 

is computed to be 4600 MW. Eighty-nine per cent is in the fission fragments 

and is rapidly converted into optical radiation; the remainder is in neutrons, 

prompt gamma rays, delayed gamma rays, and beta particles, most of which are 

deposited in structures and must be carried away by coolants. 

The spectral distribution of the radiant heat fluxes from the fissioning 

plasma was calculated [14] using a one-dimensional neutron transport 

theory computer code. There is a steep temperature gradient across the 

boundary region between the fuel volume and the confining swirl flow. The 

optical radiation will therefore be that of a blackbody one optical depth 

into the steep temperature gradient, such that the emitted spectrum is that 

of a blackbody at much higher temperatures than those at the edge of the 

fuel. Measurements of the absorption coefficient of uranium plasma under 

similar conditions [15] confirm theoretical predictions. As a result, the 

radiated power has a large fraction of u.v. radiation at wavelengths less 

than 0.18 urn, which is the cutoff of the silica tubing. A remedy to this 

problem is to seed the neon swirl flow with silicon particles, which absorb


the short wavelength radiation. The associated power is, however, not all 

carried away with the buffer gas flow but can largely be reemitted in 

longer wavelength radiation. 

In experiment, isothermal two-component vortex flow simulation tests 

were conducted to demonstrate confinement by buffer gas flow within silica 

tubes. High intensity radiant flux simulation was carried out using a 

1.2 MW rf induction heater to heat a vortex stabilized argon plasma up to 

11000°K at 19 atm. The radiant flux was at 7.6 kw/cm2 , but that of a full 

scale engine would be 28 KW/cm2 . Further development of this simulation 

technique promises to approach plasma core conditions. In addition, the 

experimental results are quite encouraging for small scale in-core 

experiments. 

At ranges of pressure and thickness of interest, hydrogen and most of 

the other light gases are optically transparent at temperatures less than 

about 15000°K. Therefore, propellant seeding with micrometre sized particles 

has to be applied for absorption of the radiation from the fissioning plasma. 

Such a process appears to be more a matter of technique than physics, and 

approaches have been developed that, in experiment, have demonstrated, for 

example, the heating of a tungsten seeded argon flow up to 4500°K. Propellant 

exhaust temperatures of plasma core reactors for propulsion must be 

higher than that, however, so that seed particles will vaporize. The opacity 

of propellants with vaporized seed materials is under current investigation. 

Ballistic Piston Compressor 

A ballistic compressor is used to simulate conditions 1n the nuclear 

piston engine and to measure the thermodynamic properties of UFg under 

extreme conditions. The behavior of enriched compressed UFç under bombardment 

with fission fragments, neutrons and other nuclear radiation will be 

explored. 

Fig. 8 is a schematic diagram of the ballistic compressor. The apparatus 

is able to produce a temperature up to 10000°K at a pressure up to 5000 atm. 

The basic properties of temperature, volume, and pressure are measured and 

the equation of state for UFg is determined. The van der Waal s' coefficients, 

the ratio of specific heats for pure UFg and UFg-He mixtures, and the viscosity 

for UFg have been determined [16]. The results of these measurements 

show that by choosing optimum mixing ratios of UFg and He, values of specific 

heat ratios as high as 1.47 can be obtained. 

For research on the interaction of the compressed 235UFg with fission 

fragments, the high-pressure part of the ballistic compressors will be 

inserted in a reactor and exposed to a neutron flux. 

Nuclear Pumped Lasers 

Research on nuclear pumped lasers has been underway for several years. 

Two types of experimental configurations have been used. Tubes coated with 

uranium oxide and filled with laser gas mixtures were exposed to a neutron 

flux in a reactor. Fission fragments emanating from the coating caused 

nuclear laser pumping. Another configuration was an uncoated tube filled 

with laser gas mixtures plus a certain partial pressure of 3He. When 

exposed to a neutron flux the Зне (n,p)T reaction resulted in laser excitation. 

The results obtained can be grouped in nuclear augmentation and 

pure nuclear pumpinq. In the case of nuclear augmentation, the performance 

of an electrical discharge laser is improved by nuclear effects, in the pure 

nuclear pumping no electrical energy is used to maintain the laser action.

1A E A -S M -170/53 25 

F IG . 8 . B a llis tic p iston d e v i c e . 

Results in both categories are reviewed in [8]. Additional results on pure 

nuclear pumping are reported in [17], where an argon ion laser cavity 

without electrodes was employed. 

In-core testing of lasers is very meticulous because of the high 

radiation environment to which the optical components are exposed and the 

inaccessibility of the laser experiment in the reactor. 

Results of this research indicate the possibility of nuclear pumping 

of lasers. In a broader view they substantiate the concept of a fissioning 

plasma existing in possible nonequilibrium states. 

Cri ti cal i t.y 

Research on the criticality of low-power (500 W) gaseous core cavity 

reactors was conducted at,, the National Reactor Testing Station in Idaho, USA, 

using enriched gaseous 235UFg [18]. A relatively clean spherical geometry 

was used and thus could be analyzed by one-dimensional reactor physics codes. 

The deviations from perfect spherical geometry were experimentally evaluated 

as being worth less than 0.75 %дк. The fuel core region was 1.27 m in 

diameter in a cavity of 1.83 m in diameter and was reflected by 0.91 m of 

O7O. Correlation with theory was attempted using S4 transport theory with 

19 energy groups, seven of which were thermal. The absolute multiplication 

factor was calculated at 1.04, 3 %дк higher than the corrected experimental 

value. The worth of the addition of hydrogen for propellant flow simulation 

was underpredicted by approximately 50%.


Three critical experiments were conducted in an attempt to determine 

empirically the feasibility of the plasma-core reactor concept. One was 

without hydrogen propellant and with a 0.005-m A1 cavity wall. In the second, 

1.1 x 1021 hydrogen atoms/cm3 of simulated propellant (foamed polystyrene 

and polyethylene sheets) were added, the critical masses were 8.43 and 12.9 

kg, respectively, and the fuel worth was 2.96 %дк/кд, and 2.02 %дк/кд, 

respectively. In the third experiment a 0.008-m stainless steel liner was 

added on the cavity wall to evaluate the effect of 0.019 mean free path 

thermal absorber material. The critical mass increased to 29.2 kg, and the 

fuel worth decreased to 0.44 2>дк/кд. 

General conclusions from these and other criticality experiments, also 

involving cylindrical configurations, accompanied by theoretical analysis, 

are that a plasma-core reactor must be designed with an absolute minimum of 

nonessential reactivity penalties, that the effect of a hydrogen propellant 

flow between the fuel region and the reflector requires serious consideration, 

and that the ratio of fuel radius to cavity radius be not less than 0.5 in 

order to obtain criticality at a pressure of less than 1000 atm and at the 

projected plasma core reactor temperatures. 

Instabilities 

The nonlinear evolution of unstable sound waves in a fissioning uranium 

plasma has been calculated [19] using a multiple time-scale asymptotic 

expansion scheme. A spectrum of standing sound waves in a bounded region of 

the fissioning plasma was considered, with a constant background thermal 

neutron flux density. In the wave compressions, the fissioning power 

density, Pfiss» increases because of the increased uranium density, and in 

the rarefractions Pfiss decreases. This leads to a transfer of fission 

power to the wave. Competing with this effect is thermal electromagnetic 

radiation, which tends to transport the extra thermal energy out of the wave 

compressions. Such radiation diffusion disperses the energy accumulation in 

waves more rapidly for shorter wavelengths. This results in a critical 

wavelength below which waves are stable and above which they are unstable. 

The calculations show that nonlinear mode coupling causes an energy flow 

from the long-wavelength unstable modes to the short-wavelength modes, such 

that the system stabilizes at defined amplitudes. For plasma-core conditions 

as assumed in this analysis, this occurs at relative pressure fluctuations 

of the order of ôP/P = 10"5. In addition, neutronic feedback in the regimes 

of rarefraction contributes to stabilization. In a first-order approximation, 

the stability of fissioning plasmas seems to be indicated. However, 

the analysis needs to be expanded to include gross flow fluctuations and the 

effects of inhomogenous neutron flux and fuel distributions. 

Gaseous Core Reactor Dynamics Studies 

An analysis of the dynamics of the coaxial flow plasma-core reactor is 

presented 1n [20]. The theoretical model is described by a set of 22 first- 

order differential equations in 22 unknowns, involving neutron, heat, and 

mass balances of the system. The fuel region is assumed to remain spherical 

in shape during all deviations from steady state. Six reactivity feedback 

mechanisms are taken into account: fuel temperature, propellant temperature, 

fuel mass, propellant density, fuel cloud radius, and moderator temperature. 

According to this analysis, at 0 . H positive reactivity insertion the power 

of the reactor raises first, but rapid increases in propellant density and 

fuel temperature generate sufficient negative feedback to decrease the excess 

reactivity, which in turn reduces the power. About 200 msec after the 

initial perturbation, the propellant density feedback becomes positive and

I A E A - S M -1 7 0 /5 3 27 

causes a slow increase in power which continues later in time because of 

positive feedback from the expansion of the fuel ball. Neither the fuel mass 

nor the moderator temperature feedback are significant. 

The progression of power excursion is less than 10% within 1 sec indicating 

possibilities of easy control. The system response to larger reactivity 

insertions is qualitatively the same, but at a step insertion of $1 

reactivity, fluctuations become more rapid and larger in amplitude to cause 

more serious control problems. Whereas the system is relatively insensitive 

to the rate of fuel Inflow, it exhibits strong responses to variations of 

propellant flow. For example, losses of propellant flow result in an expansion 

of the fuel region, which is a positive feedback, and in a decrease 

of the negative reactivity of the propellant layer. Although the 

corresponding rates of power increase are larger than those of the previously 

discussed reactivity insertion, the time scale is likewise in 

seconds. 

Similar analysis using a digital computer simulation program has been 

conducted for the nuclear light bulb concept [21] and shows that such a 

system can be controlled by the fuel flow rate, regulated by valves that 

are activated in response to the amount of neutron flux increases and to 

the rate of such neutron flux increases. 

Fissioning Plasma Research Facility 

A significant advance in understanding fissioning plasmas is expected 

to result from investigations conducted in a special research facility. 

Such a Fissioning Plasma Research Facility is presently projected as a 

system involving a solid fuel driver reactor particularly designed to 

produce an unperturbed thermal neutron flux at 10>5 n/cm2 sec in a 

relatively large inside test volume and in interchangeable test section to 

investigate the various configurations of fissioning plasmas derived from 

the concepts and schemes presented earlier. A primary objective, however, 

would be to create a steady state fissioning plasma for basic research, 

under conditions best suited for comprehensive diagnostics. 

A possible fissioning plasma research facility is shown in Fig. 9. The 

reactor and test section are contained in a pressure vessel for operation 

at 200 to 300 atm. The top section plus the upper part of the Be reflector 

and the test section can easily be removed for interchanging experiments. 

At the bottom, not shown in the figure, are an effluent handling and a 

cleanup system. Almost all reactivity is contained in the solid fuel. 

Feedback from the fissioning plasma appears to be negligible and small 

enough to be overridden by conventional control methods. There appear 

several tradeoffs resulting from the best choices of fuel elements, coolants, 

and moderator-reflector materials as to the required power level of the 

reactor and the affiliated coolant flow capacities. A desirable feature 

would be the possibility of boosting the neutron flux in pulsed operation up 

to loi6 n/cm2 sec and higher. 

In the depicted scheme, the coaxial flow concept of fissioning plasma 

confinement is shown in which seeded hydrogen enters a spherical cavity 

tangentially through an array of slots, while enriched uranium fuel is fed 

through a central cadmium-shielded pipe system. In the cavity, the uranium 

undergoes fission, thereby creating a fissioning uranium plasma fireball. 

The edge of the fuel temperature has to be not less than that of uranium 

evaporation. A typical temperature profile for an in-core coaxial flow configuration 

operating at a pressure of 200 atm is shown in Fig. 10. In the 

central region, the fissioning plasma has a temperature of about 20000°K.


TO EFFLUENT 

CLEANUP 

F I G .9 . P o ssib le fissio n in g p la sm a re s e a r ch f a c i li t y . 

At the edge of the fuel, the temperature drops to about 5000°K, a temperature 

at which the uranium is expected not to condense (exact data for the 

uranium vapor pressure at the edge of the fuel are not yet at hand; however, 

recent measurements [22] allow for confident estimates and extrapolations). 

For a pressure of 300 atm and an unperturbed neutron flux of 10l5 n/cm2 sec, 

the fission power is 14 kW/g, and the edge of the fuel temperature is 7400°K. 

At the wall, the flow has absorbed all radiation such that the cavity wall 

remains essentially at room temperature. In this case the cavity would 

appear black for optical observation from the wall region, for diagnostics 

purposes, an undesirable effect. 

Calculations of the total power balance for such a system, with a 

plasma diameter of about 0.38 m, show that the fission power in the plasma 

is a few megawatts, while the driver reactor has to operate at 50 to 200 

megawatts, depending on reactor design. Appreciable alterations of the 

power balance should result from variations of the radiant heat flux. When,

IA E A -S M -1 70/53 29 

FUEL 

EDGE CAVITY 

F IG . 1 0 . T e m p e r a tu r e p r o file in test c a v it y . 

for example, in the cavity an argon flow is used instead of hydrogen flow, 

the possibility of increased seed loading results in such greatly enhanced 

reflection of radiation back to the plasma that plasma conditions are maintained 

even if fission power drops to 0.5 MVJ or the temperature may be 

increased if the power level is maintained. Simultaneously, the pressure 

may vary to about 50%. An unseeded flow may be used in conjunction with 

reflecting cavity walls, as to control the power loss from the plasma. It 

appears thus that a fissioning uranium plasma research facility can be built 

with some flexibility in respect to power, temperature, and pressure. 

Experimental investigations of the overall power balance, and some 

details of radiation transport and stability, can be carried out by measuring 

cavity outlet flow temperature, cavity wall temperature, cavity neutron 

flux, cavity pressure, and the variations thereof depending on perturbations 

of propellant and fuel flow rates and neutron flux density. It should be 

possible to deduce various reactivity feedback coefficients from such 

measurements to supplement analysis of self-critical systems. Diagnostics 

of the fissioning plasma, for example, the determination of the spectral 

power distribution of thermal radiation, the spatial temperature distribution 

in the fissioning plasma, and the possible nonequilibrium states of 

excitation and ionization does not appear to be impossible, but development 

of special technigues may be required. 

Beyond the purpose of obtaining basic information a fissioning plasma 

research facility should be used to test functional components of plasma- 

core reactor applications, such as propulsion in space, MHD power generation, 

and the nuclear pumping of lasers.


Small Light Bulb Engine 

The critical fuel density and the size of a cavity reactor depend on the 

flow of thermalized neutrons back into the cavity. In the plasma reactor concepts 

previously discussed, the high-temperature propellant flow in between 

the fissioning plasma and the moderator-reflector region represents a significant 

neutron flux barrier. A concept [23] has been forwarded to largely 

circumvent this problem by dividing the surface area surrounding the fissioning 

plasma such that only a part of it is propellant flow and the other is an 

optically reflecting material that is highly transparent for neutrons. Part 

of the thermal radiation from the fuel region is directly absorbed in an array 

of segmented propellant flow ducts embedded in the reflecting cavity walls. 

Another part of the radiation is focused indirectly by reflection from such 

walls to such ducts. In addition, use is made of the large transparency of 

cold beryllium for thermal neutrons having energies below 0.006 eV. 

A figure of merit for the performance of reflector-moderator materials in 

cavity reactors is the ratio of the square root of the age of fission neutrons 

and the thermal neutron mean free path. For example, if this ratio is Z.25, 

that is, for a graphite moderator at 300°K, the critical density for 235U in a 

spherical cavity of 1 m radius must be greater than 10Î9 atoms/cm3. In 

contrast, a beryllium moderator at 100°K yields 0.47 for this ratio with a 

resulting critical density of 2 to 4 x 10' 7 atoms/cm3. 

The combined effects of a super-cooled beryllium neutron moderator and 

drastically reduced propellant flow areas should result in appreciably 

reduced critical mass for the plasma-core reactor and a low operational 

power. The cold beryllium has to be surrounded by a D£0 reflector to prevent 

neutron leakage from the system. Analysis was conducted for a spherical 

geometry using one-dimensional multi group neutron transport theory calculations. 

Seventeen neutron energy groups were employed, including five 

thermal groups of which two were below 0.006 eV. Scattering cross sections 

were taken from literature or were computed by standard methods. The neutron 

transport calculations were performed on a computer with the ANISN code. The 

system involved an argon buffer gas flow for the confinement of the fissioning 

plasma within the cavity and away from the walls. Results show that moderator 

temperature is a strong negative reactivity feedback. For example, 

using 233U, critical mass is slightly higher than 1 kg at a beryllium 

temperature of 40°K. It increases to about 2.8 kg at room temperature. The 

use of 235U instead of 233U results in an increase of the critical mass of 

about 20%. The presence of hot hydrogen ,in the discrete propellant channels 

does not appear to have a large effect on critical mass for the system 

studied. 

Operating power depends largely on the reflectivity of the reflecting 

surfaces of the cavity, which in the calculations is assumed to be of the 

order of 0.9. Radiation damage may, however, degrade this quality. With 

the previously mentioned temperature requirements for the fissioning plasma, 

the power is calculated to be in the range of 40 to 400 MW. The pressure 

may vary from 250 to 500 atm, and the weight of the system, including a 

pressure shell, is in the range of 16000 to 22000 kg. Applications are seen 

for space propulsion at specific impulse values as large as 1550 sec and for 

MHD power conversion. 

NUCLEAR DATA REQUIREMENTS 

The special characteristics of plasma-core reactor schemes pose a number 

of problems for computing criticality conditions not hitherto encountered in

IAEA-SM * 1 70/53 31 

Temperature, °K 

F IG . 1 1 . U r a n iu m -p la s m a c o m p o s itio n at pressure o f 5 00 a tm ospheres [ 3 2 ] . 

reactor physics calculations. More precise knowledge of certain nuclear data 

that play a more important role in plasma-core reactor schemes is required. 

A predominant new aspect is the intimate relationship between plasma physics 

and reactor physics. For typical plasma-core reactor conditions at 40000°K 

and 500 atm, more than 70% of the particles that account for this pressure 

are electrons. About 15% are U IV, as can be seen from Fig.' 11. Composition 

calculations have thus to be included in criticality calculation and their


accuracy is as important as that of the nuclear calculations. Theoretical 

approximations have been performed [24] and the results incorporated in 

current plasma-core reactor analysis. 

Data required for improved composition calculations are electronic partition 

functions and the ionization energies for the uranium atom and its 

ions. The partition functions are not yet known to a desirable degree of 

precision. Ionization energies are theoretically predicted but not yet 

verified by experiment. 

For precisely predicting the radiant heat transfer, depending on the 

plasma composition, transition probabilities and atomic energy levels of the 

uranium atom and its ions have to be known as well as the optical absorption 

and emission coefficients of the uranium plasma. A weak reactivity feedback 

exists depending on these quantities, which in turn can alter the power and 

subsequently the plasma temperature that governs its composition. 

Some measurements of emission and absorption coefficients exist [15]. 

Also transition probabilities for U I and U II are known [25]. However, 

the transition probabilities for U III and U IV are not known. U III and 

U IV will be major species in the reactor core. 

At a fuel temperature of the order of 40000°K (or about 4 eV), the 

neutrons see high target velocities; the result is reduced average fission 

cross sections. This fuel temperature effect does not appear to be 

critical (owing to the large mass of the uranium nucleus); however, it is 

not negligible. An increase of the critical mass by less than 5% is 

typical. Possible bulk motion of the fuel would result in similar effects. 

More important is the upscattering of thermal neutrons by the hot 

hydrogen propellant [26, 27] which in plasma-core reactor schemes is placed 

between the fuel and the moderator. The reflected and moderated neutrons 

have to pass through this high-temperature hydrogen region before they can 

reenter the fuel region. Upscatter of neutron energy results in a substantial 

penalty for the critical mass requirement. This effect can become 

so severe that for a given temperature a maximum operating pressure and 

hydrogen layer thickness exist beyond which criticality cannot be achieved. 

Because of the strong negative reactivity feedback of the propellant flow, 

a sudden interruption of this flow can result in a severe reactor power 

excursion. 

In the coaxial flow concept hydrogen migrates into the fuel region by 

diffusion and eventually will establish and maintain a certain hydrogen 

partial pressure in the fuel region. The temperature of the hydrogen 1n the 

fuel region will be equal to the fuel temperature. Fig. 12 shows the consequences 

for the 500-atm case assuming a mixing ratio of 1:1. At 40000°K, 

about 68% of the particles would be electrons, 15% would be protons, 10% 

would be U IV, 4% U III, and 4% U V. Because of the high temperature of the 

hydrogen ('4 eV) a substantial hardening of the neutron spectrum would occur, 

with a larger penalty for critical mass requirement than due to the hardening 

caused by the hydrogen in the working fluid. Competing with this effect is 

the moderation of fission neutrons by this hydrogen component. 

In order to compute all these effects properly, a better knowledge of 

the still unresolved resonances would be helpful. Also computation models 

for scattering kernels for hydrogen up to 40000°K are required. Doppler coefficients 

for similar temperatures are also required. New codes for criticality 

calculations involving the effects of fuel mixing ought to be 

developed.

IA E A -S M -170/5 3 33 

Temperature, °K 

F IG . 1 2 . C o m p o s itio n o f h y d r o g e n -u r a n iu m p la sm a at pressure o f 5 00 a tm o s p h e r e s. M ix in g r a tio = 1 :1 [ 3 2 ] . 

In contrast to conditions in solid-core reactors, the fuel in plasma 

core reactors has such a short residence time in the core that a portion of 

the delayed neutrons do not contribute to criticality. According to [28] 

there are more delayed neutrons in the low-energy region than previously 

assumed. These are competing effects whose relative contributions to 

criticality computations require more attention. Special analysis of the 

delayed neutron spectrum appears to be in order.


The radial diffusion coefficient for the plasma core, including modifications 

due to deviations from true spherical shape of the fuel region, 

needs to be developed for a good description of the flux distribution. Such 

deviations of the fuel geometry are caused by the proximity of the nozzle 

and by dynamic effects in the uranium plasma like eddies and pressure 

oscillations. 

Another major difference between plasma-core reactors and solid fuel 

reactors is that the interaction mean free path of neutrons is equal to or 

larger than the core diameter. This has an effect on the moderator design 

requirements for reactor control. The reactor has to be undermoderated to 

achieve a negative temperature coefficient. 

Gamma ray heating of the moderator and reflector is important in space 

propulsion and should be calculable to a better precision [29]. Heat loads 

in the range of 300 to 400 MW will have to be radiated to space. Calculated 

gamma ray heating may be low by 35% to 60%. Relying on calculations, the 

gamma ray heat shield of a 6000 MW reactor has heat loads of 100 W/g, which 

are present day technology maximum, but in actual operation the load might 

be 150 W/g, which would be intolerable. 

The nuclear data required to rectify this situation are neutron capture 

cross sections and gamma ray spectra emitted by low cross section elements 

like deuterium, oxygen, and beryllium. Available data are of substantial 

uncertainty; e.g., the thermal neutron absorption cross sections recommended 

in BNL-235 for D, Be and 0 list uncertainties of 20* for D, 10% for Be,and 

14% for 0. 

Radiation damage plays a most important role in the nuclear light bulb 

concept, in which the radiant (light) energy is transferred from the fissioning 

plasma to the propellant throuah fused-silica walls. Experimental 

studies [30] indicate that around 2150A the absorption coefficient of fused 

silica can increase substantially by nuclear radiation. Absorption coefficients 

induced by radiation as high as 14.5 cm"' for the 2100A band were 

reported. Other research [31] yields more optimistic results (5 cm-1). The 

consequences of a large absorption coefficient are heating of the transparent 

wall material of the nuclear light bulb engine and ultimate destruction of 

this solid interface between fuel region and working fluid. Moderate heating 

of the fused silica can, however, have a beneficial effect. At about 600°C 

to 800°C, thermal annealing of color centers takes place. In [30] an equilibrated 

condition is reported to exist in which the rate of radiation-induced 

absorption is balanced by annealing such that a steady state good transparency 

at 0.1 cm" 1 is maintained. 

Reliable information on neutron- and gamma-induced increases of the 

absorption coefficient of quartz and other transparent materials of potential 

use as barrier material (e.g., aluminum oxide, beryllium oxide, and 

titanium oxide) is essential. 

For calculations pertaining to problems germane to the plasma-core 

reactor, numerous codes established for conventional reactors have been used 

successfully (e.g., DTK, DDK, TDSN, GAM II, GATHER II, QADHD, ANISN, EXTERMI 

NATOR- I I , PHR0G, and DOT II-W). However, there is a need for development of 

new codes capable of handling specific problems of the plasma-core reactor, 

that cannot be handled or can only be handled tortuously by existing codes. 

Codes that need to be developed include those for handling extreme temperature 

and density gradients of the working fluid, the temperature and 

density gradients of hot uranium and hot hydrogen in the fuel region, and

I A E A - S M -1 7 0 /5 3 35 

neutronic feedback resulting from rarefraction waves in the fuel region. 

Also necessary is a code dealing with the radial motion of the fuel within 

the cavity. These properties eventually should be described with three- 

dimensional codes. 

For the projected fissioning plasma research facility codes to deal 

with the coupling of both fuel components, the plasma-core and the solid 

drives region are required. 

CONCLUSION 

In the foregoing it has been shown that a need for improvement of 

nuclear data exists. There is also a need for reactor codes dealing with the 

specific problems of plasma-core reactors. The most striking feature of this 

new technology however is the intimate interrelationship between reactor 

physics and plasma physics, which calls for more precise knowledge of plasma 

data that have a strong effect on the nuclear behavior of the system. These 

plasma data have to be considered in this connection as nuclear data as well. 

The following nuclear data and computational codes appear at present 

significant for plasma-core reactor analysis and design: 

(1) Neutron fission cross sections at low energies (including 

resonances) 

(2) Kernels for neutron scattering in hot hydrogen (up to 40000°K) 

(3) Spectra of delayed neutrons 

(4) Neutron capture cross sections and gamma ray spectra of low 

cross-section elements 

(5) Radiation damage of optically transparent material 

(6 ) Codes for criticality calculations involving angular and radial 

distributions, two and three dimensions, coupled fuel systems, and mixed 

fuel (U + H) 

ACKNOWLEDGMENTS 

The authors had the privilege of discussions with most of the authors 

cited in this article. Particularly valuable advice was obtained from 

F. C. Schwenk, SNSO, AEC/NASA, R. G. Ragsdale, NASA Lewis Research Center, 

and M. J. Ohanian, The University of Florida. 

REFERENCES 

[1] THOM, K., SCHNEIDER, R.T., Symposium on Research on Uranium Plasmas 

and Their Technological Applications, NASA-SP 236 (1971) (U.S. 

Government Printing Office). 

[2] RAGSDALE, R.G., Second Symposium on Uranium Plasmas: Research and 

Applications, AIAA, New York (1971). 

[3] THOM, K., Review of fission enqine concepts, J. Spacecr. Rockets, 9, 

9 (1972).


[4] RAGSDALE, R., WILLIS, E.A., Gas-Core Rocket Reactors - A new Look, 

NASA TM X-67823 (1971). 

[5] CLEMENT, J.D., WILLIAMS, J.R., Gas core reactor technology, Reactor 

Technol. 12 3 (1970). 

[6] SCHWENK, F.C., FRANKLIN, C.E., "Comparison of closed and open cycle 

systems", Symposium on Research on Uranium Plasmas and Their Technological 

Applications, NASA SP-236 (1971) (U.S. Government Printing 

Office). 

[7] LATHAM, T.S., Summary of the Performance Characteristics of the Nuclear 

Light Bulb Engine, AIAA 71-642 (1971). 

[8] THOM, K., SCHNEIDER, R.T., Nuclear pumped gas lasers, AIAA J. 10 4 (1972). 

[9] SCHNEIDER, R.T., OHANIAN, M.J., Patent disclosure to NASA, 1970. 

[10] KYLSTRA, C.D., COOPER, J.L., MILLER, B.E., "UF6 plasma engine", Second 

Symposium on Uranium Plasmas: Research and Applications, AIAA, 

New York (1971). 

[11] MASSER, C.C., Radiation hazard from backflow of fission fragments from 

the plume of a gas core nuclear rocket, Symposium on Research on 

Uranium Plasmas and Their Technological Applications, NASA SP-236 

(1971) (U.S. Government Printing Office). 

[12] WILLIAMS, R.J., KIRBY, K.D., Exploratory investigation of an electric 

power plant utilizing a gaseous core reactor with MHD conversion 

(American Nuclear Society Topical Meeting, Atlantic City, New Jersey, 

1972). 

[13] BENNETT, J.C., JOHNSON, B.V., Experimental Study of One- and Two- 

Component Low-Turbulence Confined Coaxial Flows, NASA CR-1851 (1971). 

(U.S. National Technical Information Service). 

[14] RODGERS, R.J., LATHAM, T.S., KRASCELLA, N.L., "Radiant heat transfer 

calculations for the uranium free containment region of the nuclear 

light bulb engine", Second Symposium on Uranium Plasmas: Research 

and Applications, AIAA, New York (1971). 

[15] SCHNEIDER, R.T., CAMPBELL, H.D., MACK, J.M., Part I, University of 

Florida Annual Report, NASA Grant NGL 10-005-089 (1972). 

[16] SCHNEIDER, R.T., STERRIT, D.L., LALOS, G.A., Part II, University of 

Florida Annual Report, NASA Grant NGL 10-005-089 (1972). 

[17] WALTERS, R.A., SCHNEIDER, R.T., Part III, University of Florida 

Annual Report, NASA Grant NGL 10-005-089 (1972). 

[18] LOFTHOUSE, J.H., KUNZE, J.F., Spherical Gas Core Reactor Critical 

Experiment, NASA CR-72781 (1971). (U.S. National Technical 

Information Service). 

[19] TIDMAN, D.A., "Instabilities in uranium plasmas", Second Symposium on 

Uranium Plasmas: Research and Applications, AIAA, New York (1971). 

[20] TURNER, K.H., A Dynamic Model of Coaxial Flow Gaseous Core Nuclear 

Rocket System, Ph. D. thesis, Georgia Institute of Technology (1971).

IA E A -S M -1 70/5 3 37 

[21] LATHAM, T.S., BAUER, H.E., RODGERS, R.J., "Investigation of nuclear 

light bulb startup and engine dynamics", Symposium on Research on 

Uranium Plasmas and Their Technological Applications, MASA SP-236 

(1971) (U.S. Government Printing Office). 

[22] RANDOL, A.G., Ill, SCHNEIDER, R.T., KYLSTRA, C.D., "Boiling point of 

uranium", Symposium on Research on Uranium Plasmas and Their 

Technological Applications, NASA SP-236 (1971) (U.S. Government 

Printing Office). 

[23] LATHAM, T.S., RODGERS, R.J., "Small nuclear light bulb engines with 

cold beryllium reflectors", AIAA/SAE Joint Propulsion Specialist 

Conference (New Orleans, Louisiana, 1972) 8 . 

[24] PARKS, D.E., LANE, G., STEWARD, J.C., PEYTON, S., Optical Constants 

of Uranium Plasma, NASA CR-72348 (1968). (U.S. National Technical 

Information Service). 

[25] CORLISS, C.H., BOZMAN, W.R., NBS Monograph 53 (1962). (U.S. Government 

Printing Office). 

[26] WHITMARSH, J.C., Neutronic Analysis of Open-Cycle High-Impulse Gas- 

Core Reactor Concept, NASA TMX-2534 (1972). 

[27] KUNZE, J.F., LOFTHOUSE, J.H., SHAFFER, C.J., Hydrogen effect on a 

demonstration test for open-cycle gas core reactors, American Nuclear 

Society Trans. j[5 (1972). 

[28] SLOAN, W.R., WOODRUFF, G.L., Delayed-neutron energy spectra, American 

Nuclear Society Trans. 15 (1972) 942. 

[29] LOFTHOUSE, J.H., KUNZE, J.F., YOUNG, R.C., YOUNG, T.E., Gamma heating 

in gas core rocket reflector, American Nuclear Soceity Trans. lj[ 

1 (1972) 7. 

[30] SMITH, A.B., Optical Absorption in Fused Silica at Elevated Temperatures 

During 1.5 MeV Electron Irradiation, NASA TN D-6840 (1972) 

(U.S. National Technical Information Service). 

[31] PALMA, G.E., Measurement of the UV and VUV Transmission of Optical 

Materials During High-Energy Electron Irradiation, United Aircraft 

Research Laboratories Report L-990929-3 (1972). 

[32] ATWATER, H.F., Fissioning Uranium Plasma for Rocket Propulsion, 

Ph. D. dissertation, University of Florida, Gainesville, Florida 

(1968). 

D I S C U S S I O N 

F. RUSTICHELLI: What is the situation as regards the energy loss 

of fission fragments at high tem perature? Do you need stopping power 

data relating to this condition and have you done any experiments on the 

subject? 

K. THOM: At high temperature the uranium target gas is partially 

ionized. Large Coulomb collision cro ss-se ctio n s should result in a different 

stopping power than in a neutral target gas. Important data are those on 

the number of inelastic collisions of the fission fragments with the gas 

atoms and ions versus the number of eleastic collisions, and the fractional


energy losses involved in such collisions. In addition, one would like to 

know the partition among states of ionization and excitation during the 

slowing down of the fission fragments. Ionization produces free electrons 

whose presence in the fissioning plasma can add appreciably to the total 

pressure of the system. The result could be an unacceptable increase in 

pressure and size of a plasma core reactor, i. e. from the point of view of 

achieving criticality. The effect of excitation from fission fragment interactions 

is related to electrom agnetic radiation at discrete energy levels 

from the plasma. Since the fission fragment energy is very much larger 

than the average energy of the plasma, the excitation from fission fragments 

collisions may result in a population inversion of excited states and could 

thus be exploited for the direct conversion of fission fragments energies 

into coherent light, that is into work! I think this is the m ost important 

characteristic of fissioning plasmas. 

We have conducted som e experiments in which light was, in fact, 

produced by the fission fragment interactions with gas targets. In one 

case, in which the target gas was argon, even lasing was achieved. 

Much m ore detailed data are needed, however. F o r example, in a 

high-Z target gas, such as a uranium plasma, fission fragment collision 

m ay lead to bound-bound electron transitions at energy levels ranging 

from a few eV up to many keV. Knowledge of the distribution of such 

transitions would have far-reach in g consequences.

NUCLEAR DATA REQUIREMENTS FOR 

FUSION-FISSION (HYBRID) REACTORS 

W .C . WOLKENHAUER, B.R. LEONARD, Jr. 

P acific Northwest Laboratories, 

Richland, Wash., 


Abstract 

N U CLEAR D A T A REQUIREM ENTS FOR FUSIO N -F ISSIO N (H Y B R ID ) R E A C TORS. 

I A E A - S M -1 7 0 /5 6 

T h e h yh rid (f u s io n -fis s io n ) r e a c to r is a c la s s o f p o w e r -p r o d u c in g re a c to r s w h ic h has fu s io n and fissio n 

re a c to r s as its e x t r e m e m e m b e r s . T h e r e are tw o d is tin c tly d iffe r e n t h y brid sy stem s: H ybrid system s w h ic h 

o p t im iz e o n th e b r e e d in g o f fis s ile fu e l for fissio n r e a cto r s or tritiu m for D - T fu sion r e a c to r s , and h y brid 

system s w h ic h o p t im iz e o n p o w e r p r o d u c tio n and u t iliz a t io n o f e n e r g y re s o u rc e s. S tu dies h a v e b e e n m a d e o n 

th e h y brid s in c e 1953 w ith th e m o st r e c e n t w o rk b e in g ca rrie d ou t by th e authors at B a tte lle -N o r th w e s t. 

T h e ju s t ific a t io n fo r pu rsuing th e study o f h y brid system s is th e p o s s ib ility o f a c h ie v in g a p o w e r p la n t 

w h ic h c o u p le s th e short d o u b lin g t im e s a sso c ia te d w ith th e fu s io n r e a c t o r to th e h ig h p o w e r d e n sitie s 

a s s o c ia te d w ith th e fissio n r e a c to r w h ile at th e sa m e t im e b e in g a b le to e x tr a c t p ow er fr o m th e a v a ila b le 

u ra n iu m re s e rv e s fr o m an e s s e n tia lly s a fe (s u b c r itic a l) fis s io n la t t ic e . 

T h e d e s ig n and o p t im iz a t io n o f h y brid p la n ts p la c e s n ew restrain ts o n th e re q u ire d n u c le a r d a ta n e e d e d 

fo r th e a n aly sis. A ll o f th e usu al r e a c tio n s co n s id e re d in fis s io n r e a c to r d e s ig n m ust b e c o v e r e d by th e da ta 

bu t n ow th e r e q u ire m e n t is for g o o d d a ta fr o m th e rm a l to 14 M e V . In a d d itio n , n, 2 n and n, 3n re a c tio n s 

w h ic h are n ot n o r m a lly s ig n ific a n t in fissio n r e a c to r d e s ig n b e c o m e im p o r ta n t. F in a lly , o f c o u r s e , p la sm a 

p h y s ics d a ta and r e a c t io n c r o s s -s e c t io n s o f stru ctu ral m a te r ia ls fo r 14 M e V n eu tron s a re r e q u ir e d . 

M ost h y brid c o n c e p t s are based u p on th e n u c le a r r e a c tio n s o f w ith 1 4 - M e V n eu tron s. T h e r e are 

s e v e r a l n e u tr o n -p r o d u c in g r e a c t io n s w h ic h ta k e p l a c e . T h e y in c lu d e n ,2 n , n ,3 n , and fissio n r e a c tio n s . 

W h ile d a ta o n th e se r e a c tio n s a re cu rre n tly a v a ila b le in th e E valu a ted N u cle a r D ata F ile (E N D F /B -III) 

o f th e U S A E C , c r e d ib le o p t im iz a t io n o f h y brid c o n c e p t s to d e te r m in e th e p o t e n t ia l a d v a n ta g e s ca n n o t b e 

m a d e w ith o u t s ig n ific a n t r é é v a lu a tio n o f th e d a ta f i l e . H ybrid sy stem s c a n a ls o b e d e s ig n e d based 

o n th e th o riu m fu e l c y c l e . In th is r e g a rd , th e sa m e ty p e o f d a ta is re q u ire d h e r e but th e a v a ila b le d a ta 

a re in fe r io r to th o se o f ^ U . 

The fusion-fission or hybrid reactor is generally defined as a 

Controlled Thermonuclear Reactor (CTR) with a fissionable blanket surrounding 

it. The concept is based upon the neutron multiplication properties 

of heavy isotopes in a 14 MeV (deuterium-tritiurn plasma) neutron flux and 

the large energy release of neutron-induced fission relative to neutron 

capture events or neutron absorption in lithium.[l] 

While a number of different concepts have been proposed, there appear 

to be only two distinct classes of hybrid systems. One of these is a system 

which is optimized for the breeding of fissile fuel for fission reactors. 

The other concept is the hybrid which is optimized for power production 

directly. [2] 

Because the hybrid concept is not well understood, we will first review 

the historical development of the concept. We will then develop some of the 

principle characteristics of the system. After this, a specific hybrid 

design will be given. A review of the analytical techniques applied to 

this specific design will then allow for development of the nuclear data 

required for hybrid reactor design. 

39

40 WOLKENHAUER and LEONARD 

1. History of Development 

The first suggestion for a hybrid device was apparently made in the 

early 1950's .[3] A United States patent application describing a hybrid 

was filed in 1957.[4] A British patent application was filed by Lawson, 

et al., in 1958 on a similar idea.[5] The first applicable measurements 

in the open literature appear to have been made by Weale et al., 

in 1961.[6] The most systematic study of a hybrid concept which is 

optimized for the breeding of fissile fuel for fission reactors was 

carried out by Lidsky [7]* Some of the most recent work on a hybrid 

concept optimized for power production has been carried out by Lee[8] 

and by the authors [1], There does not however, seem to have been a 

consistent development program on the hybrid concept even though it 

was first introduced some twenty years ago. Interest in the hybrid may 

grow, however, when the emphasis in fusion reactor development changes 

from technical feasibility to engineering and economic feasibility. 

2. The Characteristics of a Hybrid Reactor 

A hybrid, reactor can be defined as a CTR with a blanket which contains 

fissile or fertile material. Such a machine, independent of the 

market it is optimized for, has certain characteristics which identify 

its potential advantages or disadvantages as a source of power. 

First of all, consider the characteristics of the plasma of the 

fusion device employed in the hybrid machine. It is often mentioned 

that a possible advantage of the hybrid is that, as a result of its 

energy multiplication possibilities, it can be used with a sub-Lawson 

plasma which would allow for early exploitation of the fusion reaction. 

The plasma characteristics of a hybrid can be more accurately defined by 

pointing out that a hybrid must operate with a sub-Lawson plasma [9]. 

This conclusion results from engineering considerations. A certain 

level of energy or neutron multiplication must take place in the blanket 

in order to breed fuel for the device. For a given blanket design, there 

is a limit on blanket power density and a limit on fissile fuel depletion 

rate which can be determined for that design. For known materials, these 

blanket limits result in plasma limits which are, in all cases surveyed, 

substantially sub-Lawson in nature. Therefore, the first characteristic 

of a hybrid machine is that it must operate with a sub-Lawson plasma. 

This result implies that exotic refractory metals for structure and fuel 

cladding are not required for hybrid reactors. 

Another characteristic of hybrid machines is the nature of the 

energy multiplication. For a hybrid design with a fissile blanket,.the 

rate of multiplication, or the number of fissions per fusion event, (N) 

can be estimated by the equation [10]: 

where к is the neutron balance of the fissile blanket as usually defined 

bf standard reactor physics terminology and v is the average 

number of neutrons per fission. From this equation, one can see that 

very large energy multiplication is possible with values of к „ < 1. 

Therefore, hybrid fertile/fissile blankets will be subcriticai. For 

a deuterium-tritium plasma, the energy multiplication (Q) of a given 

design can be estimated by the equation:

IA E A -S M -1 70/56 41 

2 0 0 + 1 7 x 1 x eff 

17 

V 1 - 

eff 

assuming an average fission energy release of 200 MeV, an average fusi,on 

energy release of 17 MeV, and also assuming that all of the fusion 

energy is available to the energy balance. Therefore, a second characteristic 

of the hybrid machine can be developed. Not only does the 

hybrid operate with a sub-Lawson plasma, but also it employs a sub- 

critical blanket assembly. The design goal, of course, is to develop 

a machine with the above characteristics which has a favorable output 

to input energy balance. For a wide range of interesting designs, this 

appears to be possible. 

A third general characteristic of hybrid machines relates to the 

breeding function of the blanket. If the blanket, in its role as a 

fissile breeder, utilizes depleted or natural uranium as a fertile 

material, the bred fissile material is found to be almost all Pu-239 [1]. 

This is due to two phenomena. The hybrid reactor, if it utilizes the 

deuterium-tritium reaction, gives off 14 MeV neutrons as a primary source. 

The value of a(a = ac/


\ 

NEUTR VERTER 

S U B C R IT IC A l F IS S IO N LATTICE 

ENERGY CONVERTER 

G RAPH ITE, NATURAL U R A N IU M , H E L IU M 

(NATURAL U R A N IU M -C A R B ID f ) 

NATURAL U R A N IU M 

H E L IU M GRAPHITE j 

® ® ® ® ® 

MODERATOR L IT H IU M 

REFLECTOR A B S O R B E R 

P L A S M A G RAPH ITE íl ít h íu m 

/ 

R A D IU S 160 cm 

200 

® ® ® ® ® 

® ® ® ® ® ® 

® ® ® ® ® 

® ® ® ® © ® 

® ® ® ® ® 

F I G . l . H ybrid b la n k e t. 

In summary then, a hybrid reactor is a sub-Lawson plasma coupled to a 

subcritical fissile/fertile assembly which can produce a positive energy 

balance. Some of the potential advantages of the device are: 

о Has high energy densities associated with fission reactors. 

о Has short doubling times associated with fusion reactors. 

e Breeds relatively pure fissile material. 

о Allows for exploitation of uranium reserves in subcritical 

assemblies. 

• Eliminates major radioactive hazards associated with pure 

fusion and pure fission devices. 

® Development can progress to fruition based on known technology. 

The authors have been studying a specific hybrid design based upon 

the neutron convertor concept [1,2,9,10], One variation of this approach 

is shown in Figure 1. 

The fissile blanket is divided into a number of regions. These 

include the neutron convertor, the energy convertor, a reflector, and an 

outer absorber for tritium production. The design shown here is helium 

cooled and, at least for the energy convertor, is generally consistent 

with gas cooled fission lattice design. 

The neutron convertor concept is of general interest here as it 

serves several purposes [1]. It provides direct utilization of the U-238 

fission energy by 14 MeV neutron induced fission and multiplication of 

the 14 MeV neutron source through fission, n,2n, and n,3n reactions. The 

absorption in the convertor of these secondary neutrons and neutrons 

leaking back from the fission lattice result in further fast neutron 

fissions and neutron capture in U-238 to produce Pu-239. The lithium 

1

I A E A - S M -1 7 0 /5 6 43 

F IG .2 . S p h e r ic a l h y b r id . 

serves to breed tritium, inhibit Pu-239 fission and in addition, it 

decouples neutronically one side of the fission lattice from the other 

side of the cylinder. 

The design shown here is, in general, typical of the studies being 

carried out on this concept. The hybrid is usually studied somewhat 

independently of a specific plasma device. However, it is usually based 

on a deuterium-tritiurn plasma due to the high potential neutron multiplication 

of the energetic (14 MeV) neutrons. In addition, a specific 

blanket design will, as mentioned previously, dictate the desired plasma 

conditions. 

In contrast to this system, Figure 2 shows a spherical design developed 

by Lee [8]. In principle, this system operates much in the manner 

of that shown in Figure 1. This type of hybrid probably places more 

stringent requirements on nuclear data than the coupled convertor-thermal 

system. In order to analyze this system, one must have continuous data 

describing the slowing down of neutrons from 14 MeV to thermal energies 

throughout the system and for all isotopes of the system. 

The Analysis of a Hybrid 

In order to develop the minimum nuclear data requirements needed to 

analyze some of these previously described systems, a method of performing 

an analysis of hybrids will be described. A flow chart of the approach 

is shown in Figure 3. Other analytical techniques which have been used 

include Monte Carlo analysis and other computer codes which solve the 

neutron transport equation directly. 

The analysis of a hybrid begins with a microscopic data library for 

the required isotopes with data being available for the required reactions 

over an energy range from 14 MeV to thermal. The minimum data requirements


• POWER DISTRI BUTION . TIME DEPENDENT NUCLIDE 

DENSITIES 

F I G .3 . A n a n a ly sis m o d e l fo r h y brid r e a cto r s. 

are summarized in Figures 7 and 8 . In Figure 2, to save computer space, 

the data are collapsed by means of the neutron transport code ANISN[12] 

to a 27 energy group set. The THERM0S[13] and HRG[14] codes are used to 

calculate thermal spatial and resonance absorption spatial effects. These 

effects are particularly strong with respect to U-238 and Pu-240. The ANISN 

code is used to calculate the static neutron flux distribution. The ALCHEMY[15] 

code is used to calculate the burnup rate of the various isotopes. Dashed 

lines are used to indicate the need for periodic spectral updating of the 

data as the analysis proceeds to higher neutron exposure. The computer 

codes used here are generally available and have been used in the analysis 

of similar devices [16]. 

4. The Important Neutron Reactions 

The major neutronic reactions involved in the analysis of hybrid blankets 

are the neutron producing reactions and the fuel breeding reactions. These 

reactions are reviewed below along with some of the other relevant reactions. 

The results are then summarized to develop the minimum nuclear data needs 

for hybrid analysis. 

4.1 The Neutron Producing Reactions 

The neutron producing reactions for U-238 are shown in Figure 4 as 

a function of energy. They are the n,2n, n,3n and fission reactions and 

are shown here as a function of energy. The curves were obtained from 

version 3 of ENDF/B[17] which is the Evaluated Nuclear Data File of the

IA E A -S M -1 7 0 /5 6 45 

NEUTRON ENERGY (MeVt 

F IG .4 . N e u tr o n -p r o d u c in g r e a c tio n s o f 238U . 

NEUTRON FNERGY (MeV) 

F I G .5 . N eu tron s p r o d u c e d per n eu tron a b s orb ed fo r Z38U . 

USAEC. If these data are weighted by the specific reaction neutron production, 

a continuous curve of the number of neutrons produced per neutron 

absorbed can be developed. This composite curve is shown in Figure 5 [9]. 

If this curve is compared to experimental points, as shown on Figure 5, 

one can see that the file may not be a best estimate at 14 MeV. While 

Figure 5 demonstrates the high neutron multiplication which can be obtained 

from 14 MeV neutrons impinging upon a fissile/fertile assembly, 

it also indicates some inadequacy in the available data for neutron 

producing reactions. This inadequacy may, however, be due to inadequacies 

in the library data file description as opposed to inadequacies in the data 

themselves. In any case, the nuclear data needs for hybrid reactor analysis 

not only include specific requirements for nuclear data for energies far 

above the fission spectrum, but also, there are requirements for data on 

nuclear reactors often not given emphasis in fission reactors, (i.e., n,2n, 

n,3n).


4.2 The Fuel Breeding Reactions 

There are several neutron absorbing fuel breeding reactions associated 

with the hybrid reactor. Assuming a fusion device based upon the deuterium- 

tritium reaction, tritium must be bred at a breakeven rate by neutron absorption 

in lithium. The specific reactions are [18]: 

6Li, + ]n + 3H, + 4He„ 

о 0 1 2 

7Li, + V - 3H, + 4Не„ + ]п 

о о i ¿ о 

The ®Li reaction is a thermal neutron reaction and is exothermic. The \ i ~ 

reaction is an epithermal neutron reaction and is endothermie. In a 7 

typical hybrid blanket, about one-third of the tritium is bred by the Li, 

reaction and the rest by the thermal reaction. 

Plutonium may be bred in a hybrid blanket to supply fissile fuel 

either for energy production in the machine itself or in a separate reactor. 

The pertinent reactions are: 

238, + l„o . 239, : 239N p : 239pu 

If the fissile fuel is bred by means of neutron absorption in thorium such 

that 233u is bred as the fissile fuel, the reactions are [19]: 

232Th + 1 + 233Th I 233pa t 233u 

о 

The neutron absorption cross sections for the isotopes involved in these 

reactions must be known over the energy range from 14 MeV to thermal. 

4.3 Other Relevant Neutron Reactions 

In a hybrid blanket, energy is extracted by moderation of the energetic 

neutrons. Typical moderating materials include graphite and beryllium. 

Structural materials which may be used for the vacuum wall and the blanket 

structure would be alloys of stainless steel in contrast to the exotic 

metals such as niobium, and vanadium which have been proposed for "pure" 

fusion reactors. Therefore, inelastic and elastic scattering data are 

required for these materials, along with neutron absorption data, for the 

whole energy range from 14 MeV to thermal energies. Supplementary information 

on the neutron damage characteristics of these materials as a function 

of energy may also be required. 

5. Minimum Data Requirements 

The data requirements for hybrid analysis are dictated, in part, 

by the complexity of the transmutation chain for fertile materials in a

NOT AVAILABLE 

IN DEPLETED 

LATTICE 

I A E A - S M -1 7 0 /5 6 47 

241p 

n,r 

n,r 

n,y 

n.r 

n,2nti n.r 

242, Pu 

F I G .6 . T h e u ra n iu m tra n sm u ta tion c h a in in a h ybrid b la n k e t. 

14 MeV neutron flux. Figure 6 displays the uranium transmutation chair, 

in a high energy flux. One can see that such reactions as n,2n, which have 

a threshold in the range of 8 MeV, become important in the hybrid system. 

The nuclear data needs for the analysis of a hybrid lattice such as 

shown in Figure 1 and which uses the uranium burnup chain shown in Figure 6 

can be developed for the analysis model shown in Figure 3. Such a compilation 

of requirements is shown in Figure 7. 

The data needs are so extensive in part, because the uranium burnup 

and transmutation equations have been shown to be quite complex. In addition, 

one needs to analyze fusion fuel breeding, neutron moderation, 

neutron production, and possible damage effects. The sum of these requirements 

leads to the extensive compilation listed in this figure. 

Figure 7 itemizes the data requirements for the analytical model. 

However, there are additional specific data requirements over certain energy 

ranges which are of special concern. These requirements are shown in 

Figure 8. 

While plasma reaction data is not of great importance directly in 

hybrid design, there will eventually develop a need for accurately controlling 

the degree to which the plasma lacks being a breakeven plasma. 

For fusion reactors, the emphasis has been placed upon knowing the charged- 

particle reaction cross section in the range of 10-100 keV. Because hybrid 

reactors require a degraded plasma, accurate data must be obtained in the 

range of a few keV. Because the cross section is very small and changing 

rapidly in this energy region, accurate data in this range might be difficult 

to obtain [20]«

WOLKENHAUER and LEONARD 

F I G .7 . M in im u m d a ta r e q u ire m e n ts for h y brid d e s ig n . 

ISOTOPE REACTION ENERGY RANGE COMMENT 

239Pu FISSIO N 10-15MeV INTERACTION OF 14MeV AND DEGRADED 

NEUTRONS WITH 232U, 238U, AND 239Pu 

LEAD TO NEED FOR IMPROVED DATA 

238U AND 232Th V 8-15MeV 

n, 2n THERMAL-15MeV 

n, 3n THERMAL-15MeV 

INELASTIC SCATTER 8-14MeV 

RESONANCE CAPTURE THERMAL- IMeV IMPORTANT FARTHER OUT IN THE BLANKET 

Fe CAPTURE THERMAL- 2MeV STAINLESS STEEL IS LIKELY 

H YBRID STRUCTURAL MATERIAL. 

П, 2n THERMAL-14MeV 

П, 3n THERMAL-14MeV 

ELASTIC SCATTER THERMAL-14MeV 

INELASTIC SCATTER THERMAL-14MeV 

F IS S IO N NEUTRON SPECTRA 4-15MeV THIS IS NEEDED TO CALCULATE 

SPECTRA NEAR THE VACUUM WALL. 

F I G .8 . S p e c if ic d a ta w h ic h n eed im p r o v e d m e a su re m e n t.

Summary 

IA E A -S M -1 70/56 49 

At present, the nuclear data used in hybrid design are found, for the 

most part, in ENDF/B[17] and other similar data libraries. They are, 

however, all lacking in some of the required reactions either because it 

has not been evaluated or because it has not been measured. Immediate 

requirements are for improved measurements of the minimum indicated reactions 

as shown in Figure 8 for the indicated energy range. Beyond the basic 

measurements, the data must be evaluated by data evaluation experts, and 

just as importantly, it must be placed upon the available nuclear data files. 

References 

[1] LEONARD, B. R., Jr., and WOLKENHAUER, W. C., Fusion-fission hybrids: 

A subcritical thermal fission lattice for a DT fusion reactor, 

presented at a conference on Technology of Controlled Thermonuclear 

Fusion Experiments and the Engineering Aspects of Fusion Reactors, 

University of Texas, Austin, Texas, (November 1972). 

[2] LEONARD, B. R., Jr., and WOLKENHAUER, W. C., Fusion-Fission (Hybrid) 

Systems, USAEC Report, BNWL-B-162, Pacific Northwest Laboratories, 

(Feb. 1972). 

[3] POWELL, F., Proposal for a Driven Thermonuclear Reactor, USAEC 

Report, LWS-24920 (revised), (October 1953). 

[4] BARRETT, L. G., A Fusion-Fission Reactor, KAPL, Report M-LOB-14, 

(June 1957). 

[5] LAWSON, J. D., THONEMANN, P. C., POOLE, M. J., and TAIT, J. H., 

Patent Specification 830, 255, United Kingdom Patent, complete 

specification filed January 15, 1958. 

[6] WEALE, J. W., G00DFELL0W, N., MCTAGGERT, M. H., and MOLLENDER, M. L., 

Measurements of the reaction rate distribution produced by a source 

of 14 MeV neutrons at the centre of a uranium metal pile, J. Nucl. 

Energy, A/B, 14, (1961) 91. 

[7] LIDSKY, L. M, Fission-fusion symbiosis: General considerations 

and a specific example, Nuclear Fusion Reactors Conf. (September 

1969) UKAEA, Culham Laboratory, Abingdon, Berks. 

[8] LEE, J. D., Subcritical fast fission blanket, Thermonuclear Reactor 

Memorandum 20, LRL (Nov. 1970). 

[9] LEONARD, B. R., Jr., Fusion-fission hybrid systems; a presentation 

prepared for the staff of the USAEC, Div. of Controlled Thermonuclear 

Research, BNWL-B-216 (July 1972). 

[10] WOLKENHAUER, W. C., Editor, The Pacific Northwest Laboratory Annual 

Controlled Thermonuclear Reactor Technology Report - 1971, 

BNWL-1604, (July 1971). 

[ П ] Neutron Cross Sections, BNL-325, Second Edition, Supp. 2, (Feb. 1965) 

[12] ENGLE, W. W., Jr, A User's Manual for ANISN, a One-Dimensional 

Discrete Ordinates Transport Code with Anisotropic Scattering, 

K-1693, (March 1967)


[13] SKEEN, D. R. and PAGE, L. J., THERMOS/BATTELLE: The Battelle 

Version of the THERMOS Code, BNWL-516, (September 1967). 

[14] CARTER, J. L., HRG-3: A Code for Calculating the Slowing Down 

Spectrum in the P-l or B-l Approximation, BNWL-1432 (June 1970). 

[15] DUANE, B. H., Time-Variant Isotopic Transmutation, GE-HL Program 

ALCHEMY, HW-80020, (December 1963) 

[16] ABDOR, M , and MAYNARD, C. W., Computational Techniques for Neutronics 

and Photonics Calculations for Fusion Reactor Blankets and Magnet 

Shields, FDM3, Nucl. Engng. Report, University of Wisconsin, Madison, 

Wisconsin, (June 1972) 

[17] HONECK, H. C., ENDF/B, Specifications for an Evaluated Nuclear 

Data File for Reactor Applications, BNWL-50066, USAEC (1966). 

[18] STEINER, D., The nuclear performance of fusion reactor blankets, 

Nucl Applications & Tech. Vol 9, (July 1970). 

[19] GLASSTONE, S., and SESONSKE, A., Nuclear Reactor Engineering, 

D. Van Nostrand Company, Inc., (1967). 

[20] GLASSTONE, S., and LOVBERG, R. H., Controlled Thermonuclear Reactions, 

D. Van Nostrand Company, Inc., Princeton, N. J., (1960). 

D IS C U S S IO N 

A .M . WEINBERG: How far sub-Lawson is the plasma? 

W .C . WOLKENHAUER: F o r the device considered by the authors, 

the design called fo r an пт of 3. 5 X 1013 and an ion temperature of 10 keV. 

Thus the device operates one decade below the Lawson condition and, in 

addition, represents a level of technology which will be achieved shortly. 

J. J. SCHMIDT: Do you see any need for nuclear data which are not 

available from present-day compilations and evaluations such as ENDF/B 

but knowledge of which is critical and decisive for the success of your 

present design studies or those for the near future, considering that the 

hybrid reactor concept (e. g. the fusion reactor) will probably not be 

realized and find practical application before, say, the year 2000? 

W .C . WOLKENHAUER: F irst of all, the available data, as shown in 

Fig. 5 of our paper, are not adequate for hybrid design. In a typical 

E N D F/B file, one finds a m axim al point at 14 MeV and quite a few points 

below 2 M eV. The important range from 14 MeV to 2 MeV is often 

approximated by a theoretical model. 

Current predictions state that a competitive fusion reactor m ay be 

available by the year 2000. However, the technology for building the 

hybrid, if not yet in hand, should be available shortly. If fission power 

proves to be cheaper than fusion power, the hybrid will allow for exploitation 

of fissile reserves at com parable power densities in subcritical arrays 

while retaining the short doubling tim es of fusion reactors.

I A E A - S M -1 7 0 /3 9 

NUCLEAR DATA REQUIREMENTS IN THE DESIGN 

OF THE BIFOLD NUCLEAR POWER SOURCE 

W .F. STUBBINS, R. A. WOLFE 

University of C incinnati, Cincinnati, Ohio 

and 

Mound Laboratory, Monsanto Research Corporation, 

M iam isburg, Ohio, 


Abstract 

N U C L E A R D A T A R E Q U IR E M E N TS IN T H E D ES IG N O F T H E BIFO LD N U C L E A R PO W ER SO URCE. 

T h e BIFO LD N u c le a r Power Source joins SN A P is o to p ic h eat source and S N A P reactor tech n olog y to 

provid e r e lia b le u n interruptable base power w hich is augm ented du ring periods o f high-dem and power by 

operation in a c r it ic a l reactor m ode. Plu to n iu m -238 is an a lp h a -em ittin g heat source m a te ria l w h ich has 

been shown to be able to form a s m a ll c r it ic a l system. T h e design o f the reactor aspects w ith p ro d u ctio n - 

grade ^ P u (80°]o ‘»Pu, le ^ o ^ P u , and 4°fo other p lu to n iu m isotopes) req uires estim ates o f three unm easured 

b a sic nu cle a r properties: one, the fast-neutron spectrum fro m the fissio n o f ^ P u ; two, the average num ber 

o f neutrons per fission as a fu n c tio n o f neutron energy groups; and three, the delayed-neutron fra c tio n in 

^ P u fissio n . Estim ates based upon fissio n system atics g iv e u n con firm ed v alu es o f param eters w h ich d ire c tly 

a ffe c t the c r it ic a l size and co n tro l param eters. BIFO LD is a sm a ll, c o m p a c t power source using heat pipes 

w ith th e rm o e le c tric or other energ y -co n v e rtin g com ponents operating in an isoth erm a l state at its base 

power o f 11 kW t to 200 kW t or m ore to m eet dem and power needs. T h e sp lit core o f BIFOLD p erm its a ll 

o p e ra tio n a l tests to be co m p leted e c o n o m ic a lly w ith zero-p o w er reactor o peration w h ic h avoids in duced 

ra d io a c tiv ity in com ponents and the b u ild - u p o f fissio n -fra g m e n t in ven tory. V a ria tio n s in and ranges o f fin a l 

design param eters ow ing to u n certa in tie s in nu cle a r data, plans for the resolu tion o f u n certa in tie s and the 

e c o n o m ic im p a c t o f in adequate nu cle a r data sources are presented. 

I n tr o d u c tio n 

The p o s s i b i l i t y o f the j o i n t use o f i s o t o p i c h eat so u rce 

m a te r ia l as a r e a c t o r fu e l was r e c o g n iz e d becau se o f m easurements 

made to a c c e s s the c r i t i c a l i t y hazards o f p r o c e s s in g , 

s t o r in g and u sin g P lu to n iu m -2 38, (1 , 2 ) . Thus, a new and 

v e r s a t i l e power s o u rce c o n ce p t a ro se d i r e c t l y in the p r o c e s s 

o f se e k in g new and r e l i a b l e n u c le a r d a ta . 

The co n c e p t i s c a l l e d BIFOLD s in c e i t p ro d u ce s power by 

two d i s t i n c t l y d i f f e r e n t means, r a d io a c t iv e decay and n u c le a r 

f i s s i o n , in th e same d e v ic e . BIFOLD is b e l ie v e d to be unique 

in the an n als o f en ergy sou ces becau se o f t h is fe a t u r e . I t is 

d e s c r ib e d e ls e w h e r e , (3 , 4, 5 ). 

In r e c e n t y e a rs le g io n s o f d iv e r s e a p p lic a t io n s have been 

p ro p o se d and are b ein g c o n s id e r e d f o r b o th i s o t o p i c and r e a c 

t o r Systems f o r N u clear A u x ilia r y Power (SNAP) in sp a c e , under 

the seas and on la n d . N early a l l the a p p lic a t io n s are c h a r a c 

t e r i z e d by s h o r t p e r io d s o f h igh power demands and exten ded 

p e r io d s o f q u ie s c e n t o p e r a t io n w ith a te n th or le s s o f the d e 

mand l e v e l . BIFOLD p r o v id e s an u n in te r r u p t a b le base power from 

r a d io a c t iv e decay ca p a b le o f m eetin g needs o f norm al o p e r a t io n 

51

52 STUBBINS and WOLFE 

and f u n c t io n s . The base power is augmented during high demand 

power p e r io d s by o p e r a t io n in a c r i t i c a l r e a c t o r mode as a 

f i s s i o n en ergy s o u r ce . 

In fa s h io n in g a p r a c t i c a l power so u rce from the c o n ce p t 

o f dual use o f i s o t o p i c heat so u rce m a t e r ia l, 23 8p iut on i umj 

o n ly proven te c h n o lo g y is used in as in n o v a tiv e manner as p o s 

s i b l e . BIFOLD is a com pact power so u rce w ith a number o f imp 

o r ta n t advantages and can match a w ide range o f m issio n r e 

q u irem en ts. The d e s ig n o f the p r o t o t y p ic BIFOLD power so u rce 

in v o lv e s therm al arrd n u c le a r c o n s id e r a t io n s which in t e r a c t 

s t r o n g ly to d eterm ine the p a ra m eters. For exam ple, the heat 

rem oval r a te e s t a b lis h e s the s i z e o f the h eat rem oval p e n e 

t r a t io n s w hich in tu rn govern th e c o re d e n s it y . The l a t t e r 

s e t s the c r i t i c a l s i z e and the power d e n s it y . The therm al 

c o n d u c t iv it y requ irem en ts o f the fu e l g overns the p o s s ib le fu e l 

form and c o n f ig u r a t io n s , and the s i z e and number o f h eat rem oval 

p e n e t r a t io n s . The i t e r a t i v e p r o c e s s fin d s the optimum d e s ig n 

f o r the power range to match the m is s io n . A s t r o n g ly govern in g 

param eter is the tem peratu re r e q u ir e d or d e s ir e d f o r the c o n v e r 

s io n system to p r o v id e e l e c t r i c a l en ergy from the therm al en erg y. 

G a s -c o n t r o lle d heat p ip e s (6) p r o v id e heat rem oval from the 

c o r e f o r b oth the q u ie s c e n t base power from r a d io a c t iv e decay 

and the augumented power from r e a c t o r o p e r a t io n . Heat p ip e s g iv e 

s e v e r a l im portan t advantages in the form and perform an ce o f 

BIFOLD. Heat p ip e s are most e f f e c t i v e in heat rem oval and r e 

q u ir e th e s m a lle s t h eat rem oval p e n e tr a t io n s which y i e l d the 

g r e a t e s t d e n s it y , and th u s, the s m a lle s t c o r e . They have two 

o th e r a d va n ta g es, one i s the absen ce o f the need f o r power to 

pump a h eat t r a n s f e r f l u i d . The pumping power in many SNAP 

d e v ic e s is the m ajor consumer o f the en ergy r e le a s e d . The 

secon d advantage is the p o s s i b i l i t y o f o p e r a tin g BIFOLD in an 

is o th e rm a l mode from the base power to i t s maximum demand power 

l e v e l . 

In a c c o rd w ith our c o n s e r v a t iv e p o s i t i o n o f u sin g proven 

te c h n o lo g y we ch ose t h e r m o e le c t r ic elem ents w ith m odest temp 

e r a tu r e s as the e l e c t r i c a l c o n v e r s io n d e v ic e s . A n alyses show 

th a t e l e c t r i c a l c o n v e r s io n system s such as Rankine and B rayton 

c y c le s are f u l l y a d a p ta b le to BIFOLD and th erm on ics are n o t e x 

c lu d e d . In the p r o to ty p e o f BIFOLD a d e s ig n c o n s t r a in t i s th at 

the f u e l Pu02 sh ou ld remain w e ll below i t s m e ltin g tem perature 

i f one or more h eat rem oval elem ents f a i l . This c o n s t r a in t was 

chosen to a v o id c o n s id e r a t io n s w hich m ight be used to c h a lle n g e 

the f e a s i b i l i t y o f BIFOLD. The p r o to ty p e o f BIFOLD is i l l u s 

t r a t e d by a wooden model in F igu re 1 and i t s c h a r a c t e r i s t i c s 

are ta b u la te d in T able I. 

N u clear D esign o f BIFOLD 

The n u c le a r f u e l o f BIFOLD is p r o d u c tio n grade P lu to n iu m -238 

w hich is 80% Pu, 16% 239Pu and 4% o th e r plu ton iu m is o t o p e s . 

The c o m p o s itio n i s g iv e n in T able I I . I t is im portan t to n ote 

th a t the p r o t o t y p ic d e s ig n i s a p p lic a b le to a f a s t r e a c t o r w ith 

le s s or no i s o t o p i c h eat s o u rce m a t e r ia l, 238pUj an

I A E A - S M -1 7 0 /3 9 53 

F I G . l . BIFOLD d e v ic e . 

d ered but th e f a s t r e a c t o r fe a t u r e s are unchanged. The u n in 

te r r u p t a b le base power can be s e t at any v a lu e le s s than the 

maximum f o r p r o d u c tio n grade 238pu ^y d il u t in g the i s o t o p i c 

m ixtu re o r , p r e f e r a b ly , by u sin g p r o d u c tio n grade 238pu some 

o f the fu e l elem ents and none in o th e r s . 

The n u c le a r d e s ig n in v o lv e s two a s p e c t s . One i s the change 

in the fu e l owing to the alpha decay o f ^38pu and the b u ild -u p 

o f 234uranium. This r e q u ir e s the c o n t in u a l rem oval o f heat and 

r e s u lt s in th e c o n t in u a l change in the c o m p o s itio n o f the f u e l . 

The h a l f l i f e o f ^ ° P u 87.8 * 0.02 y e a rs (7) and p rod u ces 

0.56 w atts p er gram o f h eat by alpha d eca y . I t has been w id e ly

5 4 STUBBINS and WOLFE 

T A B L E I. C H A R A C T E R IS T IC S O F TH E B IF O L D SOURCE 

G eneral P erform ance Param eters 

Power Range I s o t o p ic Mode 

F ast R e a cto r Mode 

A p p lic a t io n Environm ent Sp ace, T e r r e s t r i a l , 

Under Sea 

- L ife tim e 

- C on v ersion System 

- Energy T ra n sfe r 

System 

- N u clear Fuel 

5 to 25 years 

T h e rm o e le ctric 

Heat p ip e s 

Plutonium 

(801 238Pu) 

BIFOLD P ro to ty p e (R e fe r e n c e ) D esign Param eters 

- Fuel Form 

- C r i t i c a l Mass 

- N u clear Fuel Element 

- Thermal C o n d u c tiv ity 

- M e ltin g Tem perature 

o f Fuel 

- M eltin g Tem perature 

o f Tantalum C ladding 

- Maximum Tem perature in 

Fuel Element at 

9.5 Kwt 

100 Kwt 

150 Kwt 

2 00 Kwt 

10 Kwt 

0.6 Kwe 

Up to 150 - 

2 00 Kwt 

9 to 12 Kwe 

PMC 

P lutonia-M olybdenum Cermet (PMC) 

27 .5 Kg (Pu02) 

33 .4 Kg (PMCJ 

19 each 

H exagonal 

3 .8 cm H o r iz o n ta l Width 

16 cm in le n g th 

0.0 94 w atts/cm °C 

2400°C 

3000°C 

680°C 

1100°C 

1300°C 

1530°C

T A B L E I. (cont. 

- Heat P ip e : 

D iam eter 

F lu id 

O p eratin g 

Tem perature 

- R e f l e c t o r : 

- S iz e : 

M a te r ia l 

T h ick n ess 

C o n tro l 

D iam eter in c lu d in g 

R e f l e c t o r 

H eight in c lu d in g 


- A pproxim ate W eight 

T h e r m o e le c tr ic Elem ent: 

M a te ria l 

Type 

Tem perature 

Hot J u n ctio n 

Cold J u n ctio n 

IA E A -S M -1 70/3 9 55 

1 .2 7 Cm 

P otassium or sodium (K or Na) 

640°C 

238u or W 

9.1 Cm 

R o ta tin g Drum 

38 Cm 

36 Cm 

400 Kg 

Lead T e llu r id e (PbTe) 

T ubular D esign 

640°C 

300°C 

u sed as a h eat so u rce m a te r ia l becau se o f i t s r e l a t i v e l y h igh 

s p e c i f i c heat and i t s q u it e low r a d ia t io n o f gammas. A gram o f 

238pu p rod u ces a gamma d ose r a te o f 0.6 4 Rads p er hour a t 1 

m eter in a i r . The spontan eous f i s s i o n h a l f l i f e o f 238pu 

(4 .7 7 * 0 .1 4 ) x 10*0 y e a rs (8) and w ith alm ost th re e n eu tron s 

p er f i s s i o n y i e l d s 3 x 10^ n eu tron s p er secon d p er gram. Add 

i t i o n a l n eu tron s come from the a lp h a -n e u tro n r e a c t io n w ith 

Oxygen-18 when plu ton iu m i s in the form o f an o x id e , ( 9 ) . 

P r io r to o p e r a t io n in th e r e a c t o r mode BIFOLD has b oth gamma 

and n eu tron r a d ia t io n i n t e n s i t i e s le s s than 1 0 '° as a r e a c t o r 

p ro d u cin g the same base pow er. Between in te r m it te n t r e a c t o r 

o p e r a t io n a t demand power BIFOLD has s i g n i f i c a n t l y low er r a d ia 

t i o n than a r e a c t o r p r o v id in g the base pow er. 

The change in the f u e l c o m p o s itio n by the alpha decay o f 

238pu does n ot red u ce the e x ce s s r e a c t i v i t y as the h a lf l i f e o f 

238Pu. T h is i s so beca u se the d a u g h ter, 234ц has a r e a so n a b le 

f a s t f i s s i o n c r o s s s e c t i o n , (1 0 ). The change in t o t a l f i s s i l e 

atoms is shown in F igu re 2. The e f f e c t s o f f u e l burn-up at a 

co n s ta n t power l e v e l o f 100 kwt is in c lu d e d .

56 STÜBBINS and WOLFE 

T A B L E II. T Y P IC A L P u 0 2 F U E L CO M PO SITIO N USED IN H E A T SOURCES 

1. T y p ic a l C o m p o sitio n , Ри02 

a. Oxygen 1 1 .8 w t. % 

b. P lutonium 88 .2 w t. \ 

C o n ce n tra tio n (Wt. %) 

0.00012 

80.2 

15 .9 

3.022 

0. 643 

0.132 

C o n ce n tra tio n (Wt. %) 

0. 0033 

0.130 

0 .1 40 in c r e a s e s at the 

r a te o f decay o f 

238Pu 

The t o t a l o f o th e r i s o t o p i c im p u r it ie s in c lu d in g 23lP a , 

232Th, 233U, 235U, 236U, and 227Ac does n ot ex ceed 1 w t.% o f 

the f u e l . 

I s o to p e 

236pu 

238pu 

239pu 

240pu 

241pu 

242Pu 

c . A c t in id e Im p u ritie s 

24lAm 

2 37¡v¡p 

234u 

The secon d n u c le a r a s p e c t is th a t o f f a s t r e a c t o r d e s ig n . 

The c o n fir m a tio n th a t 238pu c o u ld form a f a s t c r i t i c a l system 

was o b ta in e d by r e p la c in g an egu a l amount o f 239pu щ grams 

o f 23^Pu in a s p h e r ic a l m etal 23^Pu c r i t i c a l r e a c t o r , ( 1 ) . The 

c r i t i c a l i t y w orth o f 238Pu i s n e a r ly the same as 23” Pu in the 

n eu tron spectrum c h a r a c t e r i s t i c o f the m etal 23^Pu r e a c t o r . With 

a t h ic k heavy m etal r e f l e c t o r the c r i t i c a l mass o f a sp here o f 

m etal 23°Pu i s e stim a te d to be as l i t t l e as 7.8 k ilo g r a m s , (11, 

12, 1 3 ), and i t may be even l e s s . 

The f i s s i o n c r o s s s e c t i o n f o r 238pu was o b ta in e d the P e r 

simmon n u c le a r t e s t (14) and in e a r l i e r measurements (15) from 

a few eV to 3 MeV. The therm al f i s s i o n c r o s s s e c t i o n is 18 

barns and the therm al ca p tu re c r o s s s e c t i o n is 489 barns (1 6 ).

IA E A -S M -1 7 0/3 9 57 

TIME OF REACTOR OPERATION (YEARS) 

F IG .2 . C h a n g e in fu e l c o m p o s itio n w ith in BIFOLD c o r e du rin g r e a c to r m o d e o p e r a tio n . 

The la r g e therm al c a p t u r e - t o - f i s s i o n r a t i o makes 238Pu s a fe 

from a c r i t i c a l i t y sta n d p o in t in a f u l l y m oderated n eu tron f lu x . 

S e v e ra l n eu tron m u lt ip lic a t io n exp erim en ts w ith heat so u rce 

elem ents su p p ort t h is c o n c lu s io n (1 7 , 1 8 ). The ca p tu re and 

s c a t t e r in g c r o s s s e c t i o n s f o r 238 pu have n ot been s y s t e m a t ic a lly 

r e p o r t e d . The b e s t data are the r e s u lt s o f c a lc u l a t i o n s based on 

the o p t i c a l model (1 9 ). 

The absen ce o f data f o r 238pu n e ce s s a r y to make 

some sim p le , but v e ry q u e s t io n a b le , assu m p tion s. One assumes 

th a t the unknown c r o s s s e c t io n s are in m agnitude and b e h a v io r 

s im ila r to th o se o f r e la t e d near n u c l e i . With the e x c e p tio n 

o f f i s s i o n c r o s s s e c t io n s the b e h a v io r o f e l a s t i c , i n e l a s t i c 

and ca p tu re c r o s s s e c t io n s is p r o b a b ly r e a so n a b ly p r e d ic t a b le 

f o r n eu tron s above a few hundred k i l o v o l t s and are g e n e r a lly 

s m a ll. 

The absen ce o f r e l i a b l e n u c le a r d a ta f o r the p r i n c i p l e 

is o t o p e in BIFOLD and equ al u n c e r t a in t ie s f o r o th e r is o t o p e s 

demand a p ra g m a tic d e s ig n te c h n iq u e . Thus, f o r the p r o to ty p e 

o f BIFOLD we use a th re e group r e a c t o r c a lc u l a t i o n and the 

h om og en ization o f the c o r e . The 3 -e n e rg y groups averaged in 

a "h a rd " n eu tron spectrum and the c r o s s s e c t io n s o f the p r i n 

c i p l e is o t o p e s taken from a LASL ta b u la t io n f o r 238Pu (20) 

and ANL-5800 (21) f o r the o th e r c o n s t it u e n t s o f the c o re are 

shown in T able I I I . The n eu tron spectrum a r is in g in the f a s t 

f i s s i o n o f p r o d u c tio n grade 238Pu, is n ot known» We assume 

th a t the spectrum o f n eu tron s from f i s s i o n o f 239pu id e n t i c a l 

to th a t f o r p r o d u c tio n grade 23°Pu. As i l l u s t r a t e d below 

d i f f e r e n t n eu tron s p e c t r a s e r io u s l y a f f e c t the c r i t i c a l mass.

( 

TABLE III. 3-GROUP CROSS-SECTIONAL SET FOR A FAST-NEU TRON SPECTRUM AND USED FOR THE 

CRITICALITY CALCULATIONS OF BIFOLD SOURCE 

ISOTOPE 

ENERGY 

GROUP* 

( i ) 

V 

° f 

va_£ о с 0 t r 0 i-*-i + l a i-*-i+2 ° i - i 

238pu 1 3.58 2.47 8.84 0.062 4.38 0.145 0.097 1.61 

2 3. 01 2.0 9 6.2 9 0. 210 6.18 0. 280 0.122 3.4 5 

3 2. 93 0.98 2.87 0.272 10 .30 0. 051 0 9.0 0 

239Pu 

O ' 

О 

1 3.1 0 1.9 5 6.0 5 0 .1 0 4 .6 0.45 0.45 ------------ 

2 2.98 1.7 5 5.21 0.12 6.0 0.5 0 ------------ ------------ 

3 2.91 1 .8 0 5.24 0.35 10 .0 ------------ ------------ ------------ 

1 _ _ _ _ _ __ _________ 0.020 1.2 5 0.303 _________ 0. 927 

2 ------------ ------------ — ------------ 3.52 0. 578 ------------ 2.925 

3 ------------ ------------ — ------------ 3. 59 0.344 ------------ 3. 284 

Fe 1 _________ _________ _________ 0.005 ‘ 2.0 0 0.600 0.1 00 ------------ 

2 ------------ ------------ — 0.0 06 2.13 0.220 ------------ ------------ 

3 ------------ ------------ — 0. 006 3-24 ------------ ------------ ------------ 

*The Energy Spectrum per group was th a t e s t a b lis h e d f o r the LASL c r o s s - s e c t i o n a l se t in ANL- 

5800. 

ENERGY NEUTRON 

RANGE SPECTUM 

i (Mev)____________ (x) 

1 » - 1 . 3 5 0.575 

2 1 .3 5 - 0 .4 0.326 

3 0.4 -0 0.099 

СП 

00 

STUBBINS and WOLFE

I A E A - S M -1 7 0 /3 9 59 

N e v e r t h e le s s , we ju d g e th a t th e re is n ot g re a t u n c e r t a in ty 

in the n eu tron spectrum so i t is n ot a m ajor so u rce o f unc 

e r t a in t y in our c r i t i c a l i t y c a l c u l a t i o n s but our e x p e r ie n c e 

c a u tio n s us a g a in s t d is c o u n tin g i t . 

As a ch eck o f our th r e e -g r o u p f a s t r e a c t o r c a l c u l a t i o n s the 

c r i t i c a l m asses f o r both a bare c o re and a r e f l e c t e d c o r e were 

determ in ed w ith adequate c r o s s s e c t i o n s data and were w ith in 

f i v e p er ce n t o f the e x p e r im e n ta lly measured c r i t i c a l masses 

o f J e z e b e l (21) and Popsy ( 2 1 ) . two sm all f a s t r e a c t o r s . Conf 

ig u r a t io n s a p p lic a b le to BIFOLD w ith d i f f e r e n t arrangem ents o f 

h eat rem oval p e n e tr a t io n s and r e f l e c t o r s were a n alyzed to 

e v a lu a te the c r i t i c a l m asses. A summary is p r e se n te d in Table 

IV. 

The c r i t i c a l mass is the g o v e rn in g fe a t u r e in s e l e c t in g 

p o s s i b l e c o n f ig u r a t io n s f o r a p r a c t i c a l power so u rce s in c e the 

f u e l c o s t s are so g re a t f o r the man-made m a t e r ia ls . The s e l e c 

t i o n o f p r o d u c tio n grade 238pu as an 0x id e in molybdenum as a 

cerm et does n ot g iv e the s m a lle s t c r i t i c a l mass but i t a llo w s 

the demand power maximum to be about tw enty tim es the base 

power l e v e l . The f a c t o r o f tw enty is b e l ie v e d to be s i g n i f i c a n t 

in th a t i t g iv e s h ig h e r power than any p ro p o se d i s o t o p i c heat 

s o u rce and m atches a la r g e number o f p o s t u la t e d power needs f o r 

sp ace and undersea a p p lic a t io n s . The use o f the cerm et PMC, 

P lutonia-M olybdenum Cermet, is d ic t a t e d by th e therm al c o n 

d u c t i v i t y n e cessa ry , to meet the c r it é r iu m th a t the f u e l m e ltin g 

tem peratu re would n o t be reach ed i f one or more o f the h eat r e 

moval elem ents f a i l . A sm a lle r c o r e can be a c h ie v e d w ith 

plu ton iu m o x id e but th e maximum power is lim it e d to 60 k ilo w a t ts 

th erm al. A c o r e to p r o v id e a maximum o f a h a lf o f a megawatt 

as th e demand power is about 40 p er cen t la r g e r than the p r o t o 

type o f BIFOLD s p e c i f i e d in T able I. 

The s e l e c t i o n o f the tem peratu re at w hich th e h eat energy 

o f BIFOLD i s u sed , in our ca se the hot s id e o f the t h e r m o e le c t 

r i c c o n v e r t e r at 650°K, e s t a b lis h e s the tem peratu re a t w hich 

th e th erm al en ergy i s a c c e p te d by th e gas - c o n t r o l l e d h eat p ip e s . 

Heat p ip e s have th e advantage th a t th e h eat en ergy is t r a n s 

fe r r e d w ith a v e ry sm all therm al g r a d ie n t , so th e tem peratu re 

in the c o r e is n e a r ly the same as the h ot s id e o f the therm oe 

l e c t r i c ele m e n ts. The o p e r a t io n at h ig h e r power can be had 

w ith the same tem peratu re lim it s by in c r e a s in g the d iam eter o f 

th e h eat p ip e s t o p r o v id e f o r more h eat rem oval. The c o r e p a ra 

m eters are a d ju s te d to a ccou n t f o r th e g r e a te r p e n e tr a t io n s and 

an in c r e a s e in th e s i z e and c r i t i c a l mass o c c u r s . 

The i t e r a t i v e r e a c t o r p h y s ic s c a l c u l a t i o n r e s u lt s in a 

c r i t i c a l c o n f ig u r a t io n w hich i s s p e c i f i e d by a term c a lle d the 

" b u c k lin g " . The b u c k lin g sim u lta n e o u sly c h a r a c t e r iz e s the comp 

o s i t i o n o f th e c o r e in term s o f n u c le a r param eters and i t s 

g e o m e tr ic a l s i z e . The c o n s e r v a t io n o f n eu tron s is enhanced by 

the use o f a heavy m etal ja c k e t c o m p le te ly su rrou n d in g th e c o r e . 

T h is ja c k e t , c a l l e d the r e f l e c t o r , re tu rn s a p o r t io n o f the 

n eu tron s le a k in g away from a c o r e back to i t by n eu tron s s c a t 

t e r in g . We have used a r e f l e c t o r th ic k n e s s to maxim ize th e r e 

tu rn o f n eu tron s and m inim ized the c o r e s i z e and th e f u e l i n 

v e n to r y . The r e f l e c t o r th ic k n e s s s p e c i f i e d in T ab le I i s th a t

TABLE IV. CRITICALITY REQUIREMENTS OF DIFFERENT FORMS OF THE BIFOLD NUCLEAR POWER SOURCE 

Core Fuel Form 

C o n fig u r a tio n 

S o lid Sphere 

S o l id Sphere 

239 Pu M etal 

238 PuO^ 

R igh t C y lin d e r 238pug, 

C y lin d e r ic a l Iron 

B lock With 1 -in c h 238puÛ2 

D iam eter Fuel Pins 

C y lin d e r ic a l Iron 

B lock With % -in ch 238pug„ 

D iam eter Fuel Pins 

C r i t i c a l 

B u cklin g 

0.160 c m " 2 

0.0918 

0.0918 

0.0134 

0.0266 

Bare C r i t i c a l C r i t i c a l Mass 

Mass o f PuO? With I n f i n i t e 


15 .4 kg 

20.3 

23.2 

19 0.0 

93. 0 

5.45 kg 

9.15 

1 5 .3 (R a d ia l 

R e f l e c t o r Only) 

Core Dim ensions 

Radius H eight 

4.3 8 cm 

5.94 

5.4 1 3 .4 cm 

H exagonal Fuel 

Elements With 


238PuO? 

'2 

0.0660 31.8 17 .5 7.1 3 12.96 

H exagonal Fuel Pu02 

Elements With (801 238pu ) 0.0650 32 .4 19 .4 7.28 13 .26 

R e f l e c t o r (20% 239pu) 

H exagonal Fuel Pu02 as PMC 

Elements With (82 .5 1 Pu02) 0.0590 45 .0 27.5 8 .8 4 15.92 

R e f l e c t o r (17.5% Mo ) 

(80% 238pu ) 

(20% 239pu ) 

o> 

о 

STUBBINS and WOLFE

I A E A - S M -1 7 0 /3 9 61 

o f an i n f i n i t e r e f l e c t o r , i . e . , one f o r w hich an a d d it io n a l 

th ic k n e s s would n ot s i g n i f i c a n t l y im prove the f r a c t i o n o f n eu 

tro n s re tu rn e d to the c o r e . 

T ra n sfo rm a tio n from base power to more power by th e a d d it io n 

o f f i s s i o n power is a cco m p lish e d by changing the r e f l e c t o r p r o 

p e r t i e s by the r o t a t i o n o r in s e r t io n o f the c o n t r o l elem ents 

shown in F ig u re 1. The system is s u b c r i t i c a l w ith th e h ig h e s t 

lo s s r a te o f n eu tron s and becomes c r i t i c a l when enough n eu tron s 

are co n s e rv e d to s u s ta in the n eu tron ch a in r e a c t io n . The c o n 

t r o l elem ents a c t l i k e s h u tte r s f o r n eu tron s and are one o f the 

ways o f e f f e c t i v e l y c o n t r o l l i n g a f a s t r e a c t o r w hich i s n ot 

r e a d il y p o is o n e d ,a s are therm al r e a c to r s , w ith m a te r ia ls , such as 

cadm ium ,which a b sorb slow n e u tro n s. Removal o f f u e l or the 

s e p a r a tio n o f the c o r e p a r ts are o th e r means o f c o n t r o l l i n g 

c r i t i c a l i t y . 

V a r ia t io n s in BIFOLD Owing to U n certa in N u clear Data 

The la c k o f data and u n c e r t a in t ie s in data were e n cou n tered 

in th e d e s ig n o f the p r o t o t y p ic BIFOLD and r e q u ir e d e stim a te s 

o f some q u a n t it ie s and the judgem ent o f th e b e s t data to be 

u sed in o t h e r s . In th e ca se s where data u n c e r t a in t ie s e x i s t we 

found i t im p ortan t t o e v a lu a te th e r e s u lt in g u n c e r t a in t ie s in 

the param eters o f BIFOLD. 

Im portant u n c e r ta in param eters are the c r o s s s e c t io n s f o r 

f i s s i o n , ca p tu re and e l a s t i c and i n e l a s t i c s c a t t e r in g ; the number 

o f n eu tron s p er f i s s i o n as a fu n c t io n on n eu tron e n erg y; and the 

f r a c t i o n o f d e la y e d n eu tron s p er f i s s i o n . The f i s s i o n n eutron 

en ergy spectrum f o r the p r i n c i p l e is o t o p e in BIFOLD, 238d,, 

na* 

assumed to be i d e n t i c a l to th a t f o r 2Pu and in the absence 

o f any data the same r e l a t i o n was taken f o r the d e la y e d n eu tron 

f r a c t i o n . 

We now o u t lin e the u n c e r t a in t ie s w hich we r e c o g n iz e as 

a r is in g from the p r e s e n t s t a t e on n u c le a r d a ta . As an i n t r o 

d u c tio n we w ish to p o in t to the i n i t i a l measurements w hich gave 

r i s e to the BIFOLD c o n c e p t , , £ 1 , 2 ) . In p la n n in g f o r the p r o c e s s in g 

o f k ilo g ra m q u a n t it ie s o f Pu an assessm ent o f c r i t i c a l i t y 

c o n t r o l was made. The lo r e th a t e v en -ev en heavy n u c le i would n ot 

have therm al f i s s i o n c r o s s s e c t i o n s was w e ll e s t a b lis h e d and i t 

was e a r ly assumed th a t 238pu w ould be v e ry much lik e 23°U. 

However, c a l c u l a t i o n s based on 238jjra n i um c r o s s s e c t io n s were 

used to gu id e p la n n in g even f o r n on -th erm a l system s in absen ce 

o f d a ta . But tb g r e was o th e r in fo rm a tio n about the e x p e cte d 

p r o p e r t ie s o f Pu and a t t e n t io n was brou gh t to i t . The le s s 

d i r e c t data were the s y s te m a tic s o f f i s s i o n and p a r t i c u l a r l y the 

dependence o f th e n eu tron in d u ced f i s s i o n c r o s s s e c t i o n at 3 MeV 

w hich as a fu n c t io n o f the param eter Z ^ '^ /A in c r e a s e s n e a r ly 

l i n e a r l y (1 0 ). Thus the f a s t f i s s i o n c r o s s s e c t io n s 

is la r g e r at 3 .0 MeV than 23^Pu and much la r g e r than th a t o f 23°U. 

Z is the atom ic number and A is the mass number o f the heavy 

is o t o p e . Subsequent f i s s i o n c r o s s s e c t i o n measurements ( 1 ,1 4 ,1 5 ) 

v e r i f i e d the g r e a te r c r o s s s e c t i o n o f 2 3 8 P u . i t is s t i l l 

n e ce s s a r y to use le s s d i r e c t pdata to p r o ce e d w ith n u c le a r d e 

sig n s o f a l l but 235U and Pu system s.


A. E f f e c t o f x )(E n ) 

The s in g le n u c le a r param eter th a t most in flu e n c e s the 

e stim a te s o f the c r i t i c a l mass is the num ber_of n eu tron s r e 

le a s e d per f i s s i o n . This q u a n t it y , c a l l e d xD ( n u - b a r ) , depends 

upon the en ergy o f th e n eu tron ca u sin g f i s s i o n and has been o f 

im portan ce to us in a n a ly se s f o r c r i t i c a l i t y c o n t r o l o f p r o 

c e s s i n g , h a n d lin g , s t o r in g and_using 238pu _ j n t he absen ce 

o f r e l i a b l e data we e stim a te d z ? ( E n ) f o r therm al n eu tron s and 

as a fu n c t io n o f the n eu tron e n erg y. We b e l ie v e th a t (E) is 

la r g e r than the v a ju e s in common use and we were en cou raged by 

a measurement o f Î5 (th erm al) (22) w hich matched our p r e d i c t io n . 

о X R 

The q u a n t it y , XJ , f o r Pu has been r e p o r te d in two se p a 

r a te measurements f o r n eu tron s from sp ontaneous f i s s i o n (23, 

2 4 ). I t s dependence on n eu tron en ergy has n ot been r e p o r te d 

but two e stim a te s have been made and the average o f them is in 

common u se . They are 

= 2.8 8 + 0.097 En R e fe re n ce (19) 

z ) = 2.7 5 + 0.118 En R e fe re n ce (25) 

and t h e ir average i s z ) = 2.81 + 0.107 E . E is the n eutron 

en ergy in MeV. n 

In se e k in g the b e s t v a lu e s o f z^ C En ) we c o n s id e r e d r e p o r t s 

o f f i s s i o n s y s te m a tic s r e la t e d to n u c le a r tem perature and e x 

c i t a t i o n o f f i s s i o n fragm en ts in c lu d in g a number which r e la t e 

the n eu tron r e le a s e w ith the f i s s i o n fragm ent mass d i s t r i b u t i o n 

( 2 6 ,2 7 ,2 8 ) . Our c a lc u l a t i o n s f o r 238pu f rom the a n a ly s is o f 

Bondarenko, e t a l . (2 6) in d ic a t e d a h ig h e r v a lu e f o r therm al 

f i s s i o n and a s te e p e r s lo p e than seen in measurements o f o th e r 

is o t o p e s . We su g g e st 

Z> = 2.895 + 0 .1 29 Ед 

as a b e t t e r e stim a te f o r 238pu f a st n eu tron f i s s i o n (2 9 ). 

Our c a lc u la t e d TÙ (th erm al) = 2.8 95 is w ith in two p er cen t 

o f the r e p o r te d measurement (2 2 ). On the b a s is o f t h is a g r e e 

ment we have u sed our (ER) in our r e a c t o r a n a ly s is o f BIFOLD, 

and, in d e e d , we e x p e ct ex p e rim e n ta l c o n fir m a tio n when the 

measurements are made. F igu re 3 shows our c a l c u l a t i o n o f 238pu 

and the r e p o r t e d (En ) f o r 233U, 235ц an(j 239pu< 

The im portan ce o f x ) (En) in d eterm in in g the c r i t i c a l s iz e 

is i l l u s t r a t e d by T able V. T able V shows the c r i t i c a l mass 

f o r bare sp h eres o f p r o d u c tio n grade 238pu as an o x id e c a lc u la t e d 

u sin g -¿> (En ) o f th re e d i f f e r e n t d e p e n d e n ce s, A )_ou r c a l c u l a t i o n , 

b) the £5 (En ) in g e n e r a l use f o r 238pUj and C) z> (E^) f o r 239pu> 

(2 2 ). The r e l a t i o n betw een b u c k lin g , b 2, and the dim ension s 

f o r a bare c y l i n d r i c a l r e a c t o r is 

B2 = Æ ) 2 + (I--*.0-5.)2 H is the c y lin d e r 

H R h e ig h t and R i t s 

r a d i u s .

IA E A -S M -1 7 0 /3 9 63 

INCIDENT NEUTRON ENERGY (E„) in MeV 

F I G .3 . A v e r a g e n eu tron n u m b e r, v (E n ) . a s a fu n c tio n o f e n e r g y o f th e n e u tro n -in d u c in g fission fo r 238Pu. 

( T h e p o in ts sh ow n o n th e ^ P u c u r v e are based o n c a lc u la t io n s and n o t e x p e r im e n t a l.) 

A sm all d e c re a s e in b u c k lin g in c r e a s e s the dim ension s which add 

a s h e ll o f m a te r ia l in a manner to most e f f e c t i v e l y in c r e a s e 

th e c r i t i c a l mass. 

B_. E f f e c t o f N eutron Spectrum 

The en ergy spectrum o f prompt n eu tron s r e le a s e d in the 

f i s s i o n o f ¿ 38pu has n o t b een r e p o r t e d . U s u a lly the spectrum 

o f 239pu is u sed and p r o b a b ly is n o t f a r from the spectrum to 

be found f o r 23°Pu but in the ab sen ce o f d a ta the knowledge o f 

the e f f e c t o f spectrum is im p o rta n t. I n i t i a l l y c a lc u l a t i o n s 

were made o f the e f f e c t o f d i f f e r e n t s p e c t r a in s t u d ie s f o r the 

c r i t i c a l i t y c o n t r o l o f 238pu by Monte C a rlo c a l c u l a t i o n s (1 3 ).


T A B L E V . E F F E C T OF v (En) ON C R IT IC A L MASS 

A- t ) (E ) = 2. 895 + 0.1 29 En 

—*— n n 

B_. X> (En ) = 2.8 10 + 0.107 En 

— ^ n) = 2-880 + 0.110 En 

Neutron Energy Spectrum 

Group Range F r a c tio n 

(MeV) 

1 ° e - 1 .3 5 0.575 

2 1 .3 5 - 0 .4 0.326 

3 0 . 4 - 0 0.099 

Our Estim ate f o r 2^8pu 

In G eneral Use f o r 

238pu 

R é f. (2 1) f o r 239Pu 

Case A Case В Case 

v(E n ) 

3.5 8 3. 03 3.10 

3. 01 2.91 2.98 

2. 93 2.83 2.91 

(B u ck lin g) = B2 

0.0488 c m '2 0.0424 0.441 

Bare C r i t i c a l Mass 

4 5 .0 Kg 6 1 .0 56.3 

In o r d e r to e v a lu a te the e f f e c t o f u n c e r t a in t ie s in 238Pu 

n eu tron s p e c t r a in the param eters o f BIFOLD we used th re e d i f 

fe r e n t s p e c t r a in the c a l c u l a t i o n o f the c r i t i c a l mass. The 

s p e c tr a are shown in T able VI and are seen to be the 2^9pu 

spectrum in use (21) and two m o d if ic a t io n s o f i t w hich s h i f t 

the spectrum t o low er e n e r g ie s . This s h i f t is seen in Table 

VI to in c r e a s e the c r i t i c a l mass and is e x p e cte d f o r a p r e 

d om in a te ly 238Pu c o r e s in c e the f i s s i o n c r o s s s e c t io n becomes 

sm a lle r as the n eu tron en ergy d e c r e a s e s and the ca p tu re c r o s s 

s e c t i o n in c r e a s e s . We do n ot b e l ie v e th a t the s p e c t r a we used 

in our e a r l i e r Monte C arlo c a lc u l a t i o n s and a ls o f o r t h is study 

c o rr e sp o n d s to 23°Pu but were chosen to p r o v id e an e v a lu a t io n o f 

the e f f e c t . 

In a r e c e n t ly com p leted measurement o f the n eu tron energy 

spectrum in 2^9pu p h o t o f i s s i o n near th r e s h o ld (30) we found 

th a t th e n eu tron en ergy spectrum co rre sp o n d s to th a t o f therm al 

n eu tron f i s s i o n o f 23” pu . We e x p e ct to make s im ila r m easurements 

o f 238pu and through them we w i l l g a in some in s ig h t in to 

i t s spectrum w hich can be a p p lie d to the s p e c i f i c a t i o n o f BIFOLD.

I A E A - S M -1 7 0 /3 9 65 

T A B L E VI. E F F E C T O F N E U T R O N E N E R G Y S P E C T R A O N T H E C R I T I C A L 

M A S S O F B I F O L D 

Neutron 

Energy 

Group 

Energy 

Range 

Fraction of Neutrons in Group (a) 

^ (b) 

2CA 2LB Ж 

OO - 1 . 3 5 MeV 0.575 0. 538 0.402 

L.35 - 0.4 0.326 0. 333 0.430 

3.4 - 0 0.099 0.129 0.168 

Buckling 0.0488 0.0471 0. 0462 

Critical Mass 

of PuO-,(c) 45.0 kg 50.0 51.8 

Per Cent 

Change 11.1 15.1 

(a) The neutron fractions and do not correspond to 

238pu w hich has not been reported. They were only cnosento 

evaluate spectral effects. 

239 

(b) This column corresponds to Pu neutron spectrum in use 

(21). 

(c) The critical mass is for a non-reflected minimum right 

circular cylindrical BIFOLD core. 

C_. Delayed Neutron Fraction 

Another unknown quantity which is fundamental for nuclear 

design is the fraction of neutrons released in fission which are 

delayed. The control of a critical reactor depends on the time 

interval for all the neutrons of one generation to be replaced. 

The small number of neutrons are delayed because they are released 

coincident with the beta decay of a neutron rich fission 

fragment. The neutrons follow the radioactive half life of the 

fragment. The delayed neutrons make the effective generation 

time several seconds rather than a few microseconds or less. 

The control of a fast reactor is governed by the generation time 

in a crucial way. 

The delayed neutron fraction is called beta by reactor 

physicists. For fast and thermal neutron fission of 239pu the 

delayed neutron fraction is ß = 0.0026 - 0.0002 (21) and the


average time of retardation is 1 4 .4 seconds [ 3 1 ) . We use the 

data for 239pu the absence of data for 238pu an(j 234ц an¿ 

recognize it as a possibly serious assumption. 

Fabrication and Testing 

The BIFOLD source is a compact fast reactor as well as an 

isotopic heat source. For small compact power sources with the 

energy conversion devices coupled to the core by heat pipes 

the entire operational testing and system component verification 

for reactor operation can be done with auxilliary heating 

elements rather than reactor operation. For base power 

all tests are completed with isotopic heat. Analysis of the 

advantage of compact nuclear space power systems by Breitwieser 

(3 2 ) is applicable to BIFOLD. 

By splitting the core into halves the reactor aspects of 

BIFOLD can be completely investigated with a split-table critical 

facility. Thus, the induced radioactivity and fission 

fragment buildup from reactor operation is eliminated since all 

reactor tests can be at zero power. A second advantage of a 

split core is the redundancy in BIFOLD as a isotopic heat source 

for use. Splitting also provides for separation for storage, 

shipment and handling prior to assembly for mission purposes 

requiring demand power levels. The criticality control of 

fabrication and handling are minimized by parts which are so 

much smaller than the critical configuration. A third advantage 

is the possibility of using the disassembly of BIFOLD into 

its halves as an emergency reactor shut-down (scram) precedure. 

The advantages of BIFOLD with a split core and external 

electrical conversion devices which permits all nuclear and 

non-nuclear testing to be done without the complications of 

reactor power operation are most clearly realized when the cost 

of a power system development program is considered. The 

modular fabrication of fuel elements and heat pipes contributes 

to the economy. The importance of reliable nuclear data is 

clearly shown by the cost of design latitudes required to a c 

comodate the ranges of parameters of BIFOLD that arise in data 

uncertainties at this time. 

It is clear from Table V and Table VI that a significant 

misjudgement in critical size can result from the absence of 

reliable nuclear data. Were such to occur the redesign of the 

nuclear power system would yield different fuel element size 

and loading and general dimensional changes of the entire unit. 

The economic advantage that we believe BIFOLD has over other 

energy sources for applications with time varying power demands 

would be greatly diminished if refabrication would be required. 

Plans for the Resolution of Nuclear Data Uncertainties 

A. 0 ( E n ) 

The measurement of "0(E) is planned by using time-of- 

flight neutrons to establish En and detecting the associated 

fission event and one or more fission neutrons in coincidence 

with the fission. A statistical analysis of the single, double

IAEA-SM-17 0/39 67 

and triple neutron coincidences can yield the average number of 

neutrons released per fission by the energetic neutron. A 

neutron fission measurement at the single high energy, for 

instance E = 2.4 MeV with neutrons from the 2H ( 2H,n) He reaction 

or En = 14.0 MeV from Зн(2н,п)4не, will provide a point 

to be associated with the thermal neutron measurement (22) to 

remove considerable uncertainty in x ) (En ) for the isotopes of 

interest. 

B. Neutron Energy Spectrum 

The measurement of the energy spectrum of neutrons released 

in fission can most readily be done by continuing the photofission 

measurements completed for 239pu (30) to 238pu an(j 

2 3 4 ^ and, indeed, this is planned. The assumption that the 

spectrum found corresponds to that for neutron induced fission 

of the isotope will introduce an uncertainty and the dependence 

of the spectrum on the energy of the fast neutrons inducing 

fission will not be resolved in photofission studies. 

C_. Delayed Neutrons 

The fraction of neutrons which are delayed and the effective 

half life can only be measured when a critical assembly 

of 238pu is formed. This will be an early quantity sought from 

the first reactor tests of BIFOLD. However, a study of the 

fission fragments of the principle isotope can allow an important 

estimate of beta by identifying the precursors of the 

delayed neutrons. The radio chemical study of 238pu fission 

fragments will be useful. 

D_. Cross Sections 

The measurements of capture, elastic and inelastic scattering 

cross sections are far more difficult than the measurement 

of the fission cross section which has such a distinctive 

signature. Careful experiments will have to seek reliable data. 

Conclusions and Summary 

BIFOLD is a compact fast reactor which matches time-de- 

pendent energy needs with the reliability of an isotopic heat 

source for base power needs. Considerable uncertainties in the 

cross sections and other nuclear data exist and strongly influence 

estimates of BIFOLD's size and cost. BIFOLD has been 

studied by combining nuclear data of the principal isotopes 

with the systematics of the physics of fission to yield, as far 

as possible, consistent data for design. 

A continuing program of nuclear data acquisition for 238Pu 

and 234u is required. The data acquisition must embrace m i c r o 

scopic measurements to give cross sections and macroscopic 

measurements with critical assemblies to yield delayed neutron 

fractions and similar reactor physics quantities. The pursuit 

of the BIFOLD concept must include data acquisition and, indeed, 

BIFOLD itself can contribute considerable data.


The economics of special purpose power systems for space 

and elsewhere are favored in BIFOLD because of its energy 

producing flexibility and the prospects of low development 

costs compared to other power systems. 

The very activity of providing new and improving the r e 

liability and range of present nuclear data will yield new concepts 

in nuclear and other technologies. The origin of the 

BIFOLD concept through nuclear data acquisition efforts is 

evidence for this expectation. 

References 

(1) W. F. Stubbins, D. M. Barton and F. D. Lonadier, Nucl. 

Sei. Enging, 25 (1966)377. 

(2) W. F. Stubbins, A BIFOLD Nuclear Power Source, USAEC Report. 

MLM 1357, June 15, 1967, Declassified March 1970. 

(3) R. A. Wolfe and W. F. Stubbins, A BIFOLD Nuclear Power 

Source, USAEC Report MLM 1982, November 17, 1972. 

(4) W. F. Stubbins and R. A. Wolfe, BIFOLD Nuclear Power Source, 

To be published. 

(5) W. F. Stubbins and R. A. Wolfe, The BIFOLD Nuclear Power 

Source, Invited Paper, Am. Nucl. Soc. 19th Annual Meeting, 

June 10-15, 1973, Chicago, Illinois. 

(6) G. Y. Eastman, The Heat pipe - A Progress Report, Fourth 

Intersociety Energy Conversion Engineering Conference, 

Washington, D. C. September, 1969. 

(7) W. W. Smith, D. R. Rogers and G. L. Silver, Plutonium-238 

Isotopic Fuel Form Data Sheets, USAEC Report MLM 1691 (1971) 

(8) J. D. Hastings and W. W. Strohm, Jour. Inorganic and Nucl. 

Chem., 34. (1972) 25. 

(9) W. M. Rutherford, G. N. Huffman and D. L. Coffey, Nucl. 

Applications, 3^ (1967)366. 

(10) R. L. Henkel, Fission by Fast Neutrons, Fast Neutron Physics 

Part I I . (J. B. Marion and J. L. Fowler, Eds.) Interscience 

Publishers, New York (1963) 

(11) W. F. Stubbins, An Interim Report and Evaluation of the 

Critical Mass of Plutonium-238 Fast Neutron Assemblies, 

July 21, 1964, Unpublished. 

(12) L. L. Carter, Physics Research Quaterly Report, July-Sept. 

1964, USAEC Report HW-84369 (1964). 

(13) R. A. Wolfe, The Nuclear Criticality Safety Aspects of 

Plutonium-238, Nucl. Appl. and Tech. Aug (1970) 9. 

(14) M. G. Silbert, Fission Cross Section of Plutonium-238 

from Persimmon, USAEC Report LASL-4108-MS (1969).

I A E A - S M -1 7 0 /3 9 69 

(15) W. F. Stubbins, C. D. Bowman, G. F. Auchampaugh and M. S. 

Coops, Phys. Rev. 154 (1967) 1111. 

(16) E. K. Hyde, The Nuclear Properties of Heavy Elements. III. 

Prentice-Hall, New Jersey (196'4). 

(17) R. A. Wolfe and W. F. Stubbins, Subcritical Neutron 

Multiplication Experiments with Four S N A P - 19B (IRHS) Heat 

Sources Containing Plutonium-238, USAEC Report MLM 1523 

(1969). 

(18) R. A. Wolfe and D. A. Edling, Subcritical Neutron Multiplication 

Experiments with SNAP-19C-2 and SNAP 19B Heat 

Sources Containing Plutonium-238, USAEC Report MLM-1416 

(1967). 

244 238 

(19) A. Prince, Neutron Cross Sections for Cm and Pu , 

USAEC Report GEMP-411 (1966). 

(20) 16 Group 238Pu Cross Sections Compiled at LASL, Unpublished, 

Private Communication (1969). 

(21) Reactor Physics Constants, USAEC Report ANL-5800 (1963). 

(22) A. H. Jaffey and J. L. Lerner, Nucl. Phys., A145 (1970)1. 

(23) D. A. Hicks, J. Ise and R. V. Pyle, Phys. Rev. 101 (1956) 

1016. 

(24) W. W. T. Crane, G. H. Higgins and H. R. Bowman, Phys. Rev. 

101 (1956)1804. 

T70 

(25) Ç. L. Dunford, Evaluated Neutron Cross Section for Pu and 

244Cm, USAEC Report AI65190 (1965). 

(26) !• I- Bondarenko, D. B. Kuzminov, L. S. Kutsageva, L. I. 

Prokhorova and G. N. Smirenkin, United Nations Conf. on 

Peaceful Uses of Atomic Energy, Geneva, ( 1958)p . 353. 

(27) R. B. Leachman, Phys. Rev. 101 (1955) 1005. 

(28) J. Terrell, Phys. Rev. 1_08 (1957) 783. 

(29) R. A. Wolfe and W. F. Stubbins, An Estimate of "v(E_) for 

238pu. (To be published). 

(30) W. F. Stubbins, The Neutron Energy Spectrum in 23®Pu 

Photofission Near Threshold. Bulletin Am. Phys. Society, 

Washington D. C. Meeting, April 23-26, 1973, and to 

be published. 

(31) A. M. Weinberg and E. P. Wigner, The Physical Theory of 

Neutron Chain R e actors. Univ. of Chicago Press, Chicago, 

111. (1958). 

(32) R. Breitwieser, An Out-of-Core Thermonic-Convertor System 

for Nuclear Space Power, Third International Conference 

on Thermonic Electrical Power Generation, Julich, Germany, 

June 5-9, 1972, also NASA Tech. Memo. TMX-68049.(1972).

I A E A - S M -1 7 0 /5 8 

A STUDY OF LONG-TERM HEAT GENERATION 

IN NUCLEAR BY-PRODUCTS 

FROM LWR AND LMFBR SYSTEMS 

J. A. ANGELO, Jr., R.G. POST, 

F.E. HASKIN, C. LEWIS 

University of Arizona, Tucson, Arizona, United States of America 

Abstract 

A S T U D Y OF L O N G -T E R M H E A T G ENERATION IN NUCLEAR B Y -P R O D U C T S FROM LWR A N D LMFBR SY S T E M S . 

T h e r m a l ou tpu ts o f h i g h - le v e l r a d io a c t iv e b y -p r o d u c ts fr o m b o th a 1 0 0 0 -M W (e ) r e f e r e n c e LW R and a . 

1 0 0 0 -M W (e ) r e f e r e n c e LMFBR w e re c a lc u la t e d fo r c o o lin g tim e s ra n g in g fr o m o n e y e a r t o o n e thousand y e a r s. 

Both g r a p h ic a l and ta bu lar re p re se n ta tio n s o f th e d a ta are u s e fu l in a w id e v a r ie ty o f lo n g - r a n g e b y -p r o d u c t 

m a n a g e m e n t stu d ies. 

A r e la t iv e ly fa st and s im p le c o m p u te r c o d e , R A D E C , w as d e v e lo p e d at th e U n iv ersity t o p e r fo rm th e 

b u lk o f th e c o m p u ta tio n s . E x c e lle n t a g r e e m e n t was o b ta in e d w ith th e m o r e e x te n s iv e ORIGEN c o d e d e v e lo p e d 

at O a k R id g e N a tio n a l L a b ora tory . 

I n - c o r e e ffe c t s o f fissio n p r o d u c t tra n sm u ta tion and a c t in id e e le m e n t b u ild -u p w e re in c lu d e d in th e 

c o m p u ta tio n s and w e re fou n d t o b e s ig n ific a n t . T h e fo r m e r e f f e c t c a n a c c o u n t for as m u c h as 2 5 per c e n t o f 

th e b y -p r o d u c t a fterh ea t du rin g th e first d e c a d e o f c o o lin g p r im a r ily d u e to th e p r o d u c tio n o f ш C s in n eu tron 

absorp tio n by th e fa ir ly abu n d an t fissio n p r o d u c t 133C s. H ea t g e n e r a tio n ra tes for LWR and LMFBR b y -p r o d u c ts 

are c o m p a r a b le du rin g th e first cen tu ry o f c o o lin g but d iv e r g e ra p id ly th e re a fte r w ith th e a c t in id e e le m e n ts 

p r e d o m in a tin g a fter 1 20 y e a r s fo r th e LMFBR and a fter 2 2 5 y ea rs for th e LWR. D e t a ile d , t im e - d e p e n d e n t an aly ses 

o f th e m o r e th e r m a lly s ig n ific a n t fissio n p rodu cts and a c t in id e e le m e n t s w e re c a lc u la t e d and p lo tte d . 

One of the most significant problems facing the world's expanding 

nuclear power .industry is the safe and economic management of the 

high-level radioisotopes generated by nuclear power reactors and separated 

in the reprocessing of spent reactor fuels. These by-products contain 

radioisotopes which decay so slowly that they must be controlled for 

hundreds to thousands of years. One method that is currently being 

considered in the United States is permanent removal from the biosphere 

by storage in deep geologic formations. Geologic storage [ 1, 2] includes 

excavation of a deep cavity, filling with radioactive material, sealing and 

allowing melting of the material and the surroundings for a short distance. 

The extent of melting and the time required to reach the m a x i m u m radius 

requires detailed heat transfer analyses. Most other schemes for m a n a g e 

ment of radioactive by-products also require heat transfer calculations. 

These thermal analyses [ 3] require the development of detailed, time- 

dependent heat generation data for the radioisotopes formed in burning 

advanced reactor fuels. In addition to heat transfer studies concerned with 

permanent storage concepts, the contribution of a particular fission product 

or actinide nuclide to the total thermal power output of these high-level 

radioactive materials is frequently required in performing by-product 

management optimization studies. These studies, for example, m a y be 

concerned with reprocessing procedures, by-product thermal applications, 

or selective isotope recovery concepts. 

71

72 AN GELO e t a l. 

Since the developm ent of the first nuclear rea ctor, engineering design 

has requ ired evaluation and prediction of the heat generated by the ra d io 

active by-p rod u cts of fissio n as functions of tim e [ 4] . Since then, many 

calculations have been made to evaluate therm al pow er output as a function 

of coolin g tim e. A lm ost a ll of these past efforts, including sev era l subject 

to wide use [ 5 -7 ], made one or both of two m a jor approxim ations. The 

fir s t is to n eglect neutron capture by the fission product n uclides during 

irradiation . The secon d approxim ation om its the contribution of the tran s- 

plutonium actinides. The e r r o r s introduced w ere not readily apparent 

because the m ajority of e a rlie r decay heat studies w ere con cern ed with 

the first year or so of coolin g, follow in g discharge of the spent fuel from 

the re a cto r. It is only recen tly, with high burn-ups and lon g -term ra d ioactive 

b y-p rod u ct management, that isotop es from nuclear transm utation 

during irradiation and the actinide nuclides have becom e im portant to heat 

generation. 

A recen t study [ 8] has shown that by neglecting the p roce ss of nuclear 

transm utation fo r caesiu m [ 133Cs(n, y) 134Cs] the fission product heat 

generation rate from a typical advanced design LW R could be underestim ated 

by as much as 2 5% during the fir s t decade of decay. The 133Cs isotope is a 

fa irly abundant fission product in the therm al fission of 235U (approxim ately 

six atom s p er one hundred atom s fission ed) and has a fa irly large therm al 

capture cro s s -s e ctio n (approxim ately forty barn s). The transmuted 

population of 134Cs in discharged therm al rea ctor fuel is much higher than 

anticipated even by the m ore recen t of these studies [ 7 ]. 

The contribution of the actinide nuclides to the overa ll heat generation 

rate of radioactive by-p rod u cts has a lso been neglected in the m ajority of 

previou s decay heat studies. R ecently, calculations show [ 8] that the 

actinide n uclides contained in spent fuel from typical LWR or LM FBR system s 

are significant heat gen erators after about the first decade or two of cooling. 

T hese actinide nuclides dominate the LM FBR spent fuel therm al pow er output 

after approxim ately one century of coolin g and the LWR after about two 

centuries of coolin g. 

T o p erm it com p arison with p reviou s studies [ 1, 9 ], this study ch ose 

the nuclear by-p rod u cts from two represen tative rea ctors: a lOOO-MW(e) 

referen ce LW R anda lOOO-MW(e) referen ce LM FB R . Design and perform an ce 

TA B LE I. LWR DESIGN AND PERFORM ANCE CHARACTERISTICS [10] 

F u e l fo r m : O x id e p e lle t s 

P ow er : 

T h e r m a l e f f i c i e n c y : 

C o r e : 

A v e r a g e s p e c i f ic p o w e r 

B urn-up 

C h a rg e (U ) 

E n r ic h m e n tf^ U ) 

R e fu e llin g in te r v a l 

R e fu e llin g fr a c tio n 

3 0 8 3 M W (t h e r m a l) 

3 5 .4 % 

3 4 . 8 M W /t 

3 3 0 0 0 M W d /t 

8 8 . 6 t 

3 .3 °Jo 

~ 3 6 5 fu ll p ow er days 

1 /3

I A E A - S M -1 7 0 /5 8 73 

T A B L E II. L M F B R D E S I G N A N D P E R F O R M A N C E C H A R A C T E R I S T I C S [10] 

F u e l fo r m : 

Pow er : 

T h e r m a l e f f i c i e n c y : 

C o r e : 


B urn-up 

C h a rg e (U + Pu) 

E n rich m en t ( a 9Pu) 


R e fu e llin g fr a c t io n 

A x ia l b la n k e t: 


B urn -u p 


E n rich m en t ( ^ U ) 


R e fu e llin g fr a c tio n 

R a d ia l b la n k e t: 

A v e r a g e s p e c i f ic p ow er 

B urn -u p 


E n rich m en t ( ^ U ) 


R e fu e llin g fr a c t io n 

O x id e p e lle ts 

2 5 0 0 M W (th e r m a l) 

40% 

175 M W /t 

8 0 0 0 0 M W /t 

1 2 . 6 t 

1 5 .6 % 

153 fu ll p o w e r days 

1 /3 

5 . 5 M W /t 

2 5 0 0 M W d /t 

7 .3 2 t 

0 .3 % 

153 fu ll p o w e r days 

1 /3 

10 M W /t 

8 1 0 0 M W d /t 

2 6 .7 t 

1 .9 6 % 

1 53 fu ll p ow er d ays 

- 3 /1 6 

TABLE III. TH E RM A LLY SIGNIFICANT FISSION PRODUCT 

NUCLIDES IN T Y P IC A L ADVANCED LW R AND LM FBR SPENT 

FUEL (1 T O 1000 YEARS COOLING) 

8 5 Kr 125 Sb 14 7Pm 

9 0 S r / 9°Y * 125mTe 1 5 1 Sm 

9 5 Zr 1 2 6 Sb 15 2и Eu 

95Nb 13 4Cs Eu 

99TC 13 7C s /137mBa* 1 5 5 17 Eu 

10 6R u /106Rh* 14 4C e /14 4P r* 

S h ort-lived daughter

74 A N GELO e t a l. 

TABLE IV. TH E RM A LLY SIGNIFICANT ACTINIDE NUCLIDES 

IN T Y P IC A L ADVANCED LWR AND LM FBR SPENT FUEL 

(1 T O 1000 years cooling) 

244Cm 242PU 237Np 

243c* 241Pu 238u 

242Cm 

243aW23V 

242m. /242. * 

Âm/ Am 

2 4 1 a Am 

* S h ort-lived daughter 

240 Pu 

2 36ц 

239- Pu 235U 

238 Pu 234U 

236_ Pu 232ü 

ch a ra cteristics fo r these re a cto rs are displayed in T ables I and II 

resp ectiv ely . Extensive tim e-dependent heat generation rate data have 

been com puted, using the ORIGEN and RADEC com puter codes fo r nuclear 

by-p rod u cts fro m these two re feren ce re a cto rs. The ORIGEN isotope 

generation and depletion code was developed at Oak Ridge National 

L aboratory. T h eir calculations of the isotop ic changes that took place 

in the LWR and LM FBR nuclear fu els fo r an exposure of 33 000 M W d/t 

w ere used [ 10] . The RADEC com puter code was developed at the U niversity 

o f A rizon a to calcu late extensive heat generation rate data as a function of 

coolin g tim e fo r all fission product and actinide nuclides with significant 

heat generation (see T ables III and IV). The coolin g ranges from one to 

one thousand y e a rs. Using data calculated by ORIGEN at ORNL and 

rep orted by them [ 9] as its initial conditions, RADEC com puted the tim e- 

varying populations o f all appropriate b y-p rod u ct nuclides, determ ined the 

heat generation rate associa ted with each particular isotope, com puted a 

total therm al pow er output, and finally com puted the fraction al decay 

heat contribution fo r each therm ally significant by-p rod u ct nuclide. 

Since the actual actinide nuclide population in re p ro ce ssin g by-p rod u cts 

is extrem ely sen sitive to re p ro ce ssin g efficien cies and techniques, the 

actinide nuclide heat generation was treated separately fro m the fission 

product heat generation. In these com putations it was assum ed that 0. 5% 

of the uranium and 0. 5% of the plutonium presen t in the discharged rea ctor 

fuel appeared in the sp en t-fu el re p ro ce ssin g b y -p rod u cts. The contribution 

of each th erm ally significant nuclide as the fraction of the total fission 

product therm al p ow er output or the total actinide therm al pow er output 

as a function of decay tim e can be used in optim ization studies involving 

rep ro ce ssin g p roced u res, b y -p rod u ct therm al applications, or perm anent 

storage con cep ts.

I A E A - S M -17 0 /5 8 75 

T A B L E V. T O T A L H E A T G E N E R A T I O N R A T E F O R N U C L E A R B Y - P R O D U C T S 

F R O M A 1 0 0 0 - MWfe) R E F E R E N C E L W R 

Cooling Time 

(Years) 

Heat Generation Rate 

(W/t) ( W / M W d ) 

Fractional Contribution 

Fission Product Actinide 

1 1.026E+4 3.110E-1 96.92 3.08 

2 5.531E+3 1.676E-1 97.49 2.51 

3 3.491E+3 1.058E-1 97.16 2.84 

4 2.466E+3 7.472E-1 96.42 3.58 

5 1.914E+3 5.800E-2 95.62 4.38 

6 1.596E+3 4.835E-2 94.94 5.06 

7 1.398E+3 4.235E-2 94.42 5.58 

8 1.266E+3 3.835E-2 94.04 5.96 

9 1.172E+3 3.551E-2 93.78 6.22 

10 1.101E+3 3.337E-2 93.59 6.41 

11 1.046E+3 3.169E-2 93.47 6.52 

12 1.001E+3 3.032E-2 93.40 6.60 

13 9.620E+2 2.915E-2 93.35 6.65 

14 9.284E+2 2.813E-2 93.33 6.67 

15 8.985E+2 2.723E-2 93.33 6.67 

16 8.711E+2 2.640E-2 93.33 6.67 

17 8.460E+2 2.564E-2 93.35 6.65 

18 8.224E+2 2.492E-2 93.37 6.63 

19 8.001E+2 2.425E-2 93.40 6.60 

20 7.789E+2 2.360E-2 93.43 6.57


T A B L E VI. T O T A L H E A T G E N E R A T I O N R A T E F O R N U C L E A R B Y - P R O D U C T S 

F R O M A 1 0 0 0 - MWCe) R E F E R E N C E L W R 

Cooling Time Heat Generation Rate Fractional Contribution 

(Years) (W /t) (W /M W d) Fission Product Actinide 

5 1.914E+3 5 . 8000E-2 95.62 4.38 

10 1.101E+3 3.337E-2 93.59 6.41 

15 8.985E+2 2.723E-2 93.33 6.67 

20 7.789E+2 2.360E-2 93.43 6.57 

25 6.845E+2 2.074E-2 93.59 6.41 

.30 6.037E+2 1.829E-2 93.73 6.27 

35 5.332E+2 1.616E-2 93.84 6.16 

40 4.714E+2 1.429E-2 93.92 6.08 

45 4.172E+2 1.264E-2 93.96 6.04 

50 3.694E+2 1.120E-2 93.97 6.03 

55 3.274E+2 9.921E-3 93.93 6.07 

60 2.904E+2 8.799E-3 93.85 6.15 

65 2.577E+2 7.809E-3 93.72 6.28 

70 2.289E+2 6.937E-3 93.55 6.45 

75 2 . 035E+2 6.166E-3 93.33 6.67 

80 1.810E+2 5.486E-3 93.05 6.95 

85 1.612E+2 4.884E-3 92.72 7.28 

90 1.436E+2 4.352E-3 92.33 7.67 

95 1.281E+2 3.881E-3 91.87 8.13 

100 1.143E+2 3.465E-3 91.35 8.65

I A E A - S M -1 7 0 /5 8 

T A B L E VII. T O T A L H E A T G E N E R A T I O N R A T E F O R N U C L E A R 

B Y - P R O D U C T S F R O M A 1 0 0 0 -MWte) R E F E R E N C E L W R 


(Years) (W/t) (W /MWd) Fission Product Actinide 

100 1.143E+2 3.465E-3 91.35 8.65 

110 9.140E+1 2.770E-3 90.09 9.91 

120 7.339E+1 2.224E-3 88.50 11.50 

130 5.922E+1 1.794E-3 86.56 13.44 

140 4.806E+1 1.456E-3 84.23 15.77 

150 3.926E+1 1.190E-3 81.48 18.52 

160 3.231E+1 9.790E-4 78.29 21.71 

170 2.681E+1 8.124E-4 74.67 25.33 

180 2.245E+1 6.803E-4 70.61 29.39 

190 1.899E+1 5.755E-4 66.17 33.83 

200 1.624E+1 4.921E-4 61.41 38.59 

210 1.404E+1 4.256E-4 56.41 43.59 

220 1.229E+1 3.724E-4 51.29 48.71 

230 1.088E+1 3.297E-4 46.16 53.84 

240 9.746E+0 2.953E-4 41.13 58.87 

250 8.828E+0 2.675E-4 36.31 63.69 

260 8.082E+0 2.449E-4 31.79 68.21 

270 7.473E+0 2.265E-4 27.63 72.37 

280 6.972E+0 2.113E-4 23.87 76.13 

290 6.556E+0 1.987E-4 20.53 79.47 

77

78 ANGELO e t a l. 

T A B L E VIII. T O T A L H E A T G E N E R A T I O N R A T E F O R N U C L E A R 

B Y P R O D U C T S F R O M A 1 000-MW(e) R E F E R E N C E L W R 



50 3•694E+2 1.120E-2 93.97 6.03 

100 1.143E+2 3.465E-3 91.35 8.65 

150 3.926E+1 1.190E-3 81.48 18.52 

О О 

1.624E+1 4.921E-4 61.41 38.59 

250 8.828E+0 2.675E-4 36.31 63.69 

300 6.210E+0 1.882E-4 17.59 82.41 

350 5.110E+0 1.549E-4 8.09 91.91 

400 4.522E+0 1.370E-4 4.05 95.95 

450 4.125E+0 1.250E-4 2.37 97.63 

500 3.815E+0 1.156E-4 1.61 98.39 

550 3.553E+0 1.077E-4 1.22 98.78 

600 3.324E+0 1.007E-4 1.01 98.99 

650 3.121E+0 9.457E-5 0.87 99.13 

700 2.938E+0 8.902E-5 0.80 99.20 

750 2.772E+0 8.398E-5 0.75 99.25 

800 2.620E+0 7.940E-5 0.73 99.27 

850 2.482E+0 7.521E-5 0.72 99.28 

900 2 . 355E+0 7.136E-5 0.73 99.27 

950 2.238E+0 6.782E-5 0.74 99.26 

1000 2.131E+0 6.457E-5 0.76 99.24

I A E A - S M -1 7 0 /5 8 79 

T A B L E IX. T O T A L H E A T G E N E R A T I O N R A T E F O R N U C L E A R 

B Y - P R O D U C T S F R O M A 1 0 0 0 - M W ( e ) R E F E R E N C E L M F B R 


(Years) (W/t) ( W / M W d ) Fission Product Actinide 

1 1.432E+4 4.343E-1 95.19 4.81 

2 6.728E+3 2.040E-1 96.55 3.45 

3 3.709E+3 1.125E-1 96.38 3.62 

4 2.298E+3 6.968E-2 95.10 4.90 

5 1.613E+3 4 . 890E-2 93.38 6.62 

6 1.266E+3 3.840E-2 91.76 8.24 

7 1 . 082E+3 3.280E-2 90.50 9.50 

8 9.761E+2 2.960E-2 89.62 10.38 

9 9.104E+2 2.761E-2 89.01 10,99 

10 8.653E+2 2.624E-2 88.58 11.42 

11 8.314E+2 2.521E-2 88.27 11.73 

12 8.039E+2 2.438E-2 88.01 11.99 

13 7.803E+2 2.366E-2 87.79 12.21 

14 7.591E+2 2.302E-2 87.60 12.40 

15 7. 396E+2 2.243E-2 87.42 12.58 

16 7.214E+2 2.188E-2 87.24 12.76 

17 7.041E+2 2.135E-2 87.07 12.93 

18 6.877E+2 2.085E-2 86.91 13.09 

19 6.719E+2 2.037E-2 86.74 13.26 

20 6.567E+2 1.991E-2 86.57 13.48


T A B L E X. T O T A L H E A T G E N E R A T I O N R A T E F O R N U C L E A R 



(Years) (W/t) ( W / M W d ) Fission Product Actinide 

5 1.613E+3 4.890E-2 93.38 6.62 

10 8.653E+2 2.624E-2 88.58 11.42 

15 7.396E+2 2.243E-2 87.42 12.58 

20 6.567E+2 1.991E-2 86.57 13.43 

25 5.875E+2 1.781E-2 85.70 14.30 

30 5.272E+2 1.599E-2 84.75 15.25 

35 4.741E+2 1.438E-2 83.70 16.30 

40 4.272E+2 1.300E-2 82.54 17.46 

45 3.857E+2 1.170E-2 81.27 18.73 

50 3.489E+2 1.058E-2 79.89 20.11 

55 3.162E+2 9.589E-3 78.39 21.61 

60 2.872E+2 8.710E-3 76.78 23.22 

65 2.615E+2 7.929E-3 75.06 24.94 

70 2.386E+2 7.235E-3 73.22 26.78 

75 2.182E+2 6.617E-3 71.27 28.73 

80 2 . 001E+2 6.067E-3 69.22 30.78 

85 1.839E+2 5.578E-3 67.07 32.93 

90 1.695E+2 5.141E-3 64.83 35.17 

95 1.567E+2 4.752E-3 62.51 37.49 

100 1.452E+2 4.404E-3 60.13 39.87

I A E A - S M -1 7 0 /5 8 81 

T A B L E XI. T O T A L H E A T G E N E R A T I O N R A T E F O R N U C L E A R 




100 1.452E+2 4.404E-3 60.13 39.87 

110 1.258E+2 3.814E-3 55.17 44.83 

120 1.103E+2 3.344E-3 50.13 49.87 

130 9.780E+1 2.966E-3 45.08 54.92 

140 8.774E+1 2.661E-3 40.15 59.85 

150 7.958E+1 2.413E-3 35.43 64.57 

160 7.292E+1 2.211E-3 31.01 68.99 

170 6.746E+1 2.046E-3 26.95 73.05 

180 6.295E+1 1.909E-3 23.28 76.72 

190 5.920E+1 1.795E-3 20.02 79.98 

200 5.604E+1 1.699E-3 17.15 82.85 

210 5.337E+1 1.618E-3 14.66 85.34 

220 5.108E+1 1.549E-3 12.52 87.48 

230 4.910E+1 1.489E-3 10.70 89.30 

240 4.738E+1 1.437E-3 9.1.5 90.85 

250 4.585E+1 1.390E-3 7.84 92.16 

260 4.449E+1 1.349E-3 6.73 93.27 

270 4.326E+1 1.312E-3 5.81 94.19 

280 4.214E+1 1.278E-3 5.03 94.97 

290 4.112E+1 1.247E-3 4.38 95.62

82 ANGELO e t a l. 

T A B L E XII. T O T A L H E A T G E N E R A T I O N R A T E F O R N U C L E A R 

B Y - P R O D U C T S F R O M A 1 0 0 0 -MW(e) R E F E R E N C E L M F B R 

Cooling Time 

(Years) 

Heat Generation Rate 

(W/t) (W /M W d ) 

Fractional Contribution 

Fission Product Actinide 

50 3.489E+2 1.058E-2 79.89 20.11 

100 1.452E+2 4.404E-3 60.13 39.87 

150 7.958E+1 2.413E-3 35.43 64.57 

200 5.604E+1 1.699E-3 17.15 82.85 

250 4.585E+1 1.390E-3 7.84 92.16 

300 4.017E+1 1.218E-3 3.83 96.17 

350 3.620E+1 1.098E-3 2.12 97.88 

400 3.304E+1 1.002E-3 1.34 98.66 

450 3.034E+1 9.199E-4 0.92 99.08 

500 2.796E+1 8.480E-4 0.68 99.32 

550 2.585E+1 7.838E-4 0.52 99.48 

600 2.394E+1 7.260E-4 0.41 99.59 

650 2.221E+1 6.736E-4 0.34 99.66 

700 2.065E+1 6.261E-4 0.29 99.71 

750 1.922E+1 5.828E-4 . 0.26 99.74 

800 1.791E+1 5.432E-4 0.24 99.76 

850 1.672E+1 5.069E-4 0.23 99.77 

900 1.562E+1 4.737E-4 0.22 99.78 

950 1.461E+1 4.432E-4 0.22 99.78 

1000 1.369E+1 4.151E-4 0.23 99.77

10 г- 

T3 - i 

ï 10 

S 

_l -г 

< 10 

10 

Ï A E A - S M -1 7 0 /5 8 

-----LWR 

------LMFBR 

33000 MWd/t 

■\ 4 

t -1 I « » ni______I___I__■ n u i l 

I 10 100 

COOLING TIME (YEARS) 

F I G . l . T o t a l th erm a l pow er output for nu clear by-products from ty p ic a l LW R and L M F B R spent fu e l 

(1 to 100 years co o lin g ). 


F I G .2. T o t a l th erm a l pow er output for nu cle a r by-p roducts from t y p ic a l LW R and LM FB R spent fu e l 

(100 to 1000 yeacs co o lin g ).

8 4 AN GELO e t a l. 

S 

о 

100 

80 

60 

> - 20 

* 0 

• • • FISSION PRODUCTS 

•-•-ACTINIDES 

33000 MWd/t 

100 200 


F I G .3 . R e la tiv e c o n trib u tio n o f fissio n product and a c tin id e n u clid es to the to ta l th erm a l power output from 

t y p ic a l LW R spent fu e l. 

F I G .4 . R e la tiv e c o n trib u tio n o f fissio n product and a c tin id e n u clid es to the to ta l th erm a l power output from 

ty p ic a l LM FB R spent fu e l. 

T ables V through VIII contain the total heat generation rate data 

(fission product and actinide) for the re feren ce LW R. Sim ilarly, T ables IX 

through XII contain the LM FBR nuclear by-p rod u ct therm al pow er output 

fo r variou s coolin g tim es. Consistent with p reviou s studies [ 1, 9, 10] 

these heat generation rate data are based on one m etric tonne (t) of 

uranium ch arged to the LWR system and one m etric tonne of uranium plus 

plutonium orig in ally charged to the "h om ogen ized" LM FBR co re and 

blankets. H ow ever, in an effort to make these resu lts m ore v ersa tile and 

300

О) 

I - 

o 

I A E A - S M -1 7 0 /5 8 85 

Sr / 

106 R u / 1 

,3 4 Ce 

F IG .5 . R e la t iv e h e a t co n tr ib u tio n s o f s e le c t e d fissio n p r o d u c ts in t y p ic a l LWR spent fu e l fo r 1 to 20 y ears c o o l in g . 

 

Ш 100 

о - 

z 

1o 

80 - / 

< 

L. 

О 1 •’ 

** 60 "I; 

POWER 

* 

О 

i 

; \ 

£ 20 - i 

- 242 Cm 

---------238pu 

3 3 0 0 0 M Wd /t 

h- 

< 

-1 л 

\ 

4 J ' ' 1 1 1 

£ D 5 

< 

COOLING 

10 

TIME 

15 20 

(YEARS) 

F IG . 6 . R e la t iv e h e a t co n tr ib u tio n s o f s e le c t e d a c t in id e n u c lid e s in t y p ic a l LWR sp en t fu e l fo r 1 to 20 y ears 

c o o l in g .

8 6 ANGELO e t a l. 

7 0 

со 

Iо 

э 60 

о 

о(Г 

а 50 

Z 

о 

со 

- 40 

U. 

Ü. 

О 

»? 3 0 

? 20 

О 

> 10 

\ 

- \ 

г л 

•\ • \ 

I л 

\ 

"f- - . ____I 

0 5 10 I 20 


144 

*С , е / ,44Рг 

147 Pm 

3 3 0 0 0 MWd/t 

F I G .7 . R e la tiv e h e a t c o n tr ib u tio n s o f s e le c t e d fissio n p rod u cts in t y p ic a l LMFBR spent fu e l fo r 1 to 2 0 y ears 

c o o l in g . 

о < 

100 r - 

8 0 

60 

u j 40 

9 

О 

ui 2 0 

> 

v 

Cm 

1 Am 

' Cm 

------- —° Pu 

3 3 0 0 0 MWd/t 

I - 

< 

^=i 

UI 0 5 10 15 20 

0= COOLING TIME (Y E A R S ) 

F IG . 8 . R e la t iv e h e a t co n tr ib u tio n s o f s e le c t e d a c t in id e n u c lid e s in t y p ic a l LMFBR sp en t fu e l for 1 t o 2 0 y ears 

c o o l in g . 

potentially applicable to other burn-up scen a rios, a n orm alizin g unit, 

the w att-p er-m egaw attday (W /M W d) was a lso chosen as an ordinate in 

presenting the decay heat data. (See F igs 1 and 2). It is of interest to 

note that although the heat generation rates fo r the LWR and LM FBR 

by-p rod u cts appear to be com parable during the first century of coolin g, 

they diverge rapidly after about 100 years, with the actinide nuclides 

playing a dominant ro le in determ ining the LM FBR by-p rod u ct therm al 

pow er output.

I A E A - S M -1 7 0 /5 8 8 7 

The relative contribution of the fissio n product nuclides versu s 

the actinide nuclides to the total heat generation rate is displayed in F igs 3 

and 4 fo r LW R and LM FBR by-p rod u cts, resp ectively. 

E xtensive heat generation rate data and the a ssocia ted fraction al decay 

heat contributions fo r selected fissio n product and actinide nuclides of 

unusual th erm al sign ifican ce are presented in F igs 5 through 8. 

In sum m ary, d iscrep a n cies between the afterheat data presented in 

this study and those appearing in previous studies a rise from two 

approxim ations used by the previous studies: the n eglect of nuclear 

transm utation of fissio n product nuclides during irradiation and the heat 

contribution of the actinide nuclides. D ecay heat com putations presented 

h ere do not n eglect these contributions and provide m ore com plete lon gterm 

th erm al pow er output data, which can be utilized in a variety of 

n u clear b y-p rod u ct m anagement studies, p articu la rly those involving 

deep g eolog ic d isp osal of h ig h -level ra d ioisotop es. 

REFERENCES 

[ 1 ] C O H E N , J .J ., LEW IS, A . E . , BRAUN, R . L . , U se o f a D e e p N u cle a r C h im n e y for 

th e In -s itu I n c o r p o r a tio n o f N u c le a r -r e p r o c e s s in g W aste in M o lte n S ilic a t e R o c k , U C R L -5 1 0 4 4 , 

L a w re n ce L iv e rm o r e L a b ., L iv e rm o r e , C a li f . (M a y , 1 9 7 1 ). 

[ 2 ] SHEFF, J . R . , B a tte lle N orth w est L a b s ., R ich la n d , W a s h ., P rivate c o m m u n ic a t io n ( N o v . , 1 9 7 2 ). 

[ 3 ] AN G E LO , J. A . , J r ., H ea t T ran sfer fr o m R a d io a c t iv e W astes in D e e p R o c k , D o c t o r a l D isserta tion 

(in p r e p a ra tio n ), T h e U n iv ersity o f A r iz o n a (1 9 7 3 ). 

[ 4 ] W A Y , K . , W IGNER, E . P . , T h e ra te o f d e c a y o f fissio n p r o d u c ts, Phys. R e v . 7 3 1 1 (J u n e, 1 9 4 8 ). 

[ 5 ] PERKINS, J .F . , K IN G , R . W . , E nergy r e le a s e fr o m th e d e c a y o f fis s io n p ro d u c ts, N u c l. S e i. E n g. 3 

(1 9 5 8 ) 7 2 6 . 

[ 6 ] STEH N , J .R ., C L A N C Y , E . P ., "F is s io n -p r o d u c t R a d io a c tiv ity and h e a t g e n e r a t io n " , 2nd In t. C o n f. 

p e a c e f u l U ses a t o m . E nergy (P r o c . C o n f. G e n e v a , 1 9 5 8 ), U N , N ew Y o r k ( P /1 0 7 1 U S A ). 

[ 7 ] VARTE RESSIAN, K . A . , BURRIS, L . , F is s io n -p r o d u c t S p e c tra fr o m Fast and T h e r m a l F ission o f 235U and 

B 9 Pu, A r g . N a tl. L a b ., A r g o n n e , 111., A N L -7 6 7 8 (1 9 7 0 ). 

[ 8 ] A N GELO , J ., I t . , P O S T . R . G . , H A S K IN , F .E ., LEW IS, C . , N u c le a r b y - p r o d u c t lo n g - t e r m h ea r 

g e n e r a tio n ra te s, T ra n s. A m e r . N u c l. S o c . 15 2 (1 9 7 2 ) 6 6 3 . 

[ 9 ] O R N L -4 4 5 1 , S itin g F u e l R e p rocessin g P lants and W aste M a n a g e m e n t F a c ilit ie s , ORNL, O a k R id g e , 

T e n n . (1 9 7 0 and 1 9 7 1 ). 

[ 1 0 ] BELL, M . J . , R a d ia tio n P rop erties o f Spent P lu to n iu m F u els, O R N L -T M -3 6 4 1 , ORNL, O a k R id g e , 

T e n n . (1 9 7 2 ). 

DISCUSSION 

W.B. LEWIS: You have separated the fission -p rod u ct and actinide 

heat contributions and the com pared them. They m ay, how ever, be 

ch em ica lly separated. Only the heat fro m strontium and caesium is highly 

im portant fo r the fir s t hundred yea rs. Is not coolin g of the actinides of 

rela tiv ely m in or con cern ? 

J. A . ANGELO: On the con trary, the heat generated by the actinides 

m ay actually be a m a jor con cern even during the first hundred years of 

decay. The scen ario fo r b y-p rod u ct re p ro ce ssin g em ployed in this paper 

assum ed that only 0. 5% of the uranium and 0. 5% of the plutonium present 

in the disch arged fuel ultim ately appeared in the re p ro ce ssin g by-p rod u cts.

8 8 AN GELO e t a l. 

H ow ever, different b y -p rod u ct m anagem ent sch em es — perhaps, say, 

intact burial of the disch arged fuel — w ill resu lt in different, p ossib ly 

higher, lev els of heavy m etals appearing in the w astes. T his, of cou rse, 

could result in m uch higher "h eavy-m etal" o r actinide heat generation 

r a te s . 

D. J. HOREN: Is it obvious why the e a rlie r w ork ers ignored the 133Cs 

problem ? 

J. A. ANGELO: It was not readily obvious to m e during m y review s 

of the literatu re. Perhaps it had been assum ed that nuclear transmutation 

of the fissio n product nuclides could be n eglected in the case of short 

irradiation tim es o r low exposure lev els without introducing seriou s e rro rs. 

P erhaps they w ere lim ited in their calculations by the lack of high-speed 

com putational fa cilitie s, which would have enabled the num erical solution 

of the large num ber of coupled d ifferen tial equations d escribin g the fission 

product inventories. 

J. Y. BARRE: W ould you r con clu sion s fo r fast-neutron rea ctors be 

changed if: 

(1) a burn-up of 100 000 M W d/t was used, which is a much m ore rea listic 

value than the 33 000 M W d/t which you used? 

(2) the isotop ic com position of the initial plutonium was different from the 

one selected , which was not m entioned? 

J. A. ANGELO: The answ er to both parts of your question is yes. 

The total heat generation rate fo r the LM FBR b y-p rod u cts would be changed 

by using a different burn-up value or a different isotop ic com position of 

plutonium appearing in the re p ro ce ssin g by-p rod u cts. 

In these com putations an average equivalent exposure of 33 000 M W d/t 

was used. H ow ever, this represen ted a p ost-irra d ia tion , hom ogeneous 

blending (to create an average equivalent burn-up of 33 000 M W d/t) of d is 

charged fuel from the co re and radial and axial blanket region s. The d is 

charged c o re m ateria l itse lf experien ced a burn-up of 80 000 M W d/t as 

indicated in T able II of our paper. F u rth erm ore, it was assum ed that only 

0. 5% of the plutonium and 0. 5% of the uranium presen t in the disch arged 

fuel ultim ately appeared in the sp en t-fu el-rep rocessin g by-p rod u cts.

SECTIONS EFFICACES 

DE CREATION DE DOMMAGES 

M . LO T T *, J .P . GENTHON**, F . GERVAISE**, 

P. M A Sf, J .C . M O U G N IO TÎÎ, NGUYEN VAN DOAN** 

Commissariat à l'energie atomique, 

France 

Abstract-Résumé 

C R O S S -S E C T IO N S FOR THE C R E A T IO N OF D A M A G E . 

I A E A - S M -1 7 0 /6 5 

D iffe r e n t ia l c r o s s -s e c tio n s r e p o re se n tin g th e ra te o f c r e a tio n o f d a m a g e are e sta b lis h e d ; w ith th ese 

it is p o s s ib le to c a lc u la t e th e s im p le s t q u a n titie s a sso c ia te d w ith ir ra d ia tio n - i . e . th e e n e rg y im p a r te d to 

th e m a te r ia l in th e fo r m o f e la s t ic c o llis io n s and th e n u m b er o f d is p la c e m e n ts p e r a t o m . T h e d ata n ecessa ry 

fo r c a lc u la t in g th ese d a m a g e fu n c tio n s a re: (a ) th e n eu tron c r o s s -s e c tio n s ( e l a s t ic and in e la s tic ) w ith th eir 

an gu la r d istrib u tion s; w ith th ese it is p o s s ib le to c a lc u la t e th e s p e ctru m o f th e (p rim a r y ) r e c o il atom s 

a s s o c ia te d w ith a n eu tron c o llis io n ; (b ) th e e n e rg y g iv e n up and th e n u m b e r o f a to m s d is p la c e d b y th e 

p r im a ry a t o m , w h ic h are c a lc u la t e d b y m ea n s o f L in d h ard t’ s u n iv e r sa l c u r v e , th e results o f w h ic h are c o m p a r e d 

w ith th o se o f a c o l l i s i o n - b y - c o l l i s i o n c a lc u la t io n o f th e d is p la c e m e n t c o n e . T h e A R TU S and SOURCE c o d e s 

a re u sed in c a lc u la t in g w ith th e se d a ta th e e n e rg y im p a r te d to th e la t t ic e and th e n u m b er o f d is p la c e m e n ts 

p e r a t o m . A R T U S X is lin k e d w ith th e U K N D F f i l e . Results are g iv e n for a ll u sual ca ses o f c o m m o n m e ta ls 

and s t e e l. T h e c r o s s -s e c tio n s n e ce s sa ry fo r c a lc u la t in g rates o f c r e a tio n o f gas (H and H e) in ir ra d ia te d m e ta ls 

a re r e v ie w e d . 

SECTIO N S EFFICACES DE C R E A T IO N DE D O M M A G E S . 

D es s e c tio n s e f f ic a c e s d iffe r e n t ie lle s d e taux d e cr é a tio n d e d o m m a g e s son t é t a b lie s q u i p e r m e tte n t 

d e c a lc u le r le s grandeu rs le s plus s im p le s a s s o c ié e s à l'ir r a d ia t io n , c 'e s t - à - d i r e : l'é n e r g i e c é d é e au m a té r ia u 

sous fo r m e d e c h o c s é la s tiq u e s e t le n o m b r e d e d é p la c e m e n ts p ar a t o m e . Les d on n é e s n é ce s sa ir e s au c a lc u l 

d e c e s fo n c tio n s d e d o m m a g e sont: a) le s s e c tio n s e f f ic a c e s n e u tro n iq u e s, é la s tiq u e , in é la s tiq u e a v e c leu r 

d istr ib u tio n a n g u la ir e q u i p e r m e tte n t d e c a lc u le r le sp e c tr e des a to m e s d e r e c u l (p r im a ir e ) a sso c ié s à un c h o c 

n e u tro n iq u e ; b) l ’ é n e r g ie c é d é e e t le n o m b r e d 'a t o m e s d é p la c é s p a r c e t a to m e p r im a ir e q u i son t c a lc u lé s 

au m o y e n d e la c o u r b e u n iv e r s e lle d e L in d h ardt d on t les résultats so n t c o m p a r é s à c e u x d 'u n c a lc u l c h o c par 

c h o c d e la g e r b e d e d é p la c e m e n t . Les c o d e s d e c a lc u l ARTU S e t SOURCE tra ite n t c e s d o n n é e s p ou r c a lc u le r 

l'é n e r g i e c é d é e au réseau e t le n o m b r e d e d é p la c e m e n ts p ar a t o m e . A R TU S X est c o u p lé sur la b ib lio th è q u e 

U K N D F . Les résu ltats son t d on n és dans q u e lq u e s ca s u suels d es m é ta u x cou ran ts e t d e l'a c i e r . Les se c tio n s 

e f f ic a c e s n é c e s sa ir e s au c a lc u l d es taux d e c r é a tio n d e g a z (H e t H e) dans les m é ta u x irra d iés sont passées 

e n r e v u e . 

INTRODUCTION 

Pour caractériser l'irradiation neutronique 

des matériaux de structure des réacteurs, on s ’est longtemps 

contenté de grandeurs intégrales telles que le flux 

supérieur à 1 MeV ou l'activation d Tun détecteur à seuil. 

Compte tenu de 1 Tensemble des progrès réalisés 

dans les techniques d'examen des matériaux irradiés,dans 

la connaissance des sections efficaces et des spectres neutroniques, 

dans l Tétude des mécanismes de transfert d'énergie aux 

* C e n tr e d ’ é tu d e s n u c lé a ir e s d e F o n te n a y -a u x -R o s e s . 

* * C e n tr e d 'é tu d e s n u c lé a ir e s d e S a c la y . 

ï C e n tr e d 'é tu d e s n u c lé a ir e s d e G r e n o b le . 

C e n tr e d ’ é tu d e s n u c lé a ir e s d e C a d a r a c h e . 

89

90 L O T T e t a l. 

matériaux, il est devenu possible de rapporter les dommages à 

des grandeurs liées au matériau lui-même, par exemple : l'énergie 

cédée au réseau ou le nombre de déplacements par atome. 

L'intérêt de l'utilisation de telles unités 

apparaît encore plus nettement quand il s'agit de comparer les 

irradiations neutroniques et les irradiations ioniques. Malheureusement, 

ces grandeurs ne sont pas directement mesurables, 

elles ne peuvent qu'être calculées et pour le faire, il faut 

mettre en oeuvre un nombre important de données dont la normalisation 

est nécessaire pour que la mesure de la même grandeur 

soit indépendante de l'expérimentateur. Pour ce qui concerne 

les sections efficaces, compte tenu de la généralisation de 

l'emploi d'un nombre très restreint d'évaluations : ENDF/B [1] 

et UKNDF L2] , la normalisation devient possible et il semble 

qu'il en soit de même pour le calcul du nombre de déplacements 

par atome primaire dans un métal pour lequel l'abaque de 

LINDHARD^3] , est maintenant généralement employé. 

Après avoir rappelé les formules et les 

conventions utilisées, nous donnons les sections efficaces de 

création de dommages d'éléments entrant dans la composition 

des matériaux de structure les plus courants et celles de 

l'acier inoxydable. 

FORMALISME GENERAL 

Lors de l'interaction d'un neutron et d'un 

atome, celui-ci peut acquérir suffisamment d'énergie pour être 

déplacé de son site et déplacer à son tour de leur site, tout 

au long de son parcours, un grand nombre d'autres atomes qui 

deviennent des interstitiels et laissent sur place des sites 

lacunaires. C'est au nombre de sites lacunaires ou de paires 

lacunes interstitiels par unité de volume ainsi créés lors 

d'une irradiation qu'il est convenu, de façon générale, de rapporter 

les dommages bien que dans certains cas particuliers, 

d'autres modèles peuvent être préférables suivant les propriétés 

des matériaux étudiés. 

La connaissance des sections efficaces 

différentielles neutroniques et de l'ensemble des grandeurs 

relatives aux réactions permet de calculer le spectre des 

premiers atomes choqués, les travaux de LINDHARD permettent 

de calculer l'énergie cédée au réseau et ceux de KINCHIN et 

PEASE t4] , SIGMUND [5] , TORRENS et ROBINSON [б] , de relier 

cette énergie cédée au réseau au nombre d'atomes déplacés. 

I. ENERGIE DES PREMIERS ATOMES CHOQUES 

L'énergie T(|i)du premier atome choqué 

dans le système du laboratoire, émis dans une direction faisant 

un angle 6 tM. ( ^ = СО3 0^,м) avec la direction du neutron 

incident dans le système du centre de masse dépend du type 

d'interaction. Elle est donnée par les expressions suivantes 

où E est l'énergie du neutron incident (laboratoire) et A la 

masse atomique du noyau cible.

1 .1. Choc élastique 

I A E A -S M - 1 7 0 /6 5 91 

T N Cu.)= 

Г (1 + А)г Г 

1.2. Choc inélastique - niveaux séparés (n,n'y) 

TN/Cu)= E jl _ Ail 0_ + aA _ M 0 f l 

1 r Ci + A f\ 2. A e: 4 a 

Dans cette expression Q ^ O correspond à 

l'énergie emportée par le y dont la quantité de mouvement est 

négligée, ce qui entraîne une erreur de quelques pour mille 

sur l'énergie du primaire. 

1.3. Choc inélastique (n,n'y) niveaux non résolus 

Pour les neutrons d'énergie élevée, les 

niveaux d ’énergie ne sont pas résolus et les bibliothèques de 

données nucléaires donnent généralement le spectre d'énergie 

des neutrons émergents dans le système du centre de masse et 

leur distribution angulaire, souvent isotrope. L'énergie du 

primaire dépend alors de |Л et de l'énergie Ecu. du neutron 

émis dans la direction opposée (C.M.) par l'expression : 

1.4. Choc (n,2n) 

t n4 ( Ц , 0 = A I ^ 

й {(А+1)г A? ■ Г 

En supposant l'émission neutronique isotrope 

dans le système du centre de masse et les directions 

d'émission des deux neutrons non liées entre elles, l'énergie 

de recul moyenne de l'atome de recul est donnée par l'expression 

: 

Тгм = (а и )1 _ £ _ + Е Л -(Щ И ) + P[, / E 1 E A -Q (A ^ )\ V2I 

leАИ)2 А(АИ)(А-1) v(A+1)3 A (A-1)/ J 

où Q > 0 caractérise l'énergie de la réaction. 

1.5. Capture (ny) 

La réaction ny ne prend de l'importance 

qu'aux faibles énergies où la quantité de mouvement du neutron 

incident peut être négligée. Dans ces conditions, en faisant 

l'hypothèse simplificatrice de non-corrélation angulaire des


y émis, l'énergie de l'atome de recul est donnée par l'expression 

de M.S. WECHSLER [7] 

Y 2(АИ)Сг 

N. étant le nombre de rayons y d'énergie E.^ émis par capture 

O 

et (A+1)C l'énergie à l'état fondamental du noyau formé. 

Les valeurs de T sont extraites du 

travail de R.E. COLTMAN [15] . 7 

II. ENERGIE CEDEE AU RESEAU ET NOMBRE D'ATOMES DEPLACES 

PAR UN PRIMAIRE 

Quand l'atome primaire est de même nature 

que le matériau cible et que celui-ci est constitué d'une 

seule espèce d'atomes, l'énergie cédée au réseau Ep au cours 

du ralentissement d'un primaire d ’énergie initiale T est 

donnée par l'abaque de LINDHARD mis sous forme analytique 

par ROBINSON[8],[9] 

E = T 

° l+KgCe} 

où K est donné par l'expression : K=0,1337 7 ? ^ A -^ ^ et 

g (£'), fonction de l'énergie réduite du primaire 

£ = 1.15.10“^ z~7/3ip (eV) est donnée par l'expression 

g (£)= £+ 0,4024 &3/4+ 3,4 &1/e 

Z et A sont respectivement le numéro atomique et la masse 

atomique communs à l'atome cible et au primaire. 

Conformément au modèle de KINCHIN et PEASE 

trois cas sont considérés dans le calcul du nombre de paires 

lacunes interstitiels créés lors du ralentissement du primaire 

- T < Ed N n = 0 E,, pris arbitrairement égal 

à 40 eV dans les c a l c u l s , 

- Ed < T < E^ Njj = 1 est le seuil de déplacement 

- E ' < T N n = SEn La constante ß a été prise égal 

à 10 keV-l, 1'énergie Ep 

étant exprimée en keV. 

Cette formule correspond à la recommandation 

de l'A.I.E.A. faite au colloque de SEATTLE [13] et à 

celle faite par le Groupe de Dosimétrie de 1'EURATOM. Elle a 

été justifiée par les calculs de simulation de cascades de 

TORRENS et ROBINSON [63 et reprise dans le travail de synthèse 

de NORGETT, ROBINSON et TORRENS [ loi .

IAE A - S M - 1 7 0 /6 5 93 

L'énergie E' limite entre les deux dernières 

régions est prise telle qu'il n'y ait pas de discontinuité 

dans Np. Elle est solution de l'équation : 

p E8(Ei) = 1 

/Remarque/ Pour le graphite, 1 'A.I.E.A. [13] maintient pour 

l'instant la recommandation d'utiliser le modèle de THOMPSON 

et WRIGHT[17] pour le calcul des taux de déplacement. 

III. SECTIONS EFFICACES DE TRANSFERT D'ENERGIE ET DE TAUX 

DE DEPLACEMENT 

Par l'abaque de LINDHARD et les conventions 

exposées, on a donc fait correspondre à un primaire d'énergie 

T ( ), une énergie cédée au réseau ED ([A.) et un nombre de 

paires de FRENKEL Np (|x). Lors du bombardement d'un gramme de 

matériau pur contenant N atomes par un flux unité (cm-^s-l) de 

neutrons d'énergie E, la puissance cédée au réseau D (E) et le 

nombre de paires de FRENKEL créées par seconde DPG (E) sont 

donnés par l'expression suivante : 

N est le nombre d'atomes par gramme 

0" les sections efficaces totales des différents types 

d'interaction (élastique, inélastique...) 

p(li)les distributions angulaires d'un n e utron émergent dans 

la d irection -1JL dans le système du centre de masse 

Y = E (u.) correspond à ytE)sD(E)— - puissance cédée au 

S' réseau eV cm2/g.s 

= hL(u.) correspond à У(Е)= DPG(E) nombre de déplacement 

par gramme et par 

seconde.


Cas d'un mélange de matériaux 

Pour obtenir les grandeurs correspondant 

à un mélange de corps de numéros atomiques voisins, on ajoute 

linéairement les grandeurs relatives à chacun des constituants 

x = ç e , x c 

où O. représente le nombre de gramme du constituant i par 

L gramme de mélange. 

XV. EXEMPLES D'APPLICATIONS 

Les codes ARTUS X [11] et SOURCE [12] 

bâtis sensiblement sur les mêmes principes ont été réalisés 

pour calculer les quantités précédentes. SOURCE est en cours 

de couplage avec la bibliothèque ENDF et ARTUS X est couplé 

sur la bibliothèque UKNDF. 

Les figures n° 1 à 9 sont les résultats 

de calculs ARTUS X pour Al, Si, Cr, Fe, Ni, Cu, Zr, Mo, W. 

Les courbes en tirets correspondent à la réaction élastique, 

les courbes en pointillés aux autres réactions. 

Dans les tableaux I à IX correspondants, 

les résultats sont donnés en 99 groupes du code de transport 

ANISN [14^ , la pondération dans les groupes de basse énergie 

étant faite selon un spectre en 1/E et dans les groupes de 

haute énergie selon un spectre de fission. 

La première colonne du tableau est la 

borne inférieure du groupe, la seconde colonne l'énergie 

totale cédée par les neutrons T ( T = _/T((i)d$, la troisième 

l'énergie cédée au réseau D(E) (eV.cm2.g-l) et la quatrième 

le nombre de déplacements atomiques DPG (E) (cm^.g-l). 

De plus, nous donnons dans le tableau X les mêmes grandeurs 

pour le groupe thermique correspondant à 0,0253eV. 

Un travail semblable a été réalisé par 

D.G. DORAN [16] à partir de la bibliothèque ENDF/B pour le 

tantale et l'acier inoxydable. La comparaison entre les 

deux estimations pour l'acier inoxydable est présentée 

figure 10. Le coefficient de proportionnalité 8 utilisé 

par DORAN étant de 15,15 keV~l pour comparer les résultats 

nous avons reporté le rapport DPG (présent travail)/ 

DPG (DORAN) x 1,515. Il apparaît que les estimations sont 

en moyenne concordantes au-dessus de lO-^MeV. 

Pour les énergies inférieures, les différences 

observées tiennent à la différence entre les seuils 

de déplacement, 33 eV pour DORAN et 40 eV pour le présent 

travail et à la différence des énergies de recul T correspondant 

à une capture. ’ 

L'écart entre les taux de déplacements 

obtenus en intégrant ces deux évaluations sur un spectre de 

neutrons de fission est, compte tenu du facteur de correction 

1,515, égal à 3,5%.

Section efficace de dommage 

Energie du Neutron (M e V ) 

F I G . l . R ésultats d e c a lc u ls A R T U S X p ou r l ’ a lu m in iu m . 

I A E A - S M -1 7 0 /6 5 

СО 

СЛ


Energie du Neutron ( MeV) 

F I G .2 . R ésultats d e c a lc u ls A R T U S X p o u r le s ilic iu m .



F I G .3 . R esultats d e c a lc u ls A R T U S X p o u r le c h r o m e .


Energie du Neutron (MeV) 

F IG .4 . Résultats d e calcu ls ARTUS X pour le fer.



F I G .5 . R ésultats d e c a lc u ls A R T U S X p ou r le n ic k e l.


Г 1 

O) 

CM 

E o 

1 0 2 

101 

10‘1 

10'2 

10‘ 3 

10'7 10' 6 10"s 10-4 10'3 10'2 10‘1 10° 101 102 


F I G .6 . R ésultats d e c a lc u ls A R T U S X p ou r le c u iv r e . 

100 LOTT et al,



F IG .7 . R ésultats d e c a lc u ls A R TU S X p ou r l e z ir c o n iu m . 

I A E A - S M -1 7 0 /6 5

10'7 10-6 10'5 10-4 10'3 10'2 Ю*1 10° 101 ю 2 


F IG . 8 . R ésultats d e c a lc u ls A R T U S X p o u r le m o ly b d è n e .



F I G .9 . R ésultats d e c a lc u ls A R T U S X p ou r le tu n g stè n e .

F IG . 1 0 . C o m p a r a is o n d es v a leu rs d es auteurs a v e c c e l le s d e D o ra n . 

104 LOTT et al.

CONCLUSION 

IAE A - S M - 17 0 /6 5 105 

Nous avons posé comme un principe que les 

dommages dus à l'irradiation neutronique doivent être rapportés 

à des grandeurs liées au matériau irradié. Le nombre de 

paires lacunes interstitiels créés pendant l'irradiation n'est 

certainement pas la seule grandeur intéressante : le spectre 

d'énergie des primaires,déterminant la taille des gerbes de 

déplacement, intervient certainement particulièrement à basse 

température où la vitesse de migration des défauts élémentaires 

est trop faible pour que la gerbe soit dispersée et que l'irradiation 

du matériau puisse être considérée comme uniforme. 

Néanmoins, le nombre de déplacements atomique est actuellement 

un bon point de départ au moyen duquel il serait très souhaitable 

de faire un travail de synthèse de l'ensemble des rés- 

sultats expérimentaux disponibles sur les différents aspects 

des dommages : variation dimensionnelle, fragilisation, 

fluage. L'harmonisation du langage qui semble se faire actuellement 

est un élément indispensable pour réaliser une 

telle synthèse et nous avons mis en évidence le fait très 

positif que les deux évaluations de sections efficaces UKNDF 

et ENDF/B conduisent, à un facteur de normalisation près, 

à des résultats très voisins pour les spectres de neutrons 

rapides. 

D'une nature toute différente, mais également 

liés à l'irradiation neutronique, les taux de production 

d'impuretés dus aux réactions nucléaires sont également 

très importants à considérer, particulièrement quand les 

impuretés sont gazeuses (n,p), (n a ), car alors elles favorisent 

le gonflement qui est un problème technologique grave 

pour les réacteurs à neutrons rapides. Dans ce domaine, il 

serait très souhaitable que l'A.I.E.A. fasse également une 

recommandation.

106 L O TT e t al. 

TABLEAU I 

SECTIONS EFFICACES DE TRANSFERT D'ENERGIE ET TAUX 

DE DEPLACEMENT DANS L'ALUMINIUM (N=2.23E22 AT/G) 

B. INF

I A E A - S M -1 7 0 /6 5 107 

TABLEAU I (SUITE) 


DE DEPLACEMENT DAMS L'ALUMINIUM ( N = 2.23E22 AT/G) 

B.INF(MEV) T EV.CM2/G D EV. CM 2/G DPG CM2/G 

0.8652F--01 Г . 1362F 04 0.9504F 03 0.95C4E 01 1 ./E 

0 . 1111F 00 0.8574F 03 0.5875F 03 0.5875E 01 l . / E 

0 . 1 228F 00 0.3419F 03 0.23 26F 03 C.2326E 01 1 ./E 

0.1357F 00 0 . 1454F 04 0.9788F 03 0.9788F 01 L ./E 

0.1 500F 00 0.2679F C4 0.1790F 04 0.1790F 02 l ./ E 

0.1657F 00 0.1507F 04 0 . C987F 03 0.9987F 01 l ./ E 

0 .1 8 3 2F 00 0 . 1054F 04 0.6913F 03. 0 .6 9 1 3E 01 l ./ E 

0.2024F 00 0 . 177^F 04 0.1153F 04 0.1153F 02 l ./ E 

0.2 237F 00 0 . 1337F 04 0.8592F 03 0.8592F 01 l ./ E 

0 .2 477F 00 0.9362F 03 0.5941F 03 0.5941E 01 l ./ E 

0 . 2732e 00 0.1986F C4 0.1242F 04 0.1242E 02 FIS. 

0.3020F 00 0.1869F 04 0 . 1 152p 04 0.1152F 02 FIS. 

0.3337F 00 0.1722F 04 0.1045F 04 0.1045E 02 FIS. 

Ö.3688F 00 0.1753F 04 0 . 1050F 04 0.1C50F 02 FIS. 

0.4076F 00 0.2918F 04 0.1724F 04 0.1724F 02 - IS. 

0.4505F 00 0.2324F 04 0 . 1356F 04 0.1356E 02 F IS. 

0.4979F 00 0.2768F 04 0.1594E 04 0.1594E 02 FIS. 

0 .5502* 00 0.2513F 04 0.1425F 04 0.1425F 02 F IS . 

0.6081F 00 0.3065F 04 0 . 1705F 04 0.1705F 02 FIS. 

0.6721F 00 0.2820F 04 0.1540F 04 C.1540F 02 F IS. 

0.7427F 

0.8208F 

0.9072F 

00 

00 

00 

0.4334F 

C.3642F 

0.2903F 

04 

04 

04 

0.2323F 

0 . 1938F 

0 . 1509F 

04 

04 

04 

0.2323E 

0.193eE 

C.15C9F 

02 

02 

02 

r i s . 

FIS. 

FIS. 

0.1003F 01 0.3178F 04 0 . 1604F 04 0.1604F 02 F IS. 

0.1108F 01 0.5135F 04 0.2553F 04 0.2553E 02 F ÍS. 

0 . 1 225F 01 0.4514F 04 0.2197F 04 0.2197E 02 FIS. 

0.1353Г 01 0.4667F 04 0.2206F 04 0.2206E 02 FIS. 

0.14Q6F 01 0.4886E 04 0.2255F 04 0.2255F 02 FIS . 

0.1653F 

0.1827F 

01 

bl 

0.5426F 

0.5580F 

04 

04 

0.2433F 

0 .2 4 27F 

04 

04 

0.2433E 

0.2427E 

02 

02 

FIS. 

FIS. 

0.2019F 

0.2231F 

01 

01 

0.6745F 

0.5869F 

04 

04 

0.2854F 

0.2419F 

04 

04 

0.2854E 

0.2419F 

02 

02 

FIS. 

F IS. 

0.2466F 

0.2725F 

01 

01 

0.7873F 

0.8053F 

04 

04 

0.3096F 

0.3010F 

04 

04 

0.3096E 

0.3010F 

02 

02 

FIS. 

FIS. 

0.3012F 

0 .3 329F 

01 

01 

0.7645F 

0.8649F 

04 

04 

0.2808F 

0.3095F 

04 

04 

0.2808E 

0.3C95E 

02 

02 

FIS. 

FIS. 

0.3679F 01 0.8904F 04 0.3C72F 04 0.3C72E 02 FIS. 

0.4066F 01 0.9278F 04 0.3061F 04 0.3061E 02 = IS. 

0.4493F 01 0.9282E 04 0.2975F 04 0.2975E 02 F IS. 

0.4966E 01 0.9276F 04 0.2895F 04 0.2895E 02 FIS. 

0.5488F 01 0.9949F 04 0.2926E 04 0.2926E 02 F IS. 

0.606 5E 

0.6703F 

0.7408E 

01 

01 

01 

0.1078F 

0.1126F 

0.1102F 

05 

05 

05 

0.3034F 

0.2984E 

0.2780F 

04 

04 

04 

0.3034F 

0.2984F 

0.2780E 

02 

02 

02 

F IS . 

F IS. 

FIS. 

0.8187F 01 0.1156F 05 0.2777F C4 0.2777E 02 FIS. 

0.9048F 01 0.1187F 05 0.2769F 04 0.2769F 02 FIS. 

0.1000E 

0.1105F 

02 

02 

0 .1 293F 

0.1394E 

05 

05 

0.2862F 

0.2925F 

04 

04 

0.2662E 

0.2925E 

0 2 ' 

02 

F IS. 

FIS. 

0.1221F 

0.1350F 

02 

02 

0.1549F 

0.1719F 

05 

05 

0.3076F 

0.3221F 

04 

r>4 

0.3076E 

0.3221E 

02 

02 

FIS. 

FIS. 

0.1492F 02

108 LO TT et a l. 

TABLEAU II 


DE DEPLACEMENT DANS LE SILICIUM (N=2.14E22 AT/G) 

R. INF( MEV ) T EV.CM2/G D EV.CM 2/G DPG CM2/G 

0 .4140F-06 0.3830F 00 0.3085F 00 G. 3075E-02 l./E 

0.531 f>E- 06 0.3-’ 69F 00 0 . 2714F 00 0.27C1E-02 l./E 

0.6826F-06 0.2979E 00 0 . 2400F 00 0. 2384F-02 l./E 

0.8764E-06 0.2641 F 00 0.2128F 00 0.21C7E-02 l ./ E 

0.1125^-05 0.2405F 00 0 . 1940F 00: 0 .1 9 1 2E-02 l ./ E 

0 . 1 445F-05 0.2137F 00 0 . 17 24F 00 0 . 1689E-02 l ./ E 

o.1855 c- o5 0 .1 857F 00 0 .-1.500F 00 0. 1455E-02 l ./ E 

0.23»2F-05 0 . 1702F 00 0.1377F 00 0 .1 3 1 8F-02 l ./ E 

0.3058F-05 0.1517F "0 0.1230F 00 C . 115 4 E - 0 2 l./E 

0.3928F-05 0.1346f 00 0. 1C°4f 00 0.9976E-03 l./E 

0.5043F-05 0.1227F 00 0 . 1001F 00 С. 8770E-03 1 . /Е 

0 • 6476F-OS 0.1138F 00 '.9334F -01 0.7738E-03 l ./ E 

О.ЯИ 5e -OS 0 .1 077F 00 0.8896E -01 0.6845E-03 1 ./E 

0.1O68F-04 0.1062F oc 0 . P 840F -01 0.6205E-03 l./ E 

0.1^71- - 04 0 .1 063F 00 0.8922F -01 0. 5538F-03 l ./ E 

0 . 1760P-04 0.1072F 00 0 . 9105F -01 C.4758F-03 l ./ E 

0 .? 260F- 04 0 . 1 150F 00 0.9867F -01. 0.4285E-03 l ./ E 

0 . 2902F-04 0 . 1263F 00 0.1094F 00 0 . 3777F-03 l ./ E 

0.3727F-04 0.1.421F 00 0.1243F 00 C.3232E-03 l ./ E 

0.4785F-04 0 . 1664F 00 0.1464F 00 0 .2 8 5 1E-03 l ./ E 

0 . 6144F-04 0 . 1993F 00 0 . 1761F 00 0 . 2503E-03 1 ./£ 

0.7889^-04 0.2433F 00 0.2154F 00 0 • 2200F-03 l ./ E 

0 .1 0 1 3F-03 0 .3 0 1 7F 00 0.2669F 00 0 . 1956E—03 l ./ E 

0 .1 4 01F-03 0.3776F 00 0.3336F 00 0.1721E-03 l ./ E 

0 .1 670E-O4 0.4762F 00 0.4197F 00 C .1510E-03 l ./ E 

0 .2 1 44F—03 0.6042F 00 0.53C7F 00 0 . 1333E-03 1 ./E 

0 .2 7 4 4 F -03 0.7719F 00 0.6752F 00 0 .1 1 82E-02 l ./ E 

0 • 3536F-03 0.9855F 00 о .«5 70Г 00 0.6073F-02 l ./ E 

0.4540F—03 0 .1 260F 01 0.1091F 01 0.1.139F--01 l ./ E 

0.5829F-03 0 . 1610F 01 0.1386F 01 0.1677F-01 1 ./E 

0 . 7485F-03 0.2069F 01 0.1772F 01 C.2187F-01 l ./ E 

0 .9 6 1 1F-03 0 .2 6 6 1 E 01 0.2264F 01 0 • 2674F-01 1 . /с 

0 . 1 234F-0? 0.3425F 01. 0.2897F ■’ 1 0.3286E-01 1 . /Е 

0 . 1 585F-02 0.4401F 01 0.3698F 01 C.4048E-01 l ./ E 

0 . 2035E-02 0.5652F 01 0.4717F 01 0 .5 105E-01 l ./ E 

0.2613F-0? 0.7282F 01 0.6034F 01 ^.6317F-01 l ./ E 

0.3355F-02 0.93836 Cl 0.771 4P 01. 0.792CE-01 l ./ E 

0.4307F-0? 0.1207F 02 0.9839F 01 0.1002E 00 l ./ E 

0.5531 F-02 0.1536F 02 0.1242E 02 0.1256E 00 l ./ E 

0 .7 1 02F-02 0.1860F 02 0 . 1491e 02 C.15C4F 00 l ./ E 

0 .9 1 1 QF-0? 0.2140F 02 0 . 1700F 02 C.1706F 00 l./t 

0.1171 F- 01 0.2505E 02 0.1971F 02 C.1981F 00 l ./ E 

0.1 503F-01 0.2979F 02 0.2321F 02 C.2331E 00 i . / E 

0.1930F-01 0.3586F 02 0.2764F 02 P.277CE СО l . / t 

0.2479E-01 0.4388F 02 0.3345F 05 0.3348F 00 l ./ E 

0 . 3 183E-01 0.5464F 02 0 . 4 114F 02 0 .4 П 4 Е 00 l ./ E 

0 .4 087F-01 0.7150F 02 0.5308F 02 0.53C8E 00 l ./ E 

0 . 5247F-01 0 .1 1 8 OE 03 0.3627Г 02 0.8627F 00 1 ./E 

0 . 6738F-01 0 . 1463F 03 0. I055F 03 0.1C55E 01 l ./ E

IA E A -SM -1 7 0 /6 5 109 

TABLEAU I I ( SUITE) 


DE DEPLACEMENT DANS LE SILICIUM (N=2.14E22 AT/G) 

B.IMF(MEV) T EV .CM2/G D EV.CM2/G DPG CM2/G 

0.8652F-•01. 0 . 1 172F C3 0.8320F 02 0.8320E 00 l . / E 

0.1 I11F 00 0 . 9287F 02 0.6528F 02 C.6528F 00 l ./ E 

0 . 1 728F 00 0 . 76 91E 02 0.5362F 02 0.5362E 00 l ./ E 

0 . 1 457^ 00 0.2073F 03 0 . 1403F 03 0.14C3F 01 l ./ E 

0.1 500F 00 0 . 8 148F 03 0.5480F 03 C.5481E 01 l ./ E 

0 . 1 657F 00 0 . 1 519F 04 0.1021F 04 0.1021E 02 l ./ E 

0.1R32C 00 0.2151F 04 0.1442F 04 0.1442F 02 l ./ E 

0 .2 024Ç 00 0.2035F 04 0.1355F 04 0.1355E 02 l ./ E 

0 .2 73 7F 00 0.1675F 04 3.1105F 04 0 . 1 105E 02 l ./ E 

0.2472F 00 0 . 1413F 04 0.9203F 0.3 0.9203F 01 l./ E 

0.2732F 00 0.1 3356 04 0.P601F 03 0 .8 6 0 1 E 01 FIS. 

0.3020F 00 0 . 1300E 04 0.R272F 03 0.8272E 01 ? IS. 

0 .3 ^ 3 7F 00 0 . 1300F 04 0.8166F 03 0.8166F 01 FIS. 

0.3688F 00 0 . 1320F 04 0 . 8173F 03 0.8173F 01 FIS. 

0.4076E 00 0 . 1364F 04 0 . 8320F 03 0.8320F 01 FIS. 

0.4505F 00 0 . 1454F 04 0.8736F 03 0.8736E 01 FIS. 

0.4479F 00 0.2582F 04 0 . 1520Г 04 C.1520F 02 FIS. 

0.55021= 00 0.3339F 04 0 . 1946F 04 0.1946E 02 - IS. 

0.60R1F 00 0 .1 813F 04 0 . 1039F 04 0.1039F 02 FIS. 

0.6721F 00 0 . 1822F 04 0 . 1026F 04 0 . 1026F 02 FIS. 

0.7427F ">0 0.28°2F 04 0 . 1593F 04 0.1593 F 02 - IS. 

0.R20RF 00 0.3583F 04 0 . 1045F '■4 0.1945F 02 FIS. 

0.9072F 00 0.4073F 04 0.2163E 04 0.2163E 02 FIS. 

0 . 1003«: 01 0 .3 7 1 5F "14 0 . 1935F 04 0.1935E 02 FIS. 

0 . 1 108F 01 0 .2 7 1 2F 04 0 . 1380F 04 0 . 1380E 02 FIS. 

0.1225F 01 0.3405F 04 0.1692F 04 0.1692E 02 - IS. 

0 . 1 353F 01 0.394 2F 04 0.1,910F H 4 0.1910F 02 - IS. 

0.1496F 01 0.4725F 04 0.2228F 04 0.2228F 02 FIS. 

0 . 1 653F 01 0.5086F 04 0.2340F 04 0.2340E 02 FIS. 

0.1 P27F 01 0.6847F 04 0.3072F 04 0.307 2F 02 FIS. 

0.2019F 01 0.5176F 04 0 . 2291F 04 0 .2 291E 02 FIS. 

0.2231F 01 0.494 8F 04 0 . 2141F 04 0.2141F 02 - IS . 

0 . 2466F 01. 0.561 IF 04 0.7339F 04 0.2339E 02 r I S. 

0.2725F 0 1 0.5522E 04 0.2276F 04 0.2226F 02 FIS. 

0 .3 0 1 ?F 01 0.5535F 04 0 . 213PF 04 0 . 2 13 8 E 02 FIS. 

0.3329E 01 0.5290F 04 0 . 1963F 04 C. 1963 F 02 - I S . 

0.3679F 01 0.541 of n4 0. 191.8E 04 0. 1918E 02 F IS. 

0 .4066e 01 0.6801F 04 0.2307F 04 0.2307E 02 - IS. 

0.4493F 01 0 . 7633F 04 0.2523F 04 0.2 523 E 02 FIS. 

0.4966F 01 0.7832F 04 0.2543F 04 0.2543E 02 FIS . 

0.5488F 01, 0.8088F 04 0 . 2540Г 04 C.2549E 02 FIS. 

0 .6 0 6 5F 01 0.7905F 04 0.2380F 04 0.2380E 02 r IS. 

0.6703E 01. 0.7797F 04 0.2234F 04 0.2234E 02 FIS. 

0.740RF 01 0.8222F 04 0.2237F 04 0.2237E 02 FIS. 

0.Я187Е 01 0.8346F 04 0.2151F 04 0.2151E 02 FIS. 

0.9048F 01 0.8882F 04 0.2162F 04 0.2 1


TABLEAU I I I 


DE DEPLACEMENT DANS LE CHROME (M=1.15E22 AT/G) 

B.INF(MEV) T EV.CM2/G D EV•CM 2/G DPG CM2/G 

0 .4 1 40F—06 0.3198F 01 0 .26 72F 01 C. 2671F-01 l ./ E 

0 .5 3 1 6F-06 0.2823F 01 0.2359F 01 0.2358E-01 l ./ E 

0.6826E-06 0.2488F 01 0.2078F 01 0 . 2077E-01 l ./ E 

0.8764F-06 0.2212F 01 0.1848F 01 0 . 1 847F-01 l ./ E 

0 . 1 125F-05 0.2016F 01 0.1684F 01 0 . 1682F-01 l ./ E 

0 . 1445F-05 0.1783F 01 0.1490F 01 0.1487F-01 l ./ E 

0 . 1 855F-05 0.1530F 01 0.1279F 01 0 . 1275F-01 l ./ E 

0.2^82F-05 0.1351F 01 0.1129F 01 C. 1 125E-01 1 . / 6 

0 . 3058F-05 0.1187F 01 0.9917F 00 0.9861E-02 l ./ E 

0.3928F-06 0 . 1048F 01 0 . 8759F 00 0.8687E-02 l ./ E 

0 .5 043F-05 0.9299F 00 0.7775F 00 0.7683F-02 l ./ E 

0 .6 4 7 6 F -05 0.8256F 00 0.6906F 00 0 .6787F-02 l ./ E 

0 .8 3 1 5F-05 0.7320F 00 0.6127F 00 0 . 5974E-02 l ./ E 

0 . 1O68F-04 0.6710F 00 0.5620F 00 0.5423F-02 l ./ E 

0 .137 l e - 04 0.6067E 00 0.5087F 00 G.4833E-02 l ./ E 

0 . 1760F-04 0.5316F 00 0.4464F 00 0.4138E-02 l ./ E 

0 .2 2 6 0 F -r>4 0.4861F 00 0.4C90E 00 C.3672F-02 l ./ E 

0.2902F-04 0.4462F 00 0.3765F 00 0.3228F-02 l ./ E 

0 . 3727F-04 0.4144F 00 0.351 IF 00 0.2820E-02 l ./ E 

0 • 4785F-04 0.3935F 00 0.3350F 00 C.2464E-02 l ./ E 

0 .6 1 44F-04 0.3893F 00 0.3337F 00 0 .2 194E-02 l ./ E 

0.7889F-04 0 . 3940F 00 0.3395F 00 0.1 9 3 1 E-02 l ./ E 

0 . 1013F-03 0.4178E 00 0.3623F 00 G .1740F-02 l ./ E 

0.1301F-03 0.4567F 00 0.3985F 00 0 . 1 565E-02 l ./ E 

0.1 670F-03 0.5074F 00 0.4457F 00 C .1347E-02 l ./ E 

0 .2 1 44F-03 0.5887F 00 Г|. 5190F oo C .1204E-02 l ./ E 

0.2754F-03 0.6997F 00 0.6 182F 00 0.1C76F-02 l ./ E 

0 . 3 536F-03 . 0.8438F 00 0.7467F 00 0. 1214E-02 l ./6 

0.4540F-03 0.1039F 01 0.9186F 00 0 . 3314E-02 l ./ E 

0.5 829F-03 0.1306F 01 0.1151F 01 0.86C7E—02 l ./ E 

0 ,7 4 8 5 F -03 0.1658F 01 0 . 1457F 01 C .1801F-01 l ./ E 

0 .9 6 1 1F-03 0.2116F 01 0 . 1851F 01 0 . 2526F-01 l ./ E 

0 . 1 234F-0? 0.2786F 01 0.2423F 01 0.3123F-01 l ./ E 

0 . 1 585F-02 0.3690Б 01. 0.3193F 01 0 .3 8 1 1E-01 l . / E 

0.2035F-02 0.5239E 01 0.4518F 01 0 .5 1 0 1 E-01 l ./ E 

0 .2 6 1 3F-02 0.9658F 01 0.8282F 01 0 . 8926E-01 l ./ E 

0 .3 3 5 5 F -02 0.2789F 02 0.2378F 02 0.2485E 00 l ./ E 

0.4307F-02 0.4313F 02 0.3656E 02 0.3766E 00 l ./ E 

0.5531F-02 0.4P88F 02 0.4118F 02 0.4193E 00 l ./ E 

0 .7 1 02F-0? 0.5501F 0? 0.4604F 02 0.4663E 00 l ./ E 

0.9X 19E—02 0.365 1F 02 0.3035F 02 0.3053E 00 l ./ E 

0 .1 1 71F-01 0.2649F 02 0.2186F 02 0.2198E 00 l./ E 

0 .1 503F-01 0.2205E 0? 0 . 18C5F 02 0.1808E 00 l ./ E 

0 .1 930F-01 0.2942F 02 0.2389F 02 0.2393E 00 l ./ E 

0 • 2479F— 01 0.4287F 02 0.3448F 02 0.3454F 00 l ./ E 

0.3183F-01 0.5235E 02 0.4176F 02 0.4180E 00 l ./ E 

0.4087F—01 0 .U 5 2 E 03 0.9089F 02 0.9093E 00 l ./ E 

0.5247E-01 0.1316E 03 0.1032E 03 0.1032E 01 l ./ E 

0 . 6738F-01 0.6517F 0? 0.5060F 02 0.5060E 00 l . / E

I A E A - S M -1 7 0 /6 5 111 

TABLEAU III(SUITE) 


DE DEPLACEMENT DANS LE CHROME (N=1.15E22 AT/G) 

B.INF(MEV) T EV.CM2/G D EV.CM2/G DPG CM2/G 

0.8652F-•01 0.3382F C3 0.2594F 03 0.2594E 01 l ./ E 

0.1 U 1F 00 0 • 2 39 3 E 03 0.1875F 03 C.1825E 01 l . / E 

0.1728F 00 0.2139F 03 0.1622F 03 0.1622E 01 l ./ E 

0.1357F 00 0.5808F 03 0.4385F 03 C.4385E 01 l ./ E 

0 .1 500F 00 0.4456F 03 0 .3 3 5 1 E 03 0.3351E 01 l ./ E 

0.1657F 00 0.307*E 03 0.2304F 03 0.2304E 01 l ./ E 

0.1842F 00 0.271 IF 03 0.2020F 03 0.2020E 01 l ./ E 

0.7024F 00 0.2307F 03 0.1711F 03 0 .1 7 1 1E 01 l ./ E 

0.2737F 00 0 . ‘:*096F 03 0 .2284F 03 0.2284E 01 l ./ E 

0.2472F 00 0.7357F 03 0.1732F 03 0.1732E 01 l ./ E 

0 .? 7 3 ? f o 0 0.2007F 03 0 . 1463F 03 0 .1 4 6 3 E 01 FIS. 

0.3020F 00 0.3772F 03 0.2725F 03 0.2725E 01 FIS. 

0 . 3337F 00 0.3781F 03 0.2711F 03 0.2711E 01 : IS. 

0.3688F 00 0.4101F C3 0.2920E 03 0.2920E 01 FIS. 

0.4076F 00 0.4924F 03 0.3490E 03 0.34°0E 01 - IS. 

0.4505F 00 0.5684E 03 0.4008E 03 0.4C08E 01 FIS. 

0.4474F 00 0.5800F 03 0.4075F 03 0.4C75E 01 FIS. 

0.5502F 00 0.5047P 03 0.3511F 03 0.3511E 01 - IS. 

0.6081 F 00 0.7Ч91Е 03 0.5527F 03 0.5527E 01 FIS. 

0.6721F 00 0.6755F 03 0.4276F 03 0.4276E 01 FIS. 

0.7477F 00 0 . 1049F 04 0.7112F 03 0 . 7112E 01 FIS. 

0.8708F 00 0 .1 065F 04 0.7143E 03 C.7143E 01 FIS. 

0.9072P 00 0.9394F 03 0.6265E 03 0.6265E 01 FIS. 

0.1003F 01 0 . 1005F 04 0.6648F 03 0.6648E 01 FIS. 

0 . 1 108F 01 0 . 1030F 04 0.6738Ç 03 0.6738E 01 FIS. 

0.172 5F 01 0 .1 5 1 1Г 04 0.9719F 03 0.9719E 01 FIS. 

0.1353F 01 0.1347F 04 0.8603F 03 0.86C3E 01 = IS. 

0.1496F 01 0 . 1331F 04 0.8488F 03 0.8487E 01 FIS. 

0.1653E 01 0.1475E 04 0.9321F 03 0.9321E 01 FIS. 

0.1827F 01 0.7098F 04 0. 1310F 04 0.1310E 02 FIS. 

0.2019F 01 0.7379F 04 0.1472F 04 C.1472E 02 FIS. 

0.2231E 01 0.2286F 04 0 . 1401F 04 0 •1 4 0 1 E 02 FIS. 

0.7466E 01 0.2444F 04 0. 1481F 04 0 . 1481E 02 FIS. 

0.272 5F 01 0.2545F 04 0 . 1526F 04 0.1526E 02 FIS. 

0.3012F 01 0 .2 6 1 2E 04 0 . 1553F 04 0.1553E 02 FIS. 

0.3379F 01 0.7761F 04 0 . 1633F 04 0.16ЭЗЕ 02 FIS. 

0.3679F 01 0.2813F 04 0.1657E 04 0.1657E 02 FIS. 

0.4066F 01 0.7952F 04 0.1722F 04 0.1722E 02 F IS. 

0.4493E 01 0.3123F 04 0.1801E 04 0.1801E 02 FIS. 

0.4966F 01 0.3771F 04 0.1864E 04 0.1864E 02 FIS. 

0.5488F 01 0.3406F 04 0 . 1918F 04 0.1918E 02 FIS. 

0 .6 065E 01 0.3602É 04 0 . 1996E 04 C.1996E 02 FIS. 

0.6703F 01 0.3835F 04 0.2087E 04 0.2087E 02 FIS. 

0.7408E 01 0.4026F 04 0.2149F 04 0.2149E 02 FIS. 

0.8187F 01 0.4242E 04 0.2213E 04 C.2213E 02 FIS. 

0.9048E 01 0.4437F 04 0.2258E 04 0.2259E 02 F IS. 

O.lOOOE 02 0.4720E 04 0.2338F 04 0.2338E 02 F IS. 

0.1105E 07 0.5075F 04 0.2440E 04 0.2440E 02 FIS . 

0 . 1 221E 02 0.5497F 04 0.2564F 04 0.2564E 02 FIS. 

0.1350F 02 0.6175F 04 0.2779F 04 0.2779E 02 FIS. 

0.1492F 02


TABLEAU IV 


DE DEPLACEMENT DANS LE FER (N=1.078E22 AT/G) 

B.IN F( MEV) T EV.CM2/G D EV.CM2/G DPG CM2/G 

0 .4 1 40F-06 0.2476F 01. 0.2C73F 01 0.2C71F-01 l ./ E 

0.5316F-06 0.21P5F 01 0.1830F 01 0 .1 827E-01 l./ E 

0.6826^-06 0 . 1926F 01. 0.1613F 01 0 .161OF-O1 l ./ E 

0.8764F-06 0 . 1704F 01 0 . 1427F 01. 0.1423E-01 l./ E 

0.1 1 2 5F —05 0 .1 521F 01 0 .1 274F 01 C.1269E-01 1 ./E 

0 • 1.445F- 05 0 . 1336F 01. 0 . 1 1 19P 01 0 .1 1 13F-01 l ./ E 

0 . 1 855F-05 0.1184F 01 0.9919Г 00 0.98396-02 1 ./E 

0 .2 3 8 ?F-OR 0.ir>5OF n 0.8802F 00 C.8699E-02 1 ./e 

0.3058Г-05 0.9264F 00 0.7766F 00 n .76338-02 l ./ E 

0.3P7OC-OC 0.8216P 00 0.6891F 00 0 .6 7 2 1F-02 1 ./E 

0.5043F-O5 0.7367F 00 0.6183P 00 0 . 5 965F-0 2 l ./ E 

0 • 6476F-05 0.65R4P 00 0.5532F 00 0.5252E-02 1 ./E 

0 .8 3 1 5r - 05 0 . 5937F 00 0.4995F 00 C .4Í35E-0? l ./ E 

0.1 068F-04 0 .5 4 3 ’ F 00 0.4580F 00 0 .4 1 1 7F—02 l ./ E 

0 . l 371F- 04 0.4968F 00 0.4200F 00 0 . 3606F-02 l ./ E 

0 .1 760F-04 0.4646F 00 0.3941F 00 0 .3 1 79E-02 l . / E 

0.2260Г-04 0.4452F 00 0.3793F 00 0 .2 8 ] 4E-02 l ./ E 

0.2902F-04 0.4361F 00 0.3736F 00 0 . 2478E-02 l ./ E 

0.37?7F-04 ° . 4422F 00 0.3810F 00 0.2195F-02 l ./ E 

0.47R5F-04 0 . 4607F 00 0.3995F 00 С . 1921 F—02 l ./ E 

0 . 6 144F-04 0.49R7F 00 0.4353F 00 0 . 1692E-02 l ./F 

0 . 7RR9F- 04 0.^59°F 00 0 •4 9 1 5F 00 0 . 150CF-02 l ./ E 

0 .1 0 1 3F-03 0.6468Г 00 0.5707F 00 0 .1 326E-02 l ./ E 

0 .1 4 0 1 F-03 0.7651F 00 0.6780F 00 0.1170^-02 l ./ E 

0.1670P -0’ 0.9199F no 0 . 8179F 00 С .1023E-02 l ./ E 

0 .2 1 44F-01 0 . 1 122P 01 0.9997Г 00 0.9C70E-03 1 ./E 

0 . 2754F-03 0 .1 375F 01 0 . 1227F 01 0.7952E-03 1 . /E 

0.3536F-03 0.1691F 01 0.1507F 01 0.7074E-C3 l ./ E 

0 «4 540F-03 0.2075F 01 0 . ie44F 01 C.9336E-03 l ./ E 

0.5R29F-03 0.2531F 01 0 . 2243F 01 0.135 2E-01 1. /Е 

0 .7 4R5F-03 0.3052F 01 0.2696F 01. 0 • 3 28 9F—01 l ./ E 

0.961 IF-03 0.7863F 01 0.6746F 01 0 . 8077F-01 1. /Е 

0. 1234F-02 C.4604F 01. 0.4031F 01 0.5556E-01 l ./ E 

0 .1 5 8 5 F -0? 0.547PF 01 0.4771F 01 0.5973E-01 l . / E 

0 . 2O35F-02 0.637RF 01 0.5527F 01 0 . 6343F—01 l ./ E 

0 .2 6 1 3F-0? 0.73R3F 01 0.6361F 01 0 . 69 57F-01 l ./ E 

0.3355F-02 0.9853F 01 0.8434F 01 C.8906F-01 l . / E 

0 .4307F-02 0 . 1032F 02 0.8784F 01 0.9076E—01 l ./ E 

0.5531P-0? 0.2 097F 02 0.1773F 02 0 .1 8 1 1E 00 l ./ E 

0 .7 1 02F-02 0.4741F 02 0.3984F 02 0.4038E 00 l ./ E 

0 .9 1 1 9F-02 0 . 1970F 02 0.1644E 02 0.1655E 00 l ./ E 

0 . 1 171E-01 0.155 8^ 02 0.1291F 02 0.1300E 00 l ./ E 

0. 1503F-01 0.1281P 02 0.1054F 02 0.1056F 00 l ./ E 

0 .1 930F-01 0.6050F 01 0.4943F 01 0.4947E-01 l ./ E 

0 .2 479F-01 0.331 OF 0’ 0.2678F 03 0.2684E 01 l ./ E 

0 .3 1 R3F-01 0 . 1117P 03 0.8962F 02 0.8973E 00 l ./ E 

0.40R7F-01 0.8847^ 02 0.7032E 02 0.7036E 00 l ./ E 

0 .5 247F-01. 0.9000F 02 0.7095F 02 C.7C96E 00 l ./ E 

0.673RF-0T 0.2153F 03 0 . 1678F 03 0.1678F 01 l ./ E

I A E A - S M -1 7 0 /6 5 И З 

TABLEAU IV ( SUITE) 


DE DEPLACEMENT DANS LE FER (N=1 .07RE22 AT/G) 

B.INF(MEV) T EV.CM2/G D EV.CM2/G DPG CM?/G 

0.8652F--01 0 .1 400F 03 0. П 5


TABLEAU V 

SECTIONS EFFICACES DE TRANSFERT 0*ENERGIE ET TAUX 

DE DEPLACEMENT DANS LE NICKEL (N=1.026E22 AT/G) 

B. INF(MEV) T EV.CM2/G D EV.Cf'2/G DPG CM2/G 

0.4140Г-06 0.6241F 01 0.5176F 01 0 . 5 173F-01 L ./E 

0 .5 3 1 6F- 06 0.5503F 01 0.4563F 01 0.4560F-01 l ./ E 

0.6«26F-06 0.485PF 01 0.4024F 01 0 .4 0 2 0 F -0 1 L./E 

0.8764F-O6 0.4294F 01 0. 3561F 01 0.3556Ë-01 l ./ E 

0 . П 2 5F-05 0.3 829F 01 0.3175F 01 0 .3 1 69E-01 l ./ E 

П .1445F-05 0.3356F 01 0.2783F 01 0.2775E-01 l ./E 

0 . 1 855p-05 0 . 2960F 01 0.2455F 01 0.2444E-01 L./E 

0.2382F-05 0.2613F 01 0.2168F 01 C.2 1 54E-01 l . / E 

0 . 3058F-05 0.2321F 01 0 . 1926F 0] 0 .1 9C8E-01 l ./ E 

".3928F-05 0.2050F 01 0. 1702e 01 0 . 1679F-01 L./E 

0.5043F-05 0.1 818F 01 0.1510F 01 0 . 1480E-01 l ./ E 

0 .6 4 7 6 F -05 0 . 1617F 01 0.1344F 01 0 . 13C5F-01 L./E 

0.Я315Р-0 5 0 . 1445E 01 0.1202F 01 C.1153E-01 l ./ E 

0 . 1 068F-04 0 .1 311F 01 0 . 1092F 01 C. 1 029E-01 l ./ E 

0 . 1 371F-04 0 . 1 177F 01 0.9821F 00 C.9011E-02 l ./ E 

0. 1.760F-04 П. 1.074F 01 0.8980F 00 C.7940E-02 l ./ E 

0.2 260F-04 0.9928E 00 0.8331F 00 0.6996E-02 l ./ E 

0.2902E-04 0.9380F oo 0.7903F 00 0 .6 1 90E-02 L./E 

0 .3 7 ?7 f _04 0 . 4034F 00 0.7652F 00 0 . 5454F-02 l ./ E 

0.478 5F- 04 0.8948F 00 0.7626F 00 0.4806E-02 l ./ E 

0 .6 1 44E-04 . 0.9155F "0 0.7856F 00 0.4239Г-02 l ./ E 

0 .7 889F-04 0.9692F 00 0.8376F 00 0 . 3738E-02 l ./ E 

0 .1 0 1 3F-03 0 .1 066F ni 0.927 7F oo 0 . 3334E-02 l ./E 

0.1301F-O3 0.1204F Cl 0.1054F 01 0 . 2929E-02 l ./ E 

0 . 1 670F-03 0.1400F 01 0.1232F 'Ч 0.2580E -02 l ./ E 

0 .2 1 44F-03 0 . 1666F 01 0 . 1473F 01 0.2273E-02 l ./ E 

0 .2 754F-03 0.2019F "1 0.1791E 01 0.2003E -02 l ./ E 

0 .3 536F-03 0.2472F 01 0.2195F 01 0 . 1766F-02 l ./ E 

0.4540F-03 0 .3 0 1 5F 01 0.2675F 01 0 . 1 558E-02 L./E 

0 .5 829F-03 0.3652F 01 0.3234F 01 0.1471E-01 l ./ E 

0 • 7485F-03 0.4456F 01 0.3935F 01 0.4483E-01 l ./ E 

0 .9 6 1 1F-03 0.5569F 01 0.4900F 01 0 .666 2Г-01 l ./ E 

0.1234F-02 0.7113E 01 0.6232F 01 0 . 8542F—01 l ./ E 

0. 1 585E-0? 0 . 9299F 01 0.8107F 01 0.1024E 00 1 ./E 

0 . 2035F-02 0 . 1243F 02 0. 1C78F 02 0.1256F 00 l . /t 

0.2613F-02 0.1757F 02 0.1516F 02 0.1664E Oc- l ./ E 

0.335 5F-02 0.3023F 02 0.2593F 02 О.2749E 00 l ./ E 

0.4307F-02 0.4437F 02 0.3783E 02 0.3924E 00 l ./ E 

0.5531E-02 0.3002F 02 0.2544F 02 0.2601E 00 i ./e 

0 .7 1 02E-02 0.2592E 02 0.2182F 02 0.2211 E СО l . /Е 

0.911 9F-02 0.5303F 02 0 .4430F 02 0.4458E 00 l ./ E 

0 . 1 171E-01 0.2087F 03 0 . 1733F 03 0.1745F 01 l ./ E 

0.1.503F-01 0.3482F 03 0.2873E 03 0.2882E 01 l ./ E 

0 . 1930F—01 0.1286F 03 0 . 1053F 03 0.1054F 01 l ./ E 

0 . 2479F-01 0.1573F 03 0 . 1276F 03 0.1280E 01 l ./ E 

0.3183E-01 0.8 85 8F 02 0.7132F 02 C.7142E 00 l./E 

0.4087F-01 0.7491F 02 0.5974F 02 0.5979E 00 l ./ E 

0 . 5 247F-01 0.1981E C3 0.1562F 03 0.1562E 01 1 . /Е 

0.6738^-01 0.2558F ГЗ 0.2005F 03 0 .2 Г05F 01 l./E

IA E A -S M -n o/6 5 115 

TABLEAU V (SUITE) 


DE DEPLACEMENT DANS LE NICKEL (N=1.026E22 AT/G) 

B.INF(MEV) T EV.CM2/G D EV.CM2/G DPG CM2 /G 

0.8657F--01 0. 1980F C3 0. 1535F 03 0 . 1535E 01 l./ E 

0.1111F 0 0 0.1961F 03 0.1511F 03 0. 1 511E 01 l ./ E 

0 . 1778F 00 0.1465F 03 0.1174F "3 C.1124E 01 l ./ E 

0.1357F 00 0.387«F 03 0.2923F 03 0 .2923E 01 l ./ E 

0.1500F 00 0 . 4388F 03 0.3334F 03 0.3334E 01 l ./ E 

0.1657F 00 0.3247F 03 0.7459F 03 0.2459E 01 l ./ E 

0.1837F 00 0.3063F 03 0.2308F 03 0.2308E 01 1. /6 

0.2024F 00 0.4463F 03 0.3348F 03 0.3348E 01 l . / E 

0 .2 737F 00 0.4293F 03 0.3702F 03 C.3202E 01 l ./ E 

0 .2 4 7 ? f 00 0.3901F 03 0.2896F 03 0.2896F 01 l ./ E 

0.2732F 00 0.5100F 03 0 . 3766F 03 0.3767F 01 FIS. 

0.302 0F 00 0.4697F 03 0.3449F 03 0.3449E 01 FIS. 

0 ; 3337F 00 0 . 5 129F 03 0.3745F 03 0.3745F 01 r I S . 

0.3688F 00 0 . 3940F 03 0 . 2860F 03 C.2860E 01 FIS. 

0.4076F 00 0.5751F 03 0.4146F 03 0.4146F 01 FIS. 

0.4505F 00 0.5883F 03 0.4219F 03 0.4219 E 01 FIS. 

0.4979F 00 0.5773F 03 0.3764F 03 0.3764F 01 F IS. 

0.5502F 00 0.4780F 03 0.3381F 03 0.3381F 01 - IS . 

0 .6 0 8 )F 00 0.6803F 03 0.4787F 03 0.4782E 01 FIS. 

0.6721F 00 0.6479F 03 0.4578F 03 0.4 52 8E 01 FIS. 

0.7427F 00 0.7307E 03 0.5052F 03 0.5052E 01 - IS. 

0.8 208F 00 0 . 8378F 03 0.5740F 03 0.5749F 01 F IS. 

0.4072F 00 0.8212F 03 0.5611F 03 0.5611F 01 FIS. 

0 .1 003F 01 0.8712E 03 0.5 894F 03 0.5894E 01 FIS. 

0 .1 1 08r 01 0.1160F 04 0 . 7739F 03 0.7739E 01 FIS. 

0.122 5F 01 0 . 1386F 04 0.9178F 03 0.9178E 01 FIS. 

0.1353F 01 0 . 1 219F 04 0.8054F 03 0.8C54E 01 FIS. 

0.1496F 01 0. 1280F 04 0 . 8470F 03 C.8420E 01 FIS. 

0.1653F 01 0.1365F 04 0.8912F 03 0.8912E 01 FIS. 

0.1827F 01 0.1471F 04 0.Я528Е 03 0.9528E 01 - IS. 

0.2019F 01 0 . 1595E 04 0 . 1024F 04 0 . 1024E 02 FIS. 

0.2231F 01 0 . 1727F 04 0 . 1099F 04 0 . 1C99E 02 - IS . 

0.7466F 01 0.1816F 04 0 . 1148F 04 0.1148E 02 F IS. 

0.2725F 01 0.1837F 04 0 . 1153E 04 0.1153F 02 FIS. 

0 .3 0 1 2F 01 0 . 1832F 04 0 . 1 148F 04 0.1148E 02 FIS. 

0 .33?gp 01 0 . 1947F 04 0.1209F 04 C.12C9E 02 = IS. 

0.3679E 01 0.2050F 04 0.1267F 04 0.1267F 02 F IS. 

0.4066F 01 0.7134F 04 0.1311F 04 0 . 1311E 02 FIS. 

0.4493F 01 0.2119F 04 0 . 1305F 04 C.1305E 02 FIS. 

0.4966F 01 0.2144E 04 0 . 1318F 04 0.1318F 02 FIS. 

0 .5 4 8 8 e 01 0.7 29 9F 04 0 . 1396F 04 0.1396E 02 FIS. 

0.6065F 01 0.2423F 04 0 . 1453F 04 0.1453E 02 FIS. 

0.6703F 01 0.2526F 04 0.1494F 04 C.1494E 02 F IS. 

0.7408F 01 0.2621F 04 0. 1578F 04 0.1528F 02 FIS. 

0.8187F. 01 0.2764F 04 0 . 1586F 04 0.1586F 02 FIS. 

0.9048F 01 0.2973F 04 0 . 1650E 04 C.1650E 02 F IS . 

0.1000F 0? 0.3108F 04 0 . 1723F 04 0.1723E 02 F IS. 

0.1105F 02 0.3324F 04 0 . 1809F 04 0 .1 8 0 9 E 02 FIS. 

0.1271F 02 0.3627F 04 0 . 1935F 04 0.1935E 02 F IS. 

0.1350F 02 0.4034F 04 0.2108F 04 0.2108F 02 FIS. 

0.1492F 0?


TABLEAU VI 


DE DEPLACEMENT DANS LE CUIVRE (N=0.9479E22 AT/G) 

B.IN F( MEV ) T E V . C M 2 / G D EV.CM2/G DPG CM 2/G 

0 .4 1 40F-06 0.3141E 01 0.2R13F 01 C .2812F- 01 l./E 

0.5316F-06 0 .2 7 8 2 e 01 0 .7 3 4 7 e 01 0.2341E- 01 l./E 

0.6P26F-06 0.2478F 01 0.2087F 01 0.2085F-■01 l./E 

0 .8 764F-06 0.2169E 01 0.1876F 01 0.1824F- 01 l./E 

0 . 1 175F-05 0 . 195RF 01 0.1649F 01 0 . 1646F- 01 1 . /Е 

0 . T 445F-05 0.1774F 01 0.1452E 01 0.1448F-•01 l ./ E 

0.1R55F- 05 0 . 1470F Cl 0.1238F 01 0.123 3F-•01 l ./ E 

0.2187F-05 0 . 1290F 01 0 . 10R6F 01 0 .lóele- 01 l ./ E 

0 • Ю58Р- 05 0 .1 1 ?1F 01 0.9461F 00 о . 9392E-■02 l ./ E 

0 . 3474F-05 0.9787F 00 0.8 7 4 1 e 00 C.8153E-•02 l ./ E 

0 . 5043F -05 0 . P 5 21F 00 0.7187F 00 0.7069E-■02 l . / t 

0 .6 4 7 6 F -05 0.741 1 F 00 0.6248F 00 0.6103F-•02 l ./ E 

0 . 8 * 1 5F-05 0.6445E 00 0 .5 4 3 8 e 00 C.5253F- 02 l ./ E 

0 .1 06RF-04 0.S7R4F 00 0.4884F 00 0.4647F-■02 L./E 

0.1171 F -04 0.5096F 00 0 .4309F 00 0.4006F-■02 1. /Е 

0 • 1760F-04 0.4 7 8 9 e 00 0.36 35E 00 0.3247F- 02 L./E 

0 .2 760F-0^ 0.3771F 00 0.3707F 00 0.271 I f-•02 L./E 

0 . 7907F- 04 0.3 334e 00 0.2845e 00 О.2212E-■02 L./E 

0.3777E-04 0.1045F 00 0.2613F 00 0.1804t-•02 1 ./E 

0.47R5F-04 0. ?RRQF 00 0.2495F 00 0.1459F-■02 l ./ E 

0.6144F-04 0.2R79F 00 0.2504e 00 0.1178F-■02 l ./ E 

0 .7 889F-04 0.101RF 00 0.2643F 00 0.9496F-■03 l ./ E 

0 . 10Ï3F-01 0.3147F 00 0 . 2949F 00 0.7905F-•03 l ./ E 

0.1 ‘ЗО! F- 01 0.1R79F 00 0.3410F 00 0.7113E-•03 l ./ E 

0.Ï67OE-01 0.4977F 00 0.4178e 00 0.1204E-•02 l ./ E 

0 .2 1 44F- 01 0.2314F 01 0 . 1990F 01 0 . 1 591F-•01 l ./ E 

0.2 754F-01 0.7004F 00 0.6204F 00 0 . 1 142F-■02 L./E 

0 .1 5 1 6 F -01 0 .8 4 8 1 E 00 0.7524F 00 СЛ 153F-•02 L./E 

0 .4 540F-01 0.7660F 02 0 .2252F 07 0.2040F 00 l ./ E 

0 . 5879F-01 0.4177F 01 0.1547F 01 0.2416E--01 L ./E 

0 .7 4 8 5 F -01 0.7197E 01 0 . 1920F 01 C.1890F- 01 l ./ E 

0 .9 6 1 1F-01 0.7710F 01 0.1936F 01 C.2487E-■01 l ./ E 

0 . 1 214F-07 0.2372F Cl 0 . 7C79E 01 0.2818E-■01 L./E 

0 . 1 5P5F-07 0.1223E 07 0.1067F 02 0.1324E 00 l./ E 

0.2035F-0? 0.2576F C2 0.2246F 02 0.2697E 00 l ./ E 

0.2613F-0? 0.9445F 01 0.8177F 01 0.9082F-•01 L./E 

0.3355F-0? 0.1251F 02 n .1 С 79E 07 0.1152E 00 l ./ E 

0 .4 3 0 7 F -0? 0.2946F 07 0 . 2523e 02 0 . 2630E 00 L./E 

0 ,5 511.F- 0? 0 .2 1 5 6 e 07 0 . 1838e 02 0.1Й85Е 00 l ./ E 

0 .7 1 07e- 07 0.4261F 02 0 .3 6 1 1F n2 0.3660E 00 l./E 

0.9119F-07 0.4993F 07 0.4205F 02 0.4250F 00 l./E 

0.1171F— 01 0.4226F 02 0.3534F 02 0.3560E 00 l./E 

0.1503F-01 0.5773E 07 0.4379E 02 0.4395F 00 l./E 

0.1930F-01 0.5764F 07 0.4753F 07 0.4757F со l./E 

0.2 479F— 01 0.7401F 07 0.6058F 07 0.6C71E 00 l./E 

0.3183F-01 0.8268F 02 0.6712F 02 0.6721E 00 1 ./E 

0.4 0 8 7 F -01 0.9700F 02 0.7811F 02 0.7818E 00 l./E 

0 .5747E -01 0.1565 E 03 0.1248F 03 0.1248E 01 l./E 

0,6738F- 01 0.1786F 03 0.1411F 03' 0.1411E 01 l./E

I A E A - S M -1 7 0 /6 5 117 

TABLEAU V I(S U IT E ) 


DE DEPLACEMENT DAMS LE CUIVRE (N=0.9479E22 AT/G) 

B.INF(MEV) T EV.CM2/G D EV. CM 2/G DPG CM2/G 

0.8652F-■01 0 . 1684F 03 0. I318E 03 0 . 131 8 E 01 l ./ E 

O . l l l l F 00 0.1592F 03 0.1238F 03 0.1238E 01 l ./E 

0.1228F 00 0.1807F 03 0 . 1399F 03 0.1399E 01 l ./ E 

0.1357F 00 0.2232E 03 0 . 1759F 03 0.1759E 01 l ./ E 

0 . 1 500F 00 0.2289F 03 0. 1758F 03 0.1758E 01 l ./E 

0.1657F 00 0.2331F 03 0.1783F 03 C.1783F 01 l ./ E 

0 . 1 83 2F 00 0.2574F 03 0 . 1960F 03 0.1960E 01 l ./ E 

0.2024F 00 0.2835F 03 0.21496 03 0.2149E 01 l ./ E 

0.2237F 00 0.4121F 03 o .2354F 03 0.2354F 01 l ./ E 

0.2472F 00 0.3437F 03 0.2581F 03 0.2581E 01 l ./ E 

0.2732F 00 0.3791 F 03 0.2835F 03 0.2835E 01 ? IS. 

0.3020F 00 0.4091E 03 0 . 3045F из 0 .3 04 5 E 01 F IS . 

0.3337F 00 0.4357F 03 0.3228F 03 0.3228E 01 PIS. 

0 . 3688F 00 0.4652F n3 0.3430F 03 0.3430E 01 F IS. 

0.4076F 00 0.4988F 03 0.3656F 03 0.3656F 01 FIS. 

0.4505F oo 0.5364E 03 0.3908F 03 0.3908E 0]. - IS . 

0.4979F 00 0.5721F 03 0.4142F 03 C.4142E 01 FIS. 

0.5502F 00 0.6049F 03 0.4352F 03 0.4352F 01 FIS. 

0.6081F 00 0.6359F 03 0.4548F 03 0.4548E 01 F IS. 

0.6721F 00 0.6783F 03 o,4823F 03 C.4823E 01 FIS. 

0 .7 4 ? ? f 00 0.7331F 03 0.5178F 03 0.5178F 01 FIS. 

0.8208F 00 0.7678F 03 0.5391F 03 0.5391F 01 - IS . 

0.9072F 00 0 . 3 146F 03 0.5680F 03 0.5680E 01 FIS. 

0.1003F 01 0.8554F 03 0.5929F 04 0 . 5929E 01 FIS. 0 . 1 108F 01 0.9141F 03 0.6293F 03 0.6293E 01 r r S. 

0 . 1 22 5F 

0 . 1 353F 

01 

01 

0.9860F 

0 . 1030F 

03 

04 

1 .6732F 

0.6983F 

03 

03 

0.6732E 

0.6983E 

01 

01 

FIS. 

? IS. 

0.1 4 e* 6F 01 0 . 1066F 04 0.7183F 03 0.7183F 01 FIS. 

0.1653F 0! 0 . 1090E 04 0.7308F 03 0.73C8E 01 FIS. 

0 .1 8 2 7F 01 0.1130F 04 0.7546F 0.3 0.7546E 01 FIS. 

0.2 019F 

0.2231F 

01 

01 

0 .1 2 1 3F 

QÍ1325F 

04 

04 

0.804 2F 

Q.8713F 

03 

03 

0 . 8 04 2 E 

C.87136 

01 

01 

FIS. 

FIS. 

0.2466F 01. 0.1406F 04 0.9190F 03 0.9190E 01 FIS. 0.2725F 01 0.1559F C4 0. 1C11F 04 0.1011E 02 FIS. 

0.3012F 01 0 . 1741F 04 0 .1 U 9 F 04 0.1 119E 02 FIS. 

0.3320F 

0.3679F 

01 

01 

0 .1 840F 

0.2029F 

04 

04 

0 . 1174F 

0 . 1282F 

04 

04 

0.1174F 

0.1282E 

02 

02 

FIS. 

FIS. 

0.4066F 01 0.2234F 04 0 . 1399F 04 C.1399F 02 F IS . 

0.4493F 01 0.2333F 04 0 . 1454F 04 0.1454E 02 FIS. 

0.4966F 

0.5488F 

01 

01 

0.2426F 

0.2 615F 

04 

r>4 

0 . 1503F 

0.1601F 

04 

04 

0.1503E 

0 .1 6 0 1 E 

02 

02 

FIS. 

FIS. 

0.606 5F 01 0.2788F 04 0 . 1685F 04 0.1685E 02 FIS. 

0.6703F 

0.7408F 

01 

01. 

0.2940F 

0.3113F 

04 

04 

0. 1753F 

0. 1830F 

Г4 

04 

C.1753E 

0.1830E 

02 

02 

FIS. 

FIS. 

0.8187F 01 0 . 3277Б 04 0 . 1898F 04 0 . 1898E 02 FIS. 

0.9048F 01 0.3 381E 04 0.1928F 04 0.1928E 02 F IS. 

0.1000F 

0 . 1 105F 

02 

02 

0.3561F 

0 .3 8 1 1F 

04 

04 

0 . 1998F 

0.2105F 

04 

04 

0.1998E 

0.2105E 

02 

02 

FIS. 

FIS. 

0.1221F 

0.1350F 

02 

02 

0.4104F 

0.4499F 

04 

04 

0.2225F 

0 . 2380F 

04 

04 

C.2225E 

0.2380E 

02 

02 

F IS. 

FIS. 

0.149 2F 02


TABLEAU VII 


DE DEPLACEMENT DANS LE ZIRCONIUM (N=0.66E22 AT/G) 

В . INF( MEV) T EV.CM2/G D EV.CM2/G DPG CM2/G 

0.4140F-06 o. 5 pa6f -01 0.5С7ЛЕ -01 0.5036F-03 1 ./6 

0 .5 ^ 1 6E-06 0.51R4E -01 0.4499F -01 0 .4 4 5 1 E-03 L ./E 

0.6P76F-06 0.46S1F -01 0.4C37F -01 C.3975E-03 l ./ E 

0.8764F-06 0.4077F -01 0.3496F -01 0 .3 4 1 7F-0 3 l ./ E 

0 .1 1 ? 5F-05 0.3663E -01 0.3181F -01 C .3080F-03 l . / E 

0 . 1.445F-05 0 . 2 ?»6r -01 0.2854F -01 0 . 7724F-03 l ./ E 

0 . 1 85 5e- 05 0.?904F -01 0.2524F -01 0.7356E-03 l ./ E 

0.73R7F-05 0.2740F -ni 0.23R4F -01. 0.2 168 F—03 l./ E 

0.305PF-05 0.7557F -01 0.7222F -0 l C• 1 945F-0 3 l./ E 

0.39?RF-O5 0.?311F -01 0 .2 0 1 5F -01 C.1 66 0E-03 l ./E 

0.5043F-05 0.2171F -01 0 . 1897F -01 0 .1 440E-03 l./ E 

0 . 6476F-05 0.2153F -01 0 .1 RR4F -01 0 . 1298F-03 l . /Е 

0 .8 3 1 5F-05 0.2135F -Cl 0 . 1874F -01 0.1121Г-03 l ./ E 

0 . 106RF-0'. 0.7237F -01 0 . 1969F -01 C.1C07E-03 l./ E 

0 . 1 371F-04 0.2 4 7 3 e -01 0.2138F -01 C.8966E-04 l ./ E 

0 . 1760F-04 0.2677Г -01 0.236RF -01 C. 7747F-04 l ./ E 

0.2760F-04 0 .3 1 ORF -01 4.2755F -01 C.7109F-04 1 ./E 

0 .2 9 0 ?c -04 0 . 36P3F -01 0.3770F -01 C.6465F-04 l . /Е 

0 .3 7 ? 7F-04 0.4421F -01 0.3932F -01 C.5639E-04 L ./e 

0 . 47R5C- 04 0.5400F -01. 0 .APO^F -01 0.4 877E-04 l./ E 

0 .6 1 44F-04 0.6774F -01. 0.5992F -01 0.4520E-04 i ./e 

0 .7 RR9F-04 0.P476F -01. 0 .7 5 1 3F -01 C.4C81F-0A l ./ E 

0.1013Р-ПЗ 0 . lORAF 00 0.Ç664F -01 C.5632F-04 l ./ E 

0 . 1301F-03 0. 1 Я 21 F no 0 . 1613F 00 0.448 3F—03 l ./ E 

0 . 1 670F-03 0 .5 6 5 1 E on 0 • 4°46E 00 C.3456E-0? l ./ E 

0 . 2 144e- 03 0.3097F 00 0.2740F 00 0.8744 E-03 l ./E 

0 .2 754F-03 0.7P24F 01 0.2465F 01 0 .1 932Г-01 l ./ E 

0.3536F-03 0.3906F no 0 . 34RnF 00 C.2572F-03 1 . / E 

0.4540F-03 0.4584F 00 0.4093F 00 0.3307F-04 l ./ E 

0.5P29F-04 0.1111F 01 0.9828F 00 C.3255F-02 l ./ E 

0 .7 4R5F-03 0 . RI 09F со 0.7725F 00 0.6577F-03 l ./ E 

0 .9 6 1 1E-03 0.O354F 00 0.8357F 00 0.5694E-02 l ./ E 

0 . 1 734F-0? 0 . 1950F 01 n.1737F 01 0 . 2 186E-01 1 . /Е 

0 . 1 5R5F-0? 0 . 2043F Cl 0.1P10F 01 0.2387E-01 l ./ E 

0.2O35F-O? 0.2513F Cl 0.2274F 01 C. 2 933F-01 l . /Е 

0 .2 6 1 3F-0? 0 .6 9 1 RP 01 0.6113F 01 C.7606E-01 l ./ E 

0.3355F-0? 0.793RF ni 0.6976F 01 0.7870F-01 l ./ E 

0 .4 3 0 7 F -03 0 . P3P5F 01 0.7340F 01 С• 7975Г-01 l ./ E 

0.5531F-O? 0 . 8847F 01 0.7706F 01 0.8101E-01 l ./ E 

0.7102F-0? 0 . 1013F 02 0.8772F 01 C.9028E-01 l ./ E 

0 .9 1 19F-0? 0 .1 337F n? 0.1151F 07 C.1175F 00 l ./ E 

0.1 171F-01 0 . 177RF 02 0. 1.477F 0? 0.1500E 00 l ./ E 

0.1 503F-01 0.2730F 0? 0.1895F 02 C.1914E 00 1 ./E 

0.1 930F- 01. 0.2877F 02 0.2426F 02 C.2441E 00 l ./F 

0 . 7479F-01 0.3691F c? 0 .3 г 98F 0? C.3106E 00 l . /Е 

0 .3 1 R3F-01 0.4775F 02 0.3941E 0? 0 .3 9 5 1E 00 l ./E 

0.40R7F-01 0 .6 0 1 9F 02 0.4985F 0? 0.4F97E 00 l ./ E 

0 .5 247e- 01 0.7679F 02 0.6273F 07 0.62eiE 00 l ./ E 

0 • 6738F-01 0 . 4635F 02 0.7863F 0? 0 .7 86 8t 00 l ./ E

IA E A -S M -1 70/65 119 

TABLEAU V II ( SU I TP ) 


DE DEPLACEMENT DANS LE ZIRCONIUM (N=0.66E22 AT/G) 

B.INF(MEV) T EV.CM2/G D EV.CM 2/G DPG CM2/G 

0 .8657F-■01 0 .1 7 1 7F CI 0 .9 8 1 4F 02 0.9815F GO 1 • /Е 

0 .1 11 1F 00 0 .1 4 1 5F 03 0.1137F 03 0 . 1 137F 01 i . / e 

П . 1 ??8L 00 0.1547F 01 0 . 1219F r'3 0.1239F 01 l ./ E 

0.1357F 00 0 .1 694F 03 0.1352F 0.3 0.1352E 01 1 . /Е 

0 . 1 500F 00 0 . 1 856c ГЗ 0 . 1476P 01 0.1476E 01 l ./ E 

0 . 1657F 

0 .1 8 3 7 e 

00 

00 

0.7035F 

0.7737F 

01 

01 

0.1613F 

0 . 1765F 

03 

03 

0.1613F 

0 . 176 5F 

01 

01 

L./E 

L./E 

0.2074F 00 0.7447F 03 0 . 1928F 03 C .1978E 01 L./E 

0.7737^ 00 0.76Я2С 03 0.2105F 01 C . 21 0 5 E 01 L./E 

0.2477F 

0 .7 732 F 

00 

on 

0 . ?°42F 

0.3734F 

O4 

03 

0.2301F 

0 . 25?OF 

01 

03 

C.2301F 

0.2520F 

01 

01 

l ./ E 

FIS. 

0.3070F 00 0.1447F 03 0 . 2676c 03 0.7676F 01 FIS. 

0.333 7c 00 0.3701F 0? 0.2861F 01 0.286 3F 01 FIS. 

0.3688P 00 0.4197F 01 0.3232F °3 0.3232E 01 FIS. 

0.4076F or 0.4874F ГЗ 0.3746F 03 0 . 374 6F 01 FIS. 

0.4505c 00 0.4978F 03 0 .3 8 1 5F 01 0 .3 8 1 5F 01 FIS. 

0.4979F 00 0 . 5710e 03 0.3980F 01 Г.398СЕ 01 FIS. 

П .5507F oo 0.5 504F 01 0.4191F 01 0.4191F 01 F IS. 

0 . 6 OS 1F oo 0.5401F 03 0.4095F 03 0.4095F 01 FIS. 

0.6771F 00 0.5909F 01 0.446 IF 03 0.4461 E 01 FIS . 

0.7427F 00 0.6200F 03 0.4661F 03 0.4661F 01 FIS. 

0.8708F 00 0.6443F 03 0.4823F из 0.4P23E 01 FIS. 

0.9077F 00 0.6448F 03 0.4806F 03 0.4806F 01. FIS. 

0 .1 003c 01 0.5785F ,_>3 0.4293F 03 0.4293F 01 FIS. 

0 . 1 108F 01 0.6147F 03 0.4539F 01 0.4539E 01 FIS. 

0.1725F 01. 0.6655F 03 0.4886F 03 0.4886E 01 F I S. 

0.1351F 01 0.6772F 03 0.4941F 03 0.4941F 01 FIS. 

0 . 1 496F 01 0.6903F 03 0.5005F 03 0.5CG5E 01 FIS. 

0 . 1 653F 01 0.7792F 03 0.5251F 03 0.5251F 01 -’ IS. 

0.1877F 01 0.7716F 03 0.5522F 03 0.5522F 01 FIS. 

0.7019F 01 0.7755F 03 0.5537F 03 0 .5 5 3 7 E 01 FIS. 

0.7731F 01 0.7986F 03 0 .5685F 03 0.5685F 01 - T S. 

0.7466F 01 0.8740F 03 0.5848F 03 0.5848E 01 F is . 

0 .7 72 5F 01 0.8573F 03 0.6079F 03 0.6029F 01 FIS. 

0.3017F 

0.3379F 

01 

01. 

0.9071F 

0.9857F 

03 

03 

0.6386F 

0.6901F 

03 

03 

0.6386E 

0.6901F 

01 

01 

z TS. 

FIS. 

0.3679F 01 0 .1 077F 04 0.7466F 03 C.7466E 01 FIS. 

0 . 4066P 01 0 .1 142F 04 0 .7 9 1 3F 03 0.7913F 01 F I S. 

0.4493F 01 0. 1.208F 04 0.P325F 0’ 0.8325F 01 - I S . 

0.4966F 01 0.1.771F 04 C.8707F 03 0.87C7E 01 - IS. 

0.5488F 01 0.1379F 04 0.9052F 03 0.9053F 01 FIS. 

0.6065F 01. 0 .1 401F 04 0.9512F 03 C.9512E 01 FIS. 

0.6703F 01. 0 .1 502F 04 0.1013Г 04 0 . 1013F 02 FIS. 

0.7408F 01 0.1678F 04 0.1124F 04 0.1124F 02 FIS. 

0.8187F 01 0 . 1864F 04 0 . 1239F 04 C.1239E 02 FIS. 

0.9048F 01 0.2036F 04 0.1343F 04 0.1343F 02 F IS. 

0 .1 000F 07 0.7716F 04 0 . 1447F 04 C.1447E 02 F IS. 

0 .1 1 05p 07 0.2523F 04 0 . 1628F 04 0.1628E 02 : IS. 

0 . 1771F 07 0.2922F 04 0.18 50F 04 C.1850F 02 FIS. 

0 .1 350F 07 0.1784F 04 0.2038F 04 0 . 2038E 02 FIS. 

0.149 ?F 0?


TABLEAU V III 

SECTIONS EFFICACES DE TRANSFERT D'ENERGIE ET 

DE DEPLACEMENT DANS LE MOLYBDENE (N = 0 .6277E27 

R.INF(MEV) T EV.CM2/G D EV.CM2/G DPG CM2/G 

TAUX 

AT/G) 

0.4140F-06 0.630nF 00 0.5 510F 00 0.5507E-02 l ./E 

0.531 6F-06 0.5393F 00 0 .4 7 1 6P 00 0.4713E-02 l ./ E 

0 .6 8 7 6 F -06 0 .4 8 3 6 c 00 0.4 730F 00 0.4 726E-0 2 i ./e 

O.8764F-06 0.4701 F 00 0.3674E 00 0 . 3669E-02 l . /Е 

0 . 1 125F-05 0.396PF 00 0 . 3471F 00 0 . 3464E-02 l ./ E 

0 . 1 445e-05 0.3787F 00 0 .2 3 1 2F 00 0.3304E-02 l ./E 

П.1 P55F-05 0 . ^cc*p 00 0.3109F 00 0.3098F-02 l . / E 

0 .7 3 8 ?e-n5 O .^SftF 00 0 . 2848F 00 0. 2 834E-02 L./E 

0.305PF-05 0.7 Я 7 ? F 00 0.751 7' 00 0.2495E-02 1 . /Е 

0. V-?Rc-r,r, 0.2380F on 0.2087F 00 0 , 2 059E-02 l . / t 

0.5O43r-05 0 .7 1 23e 00 0 . 1858E 00 0 . 1878F-02 l ./ E 

0 .6 4 7 6 F -05 0.715OF 00 0 . 1881e 00 0 . 1 P44E-07 I ./E 

O.P^15F-05 0.7869F 00 0.2510E 00 0.2462E-02 l ./ E 

0 .1 06PF-04 0.5890F 01 0 .5 1 51F 01 0 . 5 I45E -01 l ./ E 

0 . 1 T71F-04 0.741 ЯР 00 0.2116F 00 0 . 2038E-02 l ./ E 

0 .1 760F-04 0.2168F 00 0 . 1898F 00 C. 1 800E-02 l ./ E 

0.7760F-04 0.7946F 00 0 . 2579F 00 С, 2455E-02 l ./ E 

0.7907F-04 0.6767F 00 0.5971F 00 C.5763F-02 l ./ E 

0 . 3777F-04 0.P297F 02 0.7257E 07 0.7711E 00 l ./ E 

0.47P5F-04 0 .1 561F 01 0 . 1366F 01 0 .1 320E—01 l ./ E 

0 .6 1 44F-04 0.3973P 01 0.3476F 01 0.3433F-01 l . / c 

0 .7 PP9F-04 0.2154F 00 0.1893F " 0 C.1405E-02 L . /Е 

0.1013F-03 C.2457E Cl 0.2146E 01 0.2C78E-01 l ./ E 

0 .П 0 1 Р -0 3 0.1P71F 07 0 . 1637e 07 C.1605F 00 l ./ E 

0.1 670¡ -П-> 0 . 1876F 00 0.1662F 00 0 .5 9 7 5 F-03 l ./ E 

О .? 144F-03 0.7604F 00 0.2303F 00 С. 1010E-07 L ./E 

0.7754F-03 0 Л .3 5 P F Cl 0.1191F 01 0 .1 036F-01 l./ E 

0 .3536F-0* 0.7757F 01 0.6363r 01 0 . 5522E-01 l ./ E 

0.4 5 4 0 e-03 0.6760F 01. 0.5496F 01 0.4434E—01 l ./ E 

0.5P?OF-03 0 . 1847F 01 n . 162ЯЕ 01 0 . 9981E-02 1 ./6 

0.74P5e-03 0 . 1787e 01 0.1578F 01 C.8353E-02 l ./ E 

0.961 IF - 03 0.7157F Cl 0.1P97F 01 0 .1 514E-01 l ./ E 

0 . 1 734F-07 0.3195F 01. 0.7813F 01 0 . 2988F-01 1 . /Е 

0.15P5F-0’ 0.79BPF 01 0 ,7637F 01 С. 3036E-01 l ./ E 

0.703 5F- 07 0 . 3 107F ni 0.2737F 01 0.3196F-01 1 . n 

0 .7 6 1 3F-07 0.3445F 01 0 .3 03 7F "1 0.3422F-01 I . /Е 

0 .3 3 5 5 e-0? 0.3938F 01 0.3 4 6 0 e 01 C.3 782E-C1 l ./ E 

0.4307F-0? 0.4597F 01. 0.4075F 01 C.4295F-01 1 ./E 

0.5531F-07 0 . 5494F 01 0.4798F 01 0 .49°6E-01 l ./ E 

0 .7 1 0 7e-0? 0•6 Я 59F 01 0 .5967F 01 C.6145E-01 1 . /Е 

0.911OP-0? 0.P795F 01 0.7603F 01 C.7756E-01 1 ,/E 

0.117 IF -01 0 . I 14 7F 07 0.9817F 01 C.9946E-01 1 . / E 

0 . 1 503F-O1 0. 1501E 07 0.1287F 07 C.1291E 00 l ./ E 

0 . 1430F-01 0.1993F 07 0 . 16Q1F 02 C.1703F 00 l ./ E 

0 . ?47°F- 01. 0.2648F 0? 0.2231F 07 C.2238E 00 l . /Е 

0 .3 1 83E-01 0.3469F 07 0.79C4F 02 C.29C9E 00 l ./ E 

0.4ПЯ7Р-О1 0.4486F 07 0.3730F 02 0.3740E 00 l ./ E 

0.5 747F-01 0.579PF 07 0.4787F 07 0.4794F 00 L ./E 

0 . 6738F-01 0.7543F 07 0.6 1 8 7 e 07 0.6187E 00 l ./ E

I A E A - S M -1 7 0 /6 5 121 

TABLEAU V IIK SUITE ) 

SECTIONS EFFICACES OE TRANSFERT D'ENERGIE ET TAUX 

DE DEPLACEMENT DANS LE MOLYBDENE (N=0.6277E22 AT/G) 

B.INF(MEV) T EV.CM2/G D EV. CM 2/G DPG CM?/G 

0.8652F-■01 0.1016F 03 0 . 8260F 02 0 . 8 2 6 1E 00 i. ./E 

o . m i F 00 0.1241F 03 0 . 1004F 03 0 . 1004F 01 l ./ E 

0 - 1228F 00 0.1377F 03 0.1111F 03 0.1110E 01 l ./ E 

0. 1457P 00 0.1521F 03 0.12 23F 03 0.1223E 01 l . / E 

0.1500F 00 0.1673F 03 0. 1340F 03 0 .1 340F 01 l ./ E 

0.1657F 00 0 . 1826F 03 0. 1458F 03 0.1458F 01 l ./ E 

0 . 1 «42F 00 0 . 1973F 03 0 . 1569F 03 C.1569E 01 l ./ E 

0.2024F 00 0.2122F 04 0 . I682F 04 C.1682E 01 L./E 

0 • 2 23 7F 00 0.2274F 03 0.1797E 03 0.1797F 01 l . / E 

0.2472E 0n 0.2451F C3 0.1930F 03 C.1930E 01 l ./ E 

0.2732Г 00 0.2632F 04 0.2066E л3 0.2066E 01 FIS. 

0.3020F 00 0.2823F 03 0.2207F 03 0.2207E 01 FIS. 

0.3437F 00 0.3056F 03 0.2381F 04 C.2381E 01 - I S . 

0.3688F 00 0.3318F 03 0.2575F 03 C.2575E 01 FIS. 

0 . 4076F 00 0.3508F 03 0.2714F 03 0.2714E 01 : IS. 

0.4505F 00 0.3644F 0.3 0.281 1F 03 0 .2 8 1 1E 01 FIS. 

0.4979E 00 0.3824F 03 0.2940F 04 0 ,2 9 4 OE 01 F IS. 

0.5*5026 00 0.406 6F 03 0.3113F 03 0.3113E 01 FIS. 

0.6081F 00 0.4324F 04 0.4298E 03 0.3298E 01 - I S . 

0.6721F 00 0.4571F 03 0.3475F 03 C.3475E 01 FIS. 

0.74 27F 00 0.4744F 04 0.3594F 03 0.3594E 01 F IS . 

0.8208F 00 0.4862F 03 0.3674F 03 C.3674F 01 FIS. 

0.4072F 00 0.5047F 03 0.4801F 03 0.38C2E 01 - I S . 

0.1003F 01. 0.5419F 03 0.4063F 03 0.4C63E 01 F IS. 

0.1108F 01 0.5861F 03 0.4370F 03 0.4370E 01 FIS . 

0.1225F 01 0.6044F 03 0.4490F 03 0.4490E 01 FIS. 

0.1353F 01 0.6299F 03 0.4654F 03 0.4654E 01 F IS . 

0.1496F 01. 0.6157F 03 0.4546F 03 0.4546E 01 FIS. 

0.1653F 01 0.6726F 03 0.4933E 03 0.4933 E 01 FIS. 

0.1827F ni 0.7289F 03 0.5312F 03 C.5312F 01 r IS. 

0.2019F 01 0.7804F 03 0.5649F 03 0.5649F 01 FIS. 

0.2231F 01 0.8377F 03 0.6024F 03 0.6024E 01 F IS. 

0.2466F 01 0.9008F 03 0.6435F 03 0.6435E 01 FIS. 

0.2725F 01 0.9733F 03 0.6906F 04 0.69C6E 01 FIS. 

0.3012F 01 0 .1 026F 04 0.7237F 03 C.7237E 01 F IS. 

0.3329F 01 0.1082F 04 0.7589F 03 0.7589E 01 F IS. 

0.3679F 01 0.1154F 04 0.8045F 04 0.8045E 01 FIS. 

0.4066F 01 0.1233F 04 0.8541F 03 0.8541E 01 - IS. 

0.4493F 01 0.1309F 04 0.9012F 03 0.9012E 01 FIS. 

0.4966E 01 0.1377E C4 0.94 27F 03 0 , 9427E 01 FIS. 

0.54RBF 01 0.1445F 04 0.9846F 03 0.9846E 01 FIS. 

0.6065F 01 -0. 1.529F 04 0.1036F 04 0 . 1C36E 02 FIS. 

0.6703F 01 0.1605F 04 0 . 1081F 04 0.1C81E 02 FIS. 

0.7408F 01 0.1700F 04 0 . 1138E 04 0.1138E 02 FIS. 

0.8I87E 01 0.1798F 04 0.1197F 04 0.1197E 02 FIS. 

0.9048F 01 0.1971F 04 0 . 1301F 04 C.1301E 02 PIS. 

0.1000F 02 0.2207F 04 0 . 1440F 04 0.1440E 02 F IS . 

0.1105F 02 0.2424F 04 0 . 1559F 04 0.1559E 02 FIS. 

0.1221F 02 0.2677E 04 0.1693F 04 C.1693E 0? F IS . 

0.1350F 02 0.2967F 04 0 . 1844F 04 0.1844E 02 FIS. 

0.1492F 02

122 LO TT e t a l. 

TABLEAU IX 


DE DEPLACEMENT DANS LE TUNGSTENE (N=0.327E22 AT/G) 

B. IM F (M E V ) T EV.CM2/G D EV.CM2/G DPG CH2/G 

0.4140F-06 0.9028F 00 0.8010F 00 0. 1485F-01 l ./E 

0 .5 4 1 6F-06 0.7696F 00 0.6828F 00 0.1266E-01 l . / E 

O.6826F-06 0.6 87 RP 00 0.6102E 00 0 .1 1 3 1E-01 l ./ E 

0.Я764Е-06 0.6026F 00 0 . 5347p 00 0.9909F-02 l ./ E 

0.1 1 ? 5F - 0 5 0.6384F 00 0.5664P 00 0 . 1050F-01 l ./ E 

0 . 1 445F-05 0.7135F 00 0.6330P 00 0 .1 1 73E-01 L./E 

0 . 1 P55F-05 0.P100E 00 0.7186F 00 0 . 1 332E-01 l ./ E 

0. 2 38 2F-05 0.96 0°F 00 0 . 8525F 00 0 . 1580E-01 l ./ E 

0 . 305PP- 05 0 . 1036F 02 0.9188E 01 0.1703E 00 l ./ E 

0 . 3928F-D5 0.4084F 02 0.3623F 02 0.6715E 00 L ./e 

0 . 5043F-05 0 .1 09RF 01 0.9742F 00 1804E-01 l ./ E 

0 . 6476F-05 0 . 1 195F 02 0 . 1060P 02 0.1966E 00 L ./E 

0. 841 SF-05 0 .144oF 01 0.1277F 01 0 . 2365E-01 l ./ E 

0.1 068F-04 0.4447' Cl 0.2961F 01 0.5486F-01 L./E 

0.1 371 F - 04 0.1257F 04 0.1115F 04 0.2 067F 01 1 ./Ë 

0 . 1760E-04 0 . 1243F 04 H.1094F 04 0.2027F 02 l . / E 

0 .? 260F-04 0.4850F 02 0.4 4 04F O7 0.7975E 00 l ./ E 

" .2902F-04 0.3013F 01 0.2674F 01 0.4947E-01 l ./ E 

0 .4 72 7F-04 ',0.3248F 02 0.2881F 02 C.534CE 00 l ./ E 

0.47R5F-04 0.R744F 01 0.7757Г 01 0.1436F 00 1 ./E 

0 .6 1 44F-04 0.2010F oi 0 . 1783F 01 0.3286E-01 l ./ E 

0 .7 8P9F-04 0.2135F 01 0 . 1894E 01 0 . 3485F-01 l ./ E 

0.1 01 4F —04 0l‘.2030F 02 0.1801F 02 C.3335E 00 L ./E 

0.1301F-04 0 ¿ 7 427F 01 0.6589F 01 0.1217E 00 l ./ E 

0 . 1 670F-04 0.',7 2 56F 02 0.6438F 02 0.1193E 01 l ./ E 

0 .2 1 44F-04 0 . 1823E 02 0.1617F 02 C.2991F OC l ./ E 

0 . 2754F-04 0.2954F 01 0 . 2621F 01 C.4768E-01 l ./ E 

0 .3 536F-04 0.2774E 01 0.2460F 01 0.4445E-01 l ./ E 

0 . 4540F-03 0.2581F 01 0 . 2290F 01 0.4096F—01 l ./ E 

0 .5829F-04 0.2505F 01 0.2222F 01 0.3928F-01 l ./ E 

0.7485F-03 0.2426F 01 0.2152F 01 0.3744E-01 l ./ E 

0 .9 6 1 1F-04 0.2363F 01 0.2096F 01 C.3596E-01 l ./ E 

0 . 1 234F-0? 0.2356F 01 0.2090F 01 0 .3 578F-01 l ./ E 

0 . 1 5R5F-02 0.2350F 01 0.2C85F 01 0.3559E-01 l ./ E 

0.2035F-02 0.2341F 01 0.2C77F Cl 0.3 5 3 5 E-01 l ./ E 

0 .2 6 1 3F-02 0.2334F 01 0.2071F 01 0 . 3498E—01 l ./ E 

0.3355F-0? 0.2354F 01 0.2089F 01 0.3393E-01 l ./ E 

0 .4 3 0 7 F -02 0 .2 4 1 8F 01 0.2145F 01 0.3271E—01 l ./ E 

0.5531F-02 0.2R02F 01 0.2486F 01 0.3377E-01 l . / E 

0.7102F-02 0.3397F 01 0.3014F 01 0.3613E-01 l ./ E 

0 .9 1 19F-02 0.4289F 01 0.3801F 01 0.4159E-01 l . / E 

0.11710-01 0.5455F 01 0.4816F 01 0 . 5 127E-01 l ./ E 

0 .1 503F-01 0.6951F 01 0.6118F 01 0.6393E-01 l . / E 

0 .1 930F—01 0.8874Г û i 0.7791F 01 0 •8 0 1 9F-01 l ./ E 

0.2479F-01 0.1105F 02 0.9654F 01 0.9848E-01 l./ E 

0 .3 1 83E-01 0.1347F 02 0.1169F 02 0.1188E 00 l ./ E 

0.4087F-01 0.1659F 02 0.1431E 02 0.1448E 00 l . / E 

0 .5 247F-01 0.2059F 02 0 . 1768F 02 0.1782E 00 l ./ E 

0.6738F-01 0.2573F 02 0.220ÖE 02 0.2211E 00 l ./ E

IAE A -SM -1 7 0 /6 5 123 

TABLEAU IX ( SUITE) 


DE DEPLACEMENT DANS LE TUNGSTENE (N=0.327F22 AT/G) 

B.INF(MEV) T EV.CM2/G D EV.CM2/G DPG CM2/G 

0.8652F-■01 H.3203F 02 0.2728F 02 0.2736E OC l./E 

0.1 111F 00 0 . 3578F 02 0 .3 O'5 5F 02 0 . 3041F 00 l./E 

0.1228F 00 0.3792F 0? 0.3708F 02 0.3214E 00 l./E 

0 .1 3Ç7P 00 0.40 29F 02 0.3399F 02 0.3404F 00 l./E 

0.1 ЧОП1" 00 0.4790F 02 0.361 OF 02 C.3615E 00 l ./ E 

0.1657^ 

0.1832F 

oo 

00 

0.4579F 

0 ./, floor 

02 

02 

0.3844F 

0.4102F 

02 

02 

0.3848F 

0.4105F 

00 

00 

l ./ E 

1 ./E 

0.2024F on 0.5 7 7 7 e 02 0.4406F 02 0.44C9E 00 l ./ E 

0.2237F 00 0.5710F 02 0.4755F 02 0.4757F 00 l ./ E 

0.2472F 00 0 .6 1 90P 0? 0.5141F 02 0.5142F 00 l ./ E 

0.7732F 00 0.6777F 02 0.5573F 02 0.5575F 00 FIS. 

0.3020F 00 0.721 4P 02 0.5961F 02 0.5^6?E 00 PIS. 

П .1П 7Г 00 0.7677F 0? 0.6326P 02 0.6327E 00 r I S . 

0.3 6 8 8 e 00 0.Я18ЯР 02 0.6729F 02 0.6731F 00 FIS. 0.4076F 00 0•87 5 4P 02 0.7175F 02 0.7177E 00 FIS. 0 . ASOSE 00 0.9379F 02 0.7668F 02 0 . 7670F oc = IS. 

0.4979F 00 0.1000P 03 0.8155F 07 0.8156E 00 - IS. 

0.5502F 00 0.1061F 04 0.8626F 02 0 • 8 é 2 8 E 00 FIS. 

0.6081F 00 0 . 1 178F 03 0.9147F 07 0.9149E 00 F IS . 

0 . 6771F 00 0 .1 202F n? 0 . 4723F 02 C.9724F 00 F IS. 

0 . 7477F 00 0 .1 284F 03 0 . 1036F 03 0 .1 0 3 6 E 01 - IS. 

0 . 8208F 00 0 . 1375F 03 0 . 1 106F 03 C.11C6E 01 FIS. 

0 . 9072F 00 0.1475F 03 0 . 1184F 03 C.1184E 01 FIS. 

0. 1 003F 01 0 . 1596F C3 0 . 1276F 03 0.1276F 01 FIS. 

0 . 1 10RF 01 0.1737F 03 0 . 1384F 03 0.1384F 01 F IS. 

0 . 1 72 5F 01 0 .1 894F 03 0.1503F •'’ 3 C.1503F 01 FIS. 

0.I353F 01 0.2066F 03 0 . 1634F 03 C.1635E 01 -IS . 

0 . 1 496F 

0 . 1 653F 

01 

01 

0.7244F 

0.2476F 

03 

03 

0 . 1769F 

0 . 1907E 

03 

03 

0.1769E 

0.1907F 

01 

01 

FIS. FIS. 

0 . 1 R77E 01 . 0.2627F 03 0.2060F 03 0.2060E 01 z IS. 

0.2019F 01 0.2808F 03 0 .2 1 °6F 03 0.2196E 01 FIS. 

0.2231F 01 0.2982P 03 0.2325F 03 0.2325F 01 F IS. 

0.2466F 

0.2725F 

01 

01 

0.3168F 

0.3363F 

03 

03 

0.2461F 

0.2604E 

03 

03 

0 . 2461E 

0.26C4E 

01 

01 

- IS . 

FIS. 

0.3012F 01 0.3579P C3 0.2761F 03 0 .2 7 6 1E 01 FIS. 

0.3329F 01 0.3790F 03 0.2913F 03 0.2914F 01 FIS. 

0.3679F 01 0.4873F 03 0 . 2971F 03 0.2971E 01 FIS. 

0.4066F 01 0.394 2F 03 0.3019F 03 0.3019F 01 FIS. 

0.4493F 01 0.4020F 03 0.3072F 03 0.3072F 01 FIS. 

0.4966F 01. 0.4220F 03 0.3215F 03 0 .3 2 1 5E 01 FIS. 

0.54RRF ni 0.4563P 03 0.3463F 03 C.3463E 01 = IS. 

0 . 6 06 S F 01 0.4919F 03 0.3719F 03 0.3719F 01 FIS. 

0.6703F 01 0.5370F 03 0.4040F 03 0.404DE 01 FIS. 

0.7408F 01 0.5974F 03 0.4467F 03 0.4467E 01 FIS. 

0.8187F 01 0.6583F 03 0.4896F 03 0.4896E 01 FIS. 

0.904ЯР 01 0.7488F 03 0.5525F 03 0.5525E 01 = IS. 

0.1 000“ 02 0.8 414F 03 0.6160F 03 0.6160E 01 FIS. 

0 . 1 105F 

0 . 1 721F 

0.1350F 

0.149 7F 

07 

07 

02 

07 

0.9 224F 

0.100?F 

0 . 1089F 

03 

04 

04 

0.6703E 

0 . 7226F 

0.7805F 

03 

03 

03 

C.6703E 

0.7226E 

0.7805E 

01 

01 

01 

FIS. 

FIS. 

FIS.

Elément 

TABLEAU X 

SECTIONS EFFICACES DE TRANSFERT D'ENERGIE ET TAUX DE DEPLACEMENT 

IAE A - S M - 1 7 0 /6 5 125 

REFERENCES 

[l] HONECK H.C., ENDF/B, Specifications for an evaluated 

nuclear data file for reactor applications, May (1966) 

BNL 500 66 (T-467). 

[2l PARKER, The Altermaston Nuclear Data Library, 

AWRE report NO 0.70/63. 

[3] LINDHARD J., NIELSEN V. , SCHARFF M., THOMSEN P., 

Integral equation governing radiation effects, 

MAT. fys Medd Dan Vid Selsk 33 10 (1963). 

[4 ] KINCHIN G.H., PEASE R.S., The displacement of atoms 

in solids by radiation, Rep. Progr.Phys. 18 1 (1955). 

[5 ] SIGMUND P., A note of integral equation on the 

Kinchin Pease type, Rad. Eff. 1 (1969) 15 . 

[б ] TORRENS I.М., ROBINSON М.T C o m p u t e r Simulation of 

Atomic Displacement Cascades in metals, Proc. of the 

1971 Int. Conf. Held at ALBANY, 9.11 June 1971. 

[7 ! WECHSLER M.S., Radiation effects on metal and neutron 

dosimetry, STP n° 341, p. 86,American Society for 

Testing and Materials, Philadelphia, Pa (1963). 

[8] ROBINSON M.T., Phil. Mag. 17 (1968) 639. 

[9 ] ROBINSON M.T., In nuclear fusion reactor (BNES London) 

(1970) 264 . 

[lO] NORGETT M.J., ROBINSON M.T., TORRENS I., Une méthode 

de calcul du nombre de déplacements atomiques dans 

les matériaux irradiés, Rapport CEA R-4389. 

[11] GERVAISE F., Programme ARTUS X, Communication privée. 

[12] CANCE M., CHABRY P., GENTHON J.P., Programme SOURCE, 

note CEA N 1294 (1970). 

[13] Specialist's Meeting on Radiation Damage on Graphite 

and on Ferritic and Austenitic Steel, Battelle 

Seattle Research Center, Oct. Nov. 1972. 

[14] ENGLE W.W., A Users Manual for ANISN, AEC Research 

and Development Report К 1693.

126 L O T T e t al. 

[15] COLTMAN R.R. et al., Reactor Damage in Pure Metals, 

Journal of Applied Physics 33 12 (Dec.1962). 

[le] DORAN D.G., Neutron Displacement Cross Sections 

for Stainless Steel and Tantalum based on a 

LINDHARD model, 

Nuclear Science and Engeneering 49 (1972) 130-144 . 

[17] THOMPSON M.W., WRIGHT S.B., A new damage function 

for predicting the effect of reactor irradiation 

on graphite in different neutron spectra , 

J. Nucl. Mat. 16 (1965) 146. 

DISCUSSION 

D. R. HARRIS: Can a cost analysis be ca rrie d out in ord er to estim ate 

the ben efits of nuclear data requ ired fo r radiation damage analysis as 

com pared with the costs of obtaining the data? 

M. LOTT: The p recision of the nuclear data appears to be sufficient 

at present fo r calculating the irradiation rates as defined in our paper. 

H ence, the cost of obtaining the data is negligible by com p arison with the 

benefit derived from them. M oreov er, further data m easurem ents are 

p robably not requ ired fo r fissio n rea ctors. In the case of fusion rea ctors, 

on the other hand, there is a definite lack of data.

Section II 

REACTOR TECHNOLOGY

Chairman 

W . В. LEWIS (Canada)

IAEA- SM-170/91 

ТОЧНОСТЬ ЯДЕРНЫХ ДАННЫХ И ЕЕ ВЛИЯНИЕ 

НА РАЗРАБОТКУ БЫСТРЫХ РЕАКТОРОВ. 

ПОДХОД К ВЫРАБОТКЕ ТРЕБОВАНИЙ НА 

ТОЧНОСТЬ ЯДЕРНЫХ ДАННЫХ 

Л. Н. УСАЧЕВ, В. Н. МАНОХИН, Ю. Г. БОБКОВ 

Физико-энергетический институт, 

Обнинск, 

Союз Советских Социалистических Республик 

Представлен Г.Б.Яньковым 

Abstract- Аннотация 

A C C U R A C Y OF NUCLEAR D A T A A N D ITS EFFECT ON FAST-REACTOR DESIGN. A N APPROACH TO 

SETTING UP NUCLEAR D A T A A C C U R A C Y REQUIREMENTS. 

The paper deals with the prediction of fast-reactor parameters, with the accuracy required in obtaining 

them from neutron calculations and with deliberations concerning error magnitudes. A method of determi 

ning the errors of various quantities resulting in a given value of a reactor parameter is described. In addi 

tion, the accuracy of nuclear data resulting in an error of ± 2 % in the conversion ratio is discussed: the use 

of integral experiments in relaxing the accuracy requirements for microscopic data is studied. 

Т О Ч Н О С Т Ь Я Д Е Р Н Ы Х Д А Н Н Ы Х И Е Е В Л И Я Н И Е Н А Р А З Р А Б О Т К У Б Ы С Т Р Ы Х Р Е А К Т О 

Р О В . П О Д Х О Д К В Ы Р А Б О Т К Е Т Р Е Б О В А Н И Й Н А Т О Ч Н О С Т Ь Я Д Е Р Н Ы Х Д А Н Н Ы Х . 

В данной работе обсуждаются предсказания параметров быстрых реакторов, точность 

их обеспечения нейтронными расчетами, а также из каких соображений следуют величины 

погреш ностей . Описывается метод определения совокупности погрешностей различных 

величин, обеспечивающей заданную величину погрешности реакторного параметра, идет речь 

о точности ядерных данных, обеспечивающих ± 2 % погрешности в коэффициенте воспроиз 

водства, и исследуется использование интегральных экспериментов для смягчения т р е б о 

ваний на точность микроскопических ядерных данных. 

I. ВВЕДЕНИЕ 

Деятельность по ядерным данным для реакторов имеет уже более чем 

тридцатилетнюю историю. Ее начало, по-видимому, можно исчислять с 

1939-1940 года, когда стала ясна возможность получения цепной реакции 

деления . Знание вероятностей различных взаимодействий нейтронов с 

различными ядрами определяло тогда путь получения цепной реакции 

деления. На следующем этапе развития ядерной энергетики изучение 

ядерных данных определило способность реакторов на быстрых нейтронах 

к расширенному воспроизводству ядерного горючего. К настоящему 

времени это обстоятельство привело к общему признанию этого типа 

реакторов как наиболее перспективного. На настоящем этапе развития 

ядерной энергетики пускаются опытные промышленные быстрые реакторы, 

ведутся работы по проектированию энергетики, основанной на реакторах 

такого типа . На данном этапе требуется дальнейшее уточнение наших 

знаний ядерных данных, так как имеющиеся неопределенности требуют 

слишком дорогих запасов. С другой стороны, чрезмерное уточнение 

ядерных данных также требует чрезвычайно больших вложений в развитие 

экспериментальной техники. Оценку стоимости эксперимента или совокупности 

экспериментов в зависимости от требуемой точности обычно 

129

130 У С А Ч Е В и д р . 

делают по закону обратной пропорциональности квадрату ошибки, т.е., 

если мы потребуем вдвое меньшую погрешность, то мы должны затратить 

в 4 раза больше средств для выполнения этого требования . Поэтому и 

возникает задача об обосновании требуемых точностей ядерных данных. 

Или, говоря более общими словами, возникает задача выбора оптимальной 

совокупности экспериментов, как микроскопических, так и интегральных, 

характеризуемых требуемой погрешностью для каждого типа опыта и 

обеспечивающих требуемую точность расчета реакторных параметров при 

минимальных общих затратах. 

Очевидно, что совершенно аналогичные задачи возникают при определении 

необходимых точностей в любых областях применения ядерных 

данных в науке и технологии, им и посвящен данный Симпозиум. Это же, 

впрочем, относится и к любым другим числовым данным для науки и 

технологии. Именно поэтому мы считаем полезным представить данный 

доклад на настоящем Симпозиуме, имея в виду наибольшую разработанность 

вопроса о потребностях в данных для реакторов. Подход к вопросу, 

основные понятия, методы расчета разрабатывались с 1961 года в ряде 

работ авторов из различных стран [1-19 ]. Ниже будет охарактеризован 

вклад некоторых из указанных работ в современное понимание проблемы. 

И. ЯДЕРНЫЕ ДАННЫЕ, НЕОБХОДИМЫЕ ДЛЯ РАЗРАБОТКИ БЫСТРЫХ 

РЕАКТОРОВ 

В этом разделе мы ответим на следующие вопросы: предсказания 

каких параметров быстрых реакторов и с какой точностью должны быть 

обеспечены нейтронными расчетами, из каких соображений следуют 

причины погрешностей. 

1) Расчет критической массы или эффективного коэффициента размножения 

. 

Погрешность расчета эффективного коэффициента размножения 

вследствие погрешности ядерных данных должна составлять 1 % . В докладе 

Р.С.Смита [5] обосновывается требование на точность расчета 

КЭфф в ± 1% , исходя из возможности без переделки конструкции реактора 

скомпенсировать соответствующую ошибку. С этой оценкой согласны 

авторы работы [10 ] на основе примерно тех же соображений. Что же 

касается дальнейшего уменьшения требуемой погрешности за счет 

погрешностей ядерных данных, то по мнению авторов работы [10 ], это не 

приведет к заметному уменьшению общей погрешности вследствие погрешностей 

изготовления тепловыделяющих элементов, которые ведут, 

примерно,к погрешности Кэфф.в ± 1 % . 

Требование на уменьшение этих технологических погрешностей привело 

бы к необходимости более дорогой технологии. Таким образом, 

допускается общая погрешность, за счет технологии и ядерных данных, 

равная J I2 + I2 = 1,4%. 

2) Теплофизические расчеты предельной мощности, снимаемой с 

реактора, т.е. мощности АЭС, требуют знания коэффициента неравномерности 

— отношения максимального тепловыделения к среднему. 

В докладе [11 ] показано, что существующая погрешность в ядерных 

данных приводит к неопределенности в 2,5% в указанной величине. В 

докладе [14] считается, что из экономических соображений следует 

потребовать знания этой величины с точностью в 1% .

IAEA SM-170/91 131 

3) Для безопасной эксплуатации реактора нужно обеспечить расчеты 

мощностного и температурного коэффициентов реактивности с точностью 

в ± 2 0 % [5,14 ]. 

4) Объемы добычи урана и его обогащения, так же как и объемы 

переработки топлива,необходимые для обеспечения развивающейся 

энергетики, основанной на быстрых реакторах, определяются задаваемым 

темпом развития энергетики и временем удвоения реакторов с расширенным 

воспроизводством. Время удвоения определяется как время, за 

которое число реакторов удвоится за счет воспроизводимого горючего 

без подпитки всей системы реакторов другим горючим, кроме воспроизводимого 

в них самих. 

Время удвоения обратно пропорционально коэффициенту воспроизводства 

без единицы. В ряде работ [5,10 ] на погрешность коэффициента 

воспроизводства налагается требование в ± 2%, что, грубо говоря, соответствует 

погрешности в 1 0 % во времени удвоения. Дальнейшее уменьшение 

этой погрешности было бы желательно с точки зрения уменьшения 

неопределенности времени удвоения, однако его нельзя добиться, не меняя 

и не удорожая технологии изготовления топлива по причинам, 

объясненным в п . 1 . 

5) Для определения доступности для обслуживания насосов и другого 

технологического оборудования надо знать активность натрия после 

выдержки, которая определяется процессом (п, 2п), активацию компонент 

стали за счет процессов (n,p), (n,«), (n,2n), (п,пр) и др.(вместе со знанием 

массопереноса этих компонент жидким натрием). 

Знание активности облученной стали необходимо и при проектировании 

заводов по переработке тепловыделяющих элементов . 

Указанные активности надо знать, повидимому, с точностью 20%. 

Процессы (п,р) и (п,«) ведут к накоплению газов в оболочках твэлов 

и их надо знать примерно с той же точностью. 

6) Перевозка облученного топлива на переработку требует защиты, 

величина которой определяется нейтронной активностью, накопленной в 

топливе Ст-242 и Ст-244. Нейтронную активность надо знать, повидимому, 

с точностью порядка 20% . 

7) Технология изготовления топливных элементов из плутония, 

полученного из химической переработки, определяется количеством 

накопившихся активных изотопов плутония-236 и плутония-238. В настоящее 

время неопределенности в уровне нейтронной активности оцениваются 

[11] фактором 5. Повидимому концентрации указанных изотопов надо 

знать также с точностью порядка 20% . 

8) Расчеты тепловыделения в конструкциях активной зоны требуют 

знания спектров 7-лучей деления, неупругого рассеяния, захвата. 

Во всех этих пунктах говорится о требованиях, вытекающих из технологии, 

к точностям предсказания некоторых реакторных параметров, а 

не о точностях ядерных данных, от которых эти параметры зависят . 

Непосредственно из технологических требований вытекают требования 

на точность ядерных констант только в п . 5 , да и то в очень грубом 

приближении, так как,строго говоря, числа процессов зависят как от 

сечений самих интересующих нас процессов, так и от спектра нейтронов 

в реакторе, который определяется ядерными данными всех присутствующих 

в реакторе материалов. Поэтому погрешность предсказания определяется 

не только погрешностью в знании основного интересующего нас 

процесса (например, (п,р), (п,а) и т.д.), но и погрешностями других

132 У С А Ч Е В и д р . 

величин. Из этих соображений следует, что точность сечений указанных 

процессов должна быть лучше требуемых для активации 20% , так как 

какую-то неопределенность внесут погрешности ядерных данных всех 

реакторных материалов. 

Технологические требования пунктов 6 и 7 связываются с требованиями 

к величинам погрешностей ядерных данных - сечений ряда изотопов 

цепочки превращений через уравнения кинетики, описывающие накопления 

изотопов, существенных для технологии. 

Если сначала предполагать спектр нейтронов в реакторе заданным, 

то можно определить допускаемые погрешности в средних на этом спектре 

сечениях цепочки изотопов, пользуясь уравнениями кинетики. А затем, 

имея в виду отмеченный выше эффект неопределенности спектра в реакторе, 

зависящий от неопределенностей ядерных данных всех входящих в 

состав реактора веществ, можно поставить задачу о совокупности допустимых 

погрешностей всех величин, влияющих на величину среднего 

сечения. Эта задача совершенно аналогична той, которая будет обсуждаться 

ниже, применительно к п.п.1-4. 

III. МЕТОД ОПРЕДЕЛЕНИЯ СОВОКУПНОСТИ ПОГРЕШНОСТЕЙ РАЗ 

ЛИЧНЫХ ВЕЛИЧИН, ОБЕСПЕЧИВАЮЩЕЙ ЗАДАННУЮ ВЕЛИЧИНУ 

ПОГРЕШНОСТИ РЕАКТОРНОГО ПАРАМЕТРА 

Для определения погрешностей в ядерных данных, обеспечивающих 

предсказания реакторных величин п.п. 1-4 с заданной точностью, в 

настоящее время мы имеем метод, учитывающий корреляционные свойства 

погрешностей в простой, но реалистической модели. Этот метод, по нашему 

мнению, сожет претендовать на количественное определение требуемых 

точностей . 

Относительная вариация реакторного параметра бС/С выражается 

линейно через относительные вариации (6a/a)a i j групповых величин 

типа а изотопа i в группе j с коэффициентами пропорциональности или 

чувствительности Sajj 

« C / C S a ij(6 a/a)aij 

ai j 

Коэффициенты Saij вычисляются с помощью обобщенной теории возмущений 

[ 3]. 

Для определения погрешности в реакторном параметре надо сделать 

предположение о том, как складываются вклады от многих погрешностей, 

входящих в формулу (1) . Если принять во внимание, что эти вклады 

являются случайными величинами, нескоррелированными между собой, то, 

в соответствии с правилами математической статистики, дисперсия или 

иначе квадрат стандартного отклонения реакторного параметра 

С - D 2 ( D 2 = (бС/С)2 ) выражается через дисперсии групповых микроскопических 

величин d 2 jj (d2jj = (бст/ст)îj ) следующим образом 

aij 

Такое предположение было использовано в работе Мурхэда [1], который 

вычислял коэффициенты чувствительности прямым расчетом в пятигрупповой 

модели. Гриблер, Хатчинс и Лимфорд [ 8] поставили вопрос о 

d ) 

(2 )

IAEA SM -170/91 133 

важности учета корреляции в погрешностях. Они высказали мнение, что 

реально почти каждой ядерной константе можно сопоставить 2 - 3 корреляционных 

интервала на всей энергетической оси. Зарицкий и Троянов[9], 

в своей обстоятельной работе, посвященной этому же вопросу, также 

подчеркнули роль корреляций. А в работе Зарицкого, Николаева и Троя- 

нова [ 10] была реализована мысль о выработке требований на точности 

отношений величин к стандартам, таким как v 252Cf и сечение деления 

урана-235, а также на точность самих стандартов. В работе Усачева и 

Бобкова [12] предложено погрешность разбивать на компоненты, различающиеся 

своими корреляционными свойствами . Чаще всего это три 

компоненты: 1) статистическая-некоррелированная, 2) компонента ошибки, 

перенесенная со стандарта при его использовании. Эта компонента 

присутствует в погрешностях всех величин, измеренных с помощью этого 

стандарта, 3) предполагаемая ошибка в нормировке кривой, постоянная в 

пределах выбранного корреляционного интервала и проистекающая от 

возможной систематической ошибки. Представление óct/сг в виде трех 

компонент подставляется в уравнение (1) и члены с одинаковыми компонентами, 

описывающими коррелированную ошибку, объединяются таким 

образом, что новые коэффициенты чувствительности Z ß данной корреляционной 

компоненты погрешности оказываются суммами коэффициентов 

S aij по области скоррелированности. Подробно все соответствующие 

формулы для коэффициентов Z ß расписаны в работе [12]. Теперь 

6С/С = Е Z ¡ (б ст/а)6 , где компоненты погрешности (ócr/ст)® между собой 

считаются статистически независимыми и на этом основании производится 

переход к формуле (3), аналогичный переходу от формулы (1) к 

формуле (2) 

D 2 = E z g d 2 (3) 

ß 8 ß 

задавая левую часть — погрешность реакторного параметра - , надо определить 

совокупность погрешностей отдельных величин dg . 

Очевидно, что задача в такой постановке не однозначна — можно 

по-разному распределить вклады погрешностей разных величин в погрешность 

реакторного параметра . Однако достаточно наложить условие 

минимума затрат на совокупность экспериментов, делая одновременно 

предположения об относительных величинах затрат для измерения различных 

величин с достигнутыми к данному моменту точностями и экстраполируя 

стоимость эксперимента в зависимости от величины погрешности 

£ , например, по закону 1/Е , как задача становится однозначной и 

сразу решается. Подробнее об этом написано в докладе [12]. 

Описанную методику мы проиллюстрируем на примере п.4, т.е. на 

примере требований к точности расчета коэффициента воспроизводства . 

IV. ТОЧНОСТЬ ЯДЕРНЫХ ДАННЫХ, ОБЕСПЕЧИВАЮЩИХ ± 2% ПОГ 

РЕШНОСТИ В КОЭФФИЦИЕНТЕ ВОСПРОИЗВОДСТВА 

Рассмотрена модель реактора на быстрых нейтронах, состав и размеры 

которого соответствуют электрической мощности около 1000 МВт . 

В качестве топлива используется смесь окиси урана-238 с окисью 

плутония, содержащего высшие изотопы в некоторой "равновесной" концентрации, 

а также осколки деления.

134 ’ ’ У С А Ч Е В и д р . 

ТАБЛИЦА I. ОСНОВНЫЕ ХАРАКТЕРИСТИКИ 

ИССЛЕДУЕМОГО РЕАКТОРА 

О бъем активной зоны, м 3 5 

Топливо P uC >2 + U C >2 

Средняя плотность топлива, г /с м 3 8 

О бъемное содержание, % топливо 40 

натрий 40 

сталь 20 

Обогащ ение топлива, % 11,3 

К оэффициент воспроизводства 1,41 

Равновесны е концентрации P u , % 

239Ри-61 

240Ри-30 

241Ри-6 

242Ри-3 

Содерж ание осколков — 4 % от количества (P u + U ) . 

Характеристики реактора приведены в приложениях в табл.1. 

Результаты расчета приведены в приложениях в таблицах II и III. 

Необходимо сделать некоторые пояснения к модели расчета и резуль 

татам . 

Принята некоторая упрощенная модель корреляций,-погрешностей, 

которая характеризуется следующими чертами . 

1) Числа вторичных нейтронов всех делящихся изотопов при всех 

энергиях первичных нейтронов измеряются относительно калифорниевого 

стандарта и поэтому погрешность этого стандарта входит наиболее 

весомо. 

Большие усилия во многих странах за последние десять лет и особен 

но начиная с 1966 года по абсолютному определению v калифорния-252, 

привели к результату v0 = 3,733 ± 0,0085, принятому Вторым совещанием 

экспертов МАГАТЭ по стандартам (Вена, ноябрь 1972 года). Соответственно 

этому мы приняли достигнутую погрешность в 0,3%. 

2) Считается,что для каждой величины вся область энергий разбита 

на три корреляционных интервала: 0-0,1 МэВ; 0,1-0,8 МэВ; 

0,8-10 МэВ, и погрешность каждой величины имеет компоненту постоянную 

на протяжении каждого из корреляционных интервалов. Оказывается, 

что именно эти компоненты погрешности следует принимать в расчет 

и именно на них следует выставлять требования, так как статистическая 

компонента погрешности дает значительно меньший вклад в общую погрешность 

. Квадрат вклада от статистических ошибок всех рассматри-

IAEA SM -170/ 91 135 

ваемых величин при наших предположениях об их величинах в пределах 

от 1-5% составляет всего 0,12 в общий квадрат погрешности,равный 

четырем. 

Таким образом, в табл.II приведены требования на скоррелированные 

по корреляционным интервалам компоненты погрешности, т.е. на 

ошибки в нормировке кривых сечений в пределах этих интервалов. 

Поэтому при сравнении с достигнутыми точностями данных надо исключать 

статистическую компоненту погрешности. 

3) Считается, что поток нейтронов при измерениях всех сечений 

измеряется единым методом в пределах каждого из корреляционных 

интервалов. Например, в интервалах выше 0,1 МэВ по сечению деления 

урана-235, а ниже по сечению бора и лития. Это предположение соответствует 

рекомендации измерять конкурирующие процессы в наибольшей 

степени относительно, что, как показывает расчет, уменьшает требования 

на точность измерения . Поэтому в таблице имеются достигнутые 

и требуемые точности в измерении потока, которые можно трактовать и 

как точности сечения деления урана-235, предполагая его использование 

для измерения потока нейтронов. 

Из результатов таблицы хотелось бы отметить большие требуемые 

уточнения в сечениях захвата урана-238, плутония-239, осколков деления, 

особенно в области ниже 100 кэВ, но также и до 8 0 0 кэВ, в неупругом 

рассеянии урана-238, особенно в области от 0,8 до 2,5 МэВ, v плутония-239 

Рассмотрение таблицы дает возможность определить величины, 

уточнение которых наиболее эффективно. Это те величины, существующие 

погрешности которых дают наибольшие вклады в дисперсию реакторного 

параметра, в данном случае КВ, а при достижении требуемых 

погрешностей их вклад меняется максимально, оставаясь тем не менее 

определяющим и в новом значении дисперсии реакторного параметра . 

Теперь следует обсудить место требований, полученных с точки 

зрения уточнения предсказания коэффициента воспроизводства среди 

требований, исходящих из других соображений. 

Во-первых, можно отметить сравнительно умеренный характер требований 

по сравнению с требованиями для уточнения предсказаний Кэфф. 

до погрешности в ± 1 % (см .напр.[12]). 

Однако далее при рассмотрении роли интегральных экспериментов 

мы приведем аргументы в пользу этих более умеренных требований. 

Во-вторых, надо отметить, что для установления полного списка 

потребностей для быстрых реакторов, надо привлечь и все другие 

соображения восьми пунктов раздела И, а также соображения по защите. 

С точки зрения методики использование указанных соображений проводится 

точно так же, как описано выше. Мы не будем здесь этого делать, 

так как такие списки можно найти в изданном МАГАТЭ мировом списке 

потребностей в ядерных данных R E N D A - 7 2 . Сравнение же требований 

таблиц II и III с R E N D A - 7 2 , особенно с английскими запросами Кэмпбела, 

показывает довольно хорошее их числовое согласие, хотя смысл этих 

чисел нельзя считать совпадающим, поскольку он не объяснен достаточно 

ясно в R E N D A - 7 2 . 

Дальнейшее изложение мы посвятим возможной роли интегральных 

экспериментов в ослаблении требований на точность микроскопических 

ядерных данных и общему описанию соответствующего математического 

аппарата, заимствованного из математической теории планирования 

эксперимента.

ТАБЛИЦА И. ДОСТИГНУТЫЕ И ТРЕБУЕМЫЕ ПОГРЕШНОСТИ ЯДЕРНЫХ ДАННЫХ И ИХ ВКЛАД 

В ДИСПЕРСИЮ КВ 

Изотоп Процесс 

239ри 

241Ри 

Интервал энергий, М эВ 

10,5 > E > 0,8 0,8 > E > 0,1 E < 0,1 

1 2 3 4 1 2 3 4 1 2 3 4 

а с 50 22 0,35 0,07 15 5 1,15 0,13 10 3,6 3,17 0,42 

СТр 6 6 0,00 0,00 4 4 0,00 0,00 5 3,8 0,04 0,02 

3 M 0,75 0,10 1 0,5 0,23 0,06 2 0,75 0,700 0,10 

°с 50 50 0,00 0,00 30 30 0,00 0,00 20 20 0,00 0,00 

°F 10 9 0,02 0,02 10 5 0,19 0,05 15 5 1,21 0,14 

«г 

4 4 0,01 0,01 3 2,5 0,03 0,02 2 1,6 0,04 0,02 

50 37 0,05 0,03 30 15 0,29 0,0 7 20 10 0,29 0,07 

240Ри 7 4 0,16 0,05 7 7 0,00 0,00 7 7 0,00 0,00 

V* 

3,0 2,0 0,0 6 0,03 3 3 0,00 0,00 3 3 0,00 0,00 

стс 20 10 0,19 0,05 10 3,3 1,42 0,14 15 2,7 13,5 0,43 

гзву aF 5 2 0,54 0,09 

UF 3 1,3 0,43 0,08 

Осколки 

деления 

242Ри 

23N a 

CTtr 20 20 0,00 0,00 20 20 0,00 0,00 20 20 0,00 0,00 

a F 

VF 

50 36 0,05 0,03 30 14 0,27 0,06 30 10 1,1 0,12 

50 50 0,00 0,00 30 30 0,00 0,00 20 20 0,00 0,00 

7,0 7,0 0,00 0,00 

4,0 4,0 0,00 0,00 

CTc 50 50 0,00 0,00 50 50 0,00 0,00 50 45 0,02 0,02 

fftot 

20 20 0,01 0,01 10 10 0,01 0,01 10 10 0,01 0,01 

136 УСАЧЕВ и др.

ТАБЛИЦА II . (продолжение) 

Сталь стс 50 22 0,39 0 ,0 7 30 16 0,19 0,05 30 13 0,40 0 ,08 

CTtot 20 20 0,00 0 ,00 20 20 0,01 0,01 20 20 0,00 0 ,00 

i60 °с 15 15 0,00 0 ,00 

°tot 10 9 0,02 0 ,01 10 6,0 0,07 0,0 3 10 10 0,00 0 ,00 

252c f 

0,3 0,3 0,50 0 ,50 

Поток 6 1,8 1,61 0;,15 3 2,4 0,03 0,02 4,0 2,3 0,13 0 ,04 

IAEA SM-170/91 137

ТАБЛИЦА III. ПОГРЕШНОСТИ В НЕУПРУГОМ РАССЕЯНИИ ИЗ ДАННОЙ ГРУППЫ ВО ВСЕ 

НИЖЕЛЕЖАЩИЕ И ИХ ВКЛАДЫ В ДИСПЕРСИЮ КВ 

И з о 

топ 

Интервал энергий, М э В 

10,5 - 6,5 - 4 ,0 - 2 ,5 - 1,4 - 0 ,8 - 0 ,4 - 0 ,2 - 0,1 - 

6,5 4 ,0 2 ,5 1.4 0,8 0,4 0,2 0,1 0 ,0 4 

1 30 20 20 15 10 7 7 7 7 

238 ri 2 11 14 20 4 ,5 3,0 7 7 3,4 7 

3 0,71 0 ,0 6 0,02 1,98 3 ,4 2 0,01 0,01 0 ,2 5 0 ,0 0 

4 0,1 0 0 ,0 3 0 ,02 0 ,1 7 0,2 2 0,01 0,01 0,0 5 0 ,0 0 

Оскол 1 30 30 30 30 30 30 30 30 30 

ки 2 25 30 30 15 13 30 30 24 30 

деле 3 0 ,0 3 0 ,0 0 0,01 0 ,2 2 0 ,4 5 0 ,0 0 0 ,0 0 0,0 4 0 ,0 0 

ния 4 0,02 0 ,0 0 0 ,01 0 ,0 6 0 ,0 8 0 ,0 0 0 ,0 0 0 ,0 2 0 ,0 0 

239-,-. 

P u 

1 30 30 30 30 30 30 30 30 30 

2 30 30 30 23 17 30 30 26 30 

3 0,0 0 0 ,0 0 0 ,0 0 0,04 0,1 2 0 ,0 0 0 ,0 0 0 ,0 3 0 ,0 0 

4 0,00 0 ,0 0 0 ,0 0 0,02 0,0 4 0 ,0 0 0 ,0 0 0,0 2 0 ,0 0 

138 УСАЧЕВ и др.

П римечания к таблицам II и III. 

IA E A -S M -170/91 139 

1 — погрешности, имеющие место в настоящее время. 

2 — требуемая погрешность, обеспечивающая расчет КВ 

с точностью 2 % . 

3 - квадрат вклада погрешности, имеющей место в настоящее время, 

в дисперсию КВ, равную 37. 

4 — квадрат вклада погрешности, которую надо достичь, 

в дисперсию КВ, равную 4 . 

Сумма столбцов 3 в таблицах II и III равна 37, что соответствует 

точности расчета КВ 6% . 

Сумма столбцов 4 в таблицах II и III равна 4, что соответствует 

точности расчета КВ 2 % . 

V . ИСПОЛЬЗОВАНИЕ ИНТЕГРАЛЬНЫХ ЭКСПЕРИМЕНТОВ ДЛЯ СМЯГ 

ЧЕНИЯ ТРЕБОВАНИЙ НА ТОЧНОСТЬ МИКРОСКОПИЧЕСКИХ ЯДЕРНЫХ 

ДАННЫХ 

Интегральные эксперименты использовались с самого начала работ 

по цепной реакции деления . По их результатам подгонялись ядерные 

данные. Но в начале это делалось на интуитивном уровне, без выработки 

соответствующего математического формализма . 

В работе Чечини [7], Барре, Равье [13], Пази [21], 

Роулэндса и др. [14], Хеммент и Пэндлбэри [22], Кэмпбела и Роулэнд- 

са [18], Бэллэнса [23], Драгта [24], Усачева и Бобкова [19] применен 

метод наименьших квадратов для подгонки ядерных данных, с целью 

наилучшим образом описать всю совокупность имеющихся интегральных 

экспериментов, не входя в противоречие и с микроскопическими измерениями 

. 

На основе такого подхода были существенно смягчены английские 

требования на точности ядерных данных, публикуемые в списке запросов 

R E N D A , начиная с 1966 года. Однако это делалось математически 

неформализованным способом. 

В развитие математического алгоритма, выработанного для определения 

потребностей в точностях совокупности только микроскопических 

экспериментов [12], кратко изложенного и использованного выше, был 

выработан и алгоритм для планирования совокупности микроскопических 

и интегральных экспериментов, позволяющих в частности решить задачу 

об определении смягчения требований на ядерные данные. 

В работе Усачева и Бобкова "Математическая теория эксперимента 

и обобщенная теория возмущений - эффективный подход к исследованию 

физики реакторов" [ 16] было предложено для решения комплекса задач 

подгонки ядерных данных и планирования наиболее информативных 

экспериментов использовать метод последовательного планирования 

эксперимента, изложенный, например, в книге под редакцией Налимо- 

ва В .В . [20] в статье Федорова В .В . 

В рамках метода последовательного планирования эксперимента 

было введено понятие информативности интегрального эксперимента 

относительно поставленной цели уточнения определенной реакторной 

характеристики проектируемого реактора [16]. Информативность

140 У С А Ч Е В и д р . 

определена как уменьшение дисперсии предсказания интересующей нас 

реакторной характеристики в результате проведения данного эксперимента. 

На этой основе развертывается исследование информативности 

уже проведенных интегральных экспериментов и планируемых вновь. 

Так в этой же работе исследованы эксперименты на сборках ZPR-III с 

точки зрения уточнения предсказания КЭфф реактора БН-600. Оказалось, 

что только 5 экспериментов из 20 уменьшают дисперсию предсказания, 

и особенно информативной оказалась сборка ZPR-III-29. 

В этой же работе предложен способ проведения подгонки констант 

в рамках той же идеологии, что в цитируемых выше работах, но не 

требующий обращений матриц. Все вычислительные операции сводятся 

лишь к умножению матрицы на вектор. Все дело в том, что в качестве 

первого шага выбирается совокупность только микроскопических 

экспериментов с диагонализованной, благодаря описанному выше способу 

учета корреляций, ковариационной матрицей. 

Вычисление ослабления требований на ядерные данные при использовании 

интегральных экспериментов производится следующим образом. 

Задаем набор дисперсий интересующего нас реакторного параметра от 

требуемого значения, например, четыре для коэффициента воспроизводства 

соответственно требованию точности — 2 % , до значения, имеющего 

место на данный момент, для КВ-37. 

Для выбранных значений дисперсий определяется совокупность 

требуемых точностей одних микроскопических величин, аналогично представленным 

в табл. II и III. Принимая за исходные полученные таким 

образом точности и подключая используемые интегральные эксперименты 

последовательно по одному, на основе алгоритма, описанного в работе 

[16], вычисляем дисперсию предсказания реакторной характеристики- 

цели. Вычисленные значения дисперсии откладываются на графике в 

зависимости от заданных дисперсий, соответствующих предсказаниям на 

основе только микроскопических ядерных данных. Интерполяцией определяется 

точка кривой, в которой дисперсия, вычисленная с учетом 

интегральных экспериментов, равна заданной дисперсии интересующего 

нас реакторного параметра, например, четырем в случае коэффициента 

воспроизводства. Другая координата этой точки определит сниженный 

уровень точности, требуемый от микроскопических величин. 

И для этого нового значения дисперсии интересующего нас реакторного 

параметра по описанному выше алгоритму, еще раз вычисляются 

все величины, входящие в таблицы II и III. Это и будут требования к 

микроскопическим величинам, ослабленные благодаря использованию 

интегральных измерений. 

Первые результаты, полученные на пути применения описанного 

алгоритма, привели к выводу о том, что существующие интегральные 

эксперименты на обогащенном уране могут полностью снять требования 

по уточнению ядерных величин для расчета КЭфф с точностью ± 1% больших 

урановых быстрых реакторов. Иными словами, при устанавливаемых 

в результате подгонки корреляций между константами для экстраполяции 

расчета в область очень больших реакторов достаточно и существующих 

точностей ядерных данных. 

Исследованные до сих пор интегральные эксперименты не могут 

полностью снять требований на ядерные данные, если нас интересует 

предсказание КВ. Это - эксперименты по отношениям чисел процессов 

в центре активной зоны аР8/стР9, стс8/стР9, стс9/стр9 и ctf5/ctf9 в сборке

IAEA-S M -170/91 141 

ZPR-III-48 и по КЭфф этой сборки. Все указанные эксперименты могут 

снизить требование к дисперсии в КВ всего с 4-х до 5, т.е. требования 

на микроскопические ядерные данные для обеспечения расчета КВ с 

дисперсией 4 можно будет получать по описанному выше алгоритму, 

исходя из дисперсии 5. 

Надо отметить, что выше употреблялись выражения "могут снять 

или ослабить требования", но не "снимают или ослабляют требования" по 

той причине, что к интегральным экспериментам надо относиться с очень 

большой осторожностью, поскольку для указанных целей необходимо 

полное соответствие эксперимента и его расчетной модели, не говоря 

уже об отсутствии систематической ошибки самого эксперимента. 

Чрезвычайно опасным является невыявленное несоответствие, 

которое может привести к сдвигу предсказываемых параметров, хотя 

такой сдвиг и можно обнаружить в процессе подгонки констант, благодаря 

критерию X 2 . Таким образом, наши утверждения о роли интегральных 

экспериментов следует понимать как возможности того или иного 

интегрального эксперимента; что же касается превращения этой возможности 

в действительность, то здесь требуется большая работа 

специалистов-реакторщиков по оценке каждого интегрального эксперимента 

[19], т.е. приведению его в соответствие с расчетной моделью 

и расчету коэффициентов чувствительности измеряемых величин к 

изменению ядерных данных. 

ЛИТЕРАТУРА 

[ 1] M O O R H E A D , Т . P . , in P h y s ic s of F a st and Intermediate R eacto rs, (P r o c . Sem inar, 

V ie n n a , 1961), 2, I A E A , V ie n n a (1962) 111. 

[2] G A N D I N I , A . , A N L - 6 6 0 8 (1962). 

[ 3] У С А Ч Е В , Л . H ., А т ом на я энергия (1963) 4 7 2 . 

У С А Ч Е В , Л . H . , З А Р И Ц К И Й , С . М . , Бюллетень Информационного Центра по Ядер- 

ны м Д анны м . В ы п .2 , М ., А т ом и з д а т , 1 965, стр .2 4 2 . 

[4] G R E E B L E R , P . , H U T C H I N S , В . A . , Conferen ce on Neutron C r o s s Section 

Technology, W ashington (1966). 

[5] S M I T H , R . D . , in N u c le a r Data for R eactors (P r o c . C onf. P a r is , 1966) 1, I A E A , 

Vienna (1967) 27. 

[ 6] У С А Ч Е В , Л . H ., З А Р И Ц К И Й , С . M ., Ядерные Данны е для Реакторов, (Труды К о н 

ференции, Париж, 1966) М А Г А Т Э , Вена _1_ (1967) 3 2 1 . 

[ 7] G A N D I N I , A . et a l . , in F a st Reactor P h y s ic s and Related Safety P r o b le m s (P ro c . 

S y m p .K a r l s r u h e , 1967); C E C C H I N I , G . e t a l . , C o m p a r is o n between experimental 

and theoretical integral data, 1966 (A N L - 7 3 2 0 ), p. 107. 

[8] G R E E B L E R , P . , H U T C H I N S , B . A . , L I N F O R D , R . B . , N u c l .A p p l ., 4 5 (1968) 297. 

[9] З А Р И Ц К И Й , С . M ., Т Р О Я Н О В , M . Ф ., В с б . "Фи зи ка ядерных реакторов' . В ы п .2, 

М . , А т ом и з д а т , 1 9 7 0 , с т р. 168. 

[10] З А Р И Ц К И Й , С . М . , Н И К О Л А Е В , M . Н Т Р О Я Н О В , М . Ф Доклад на Совещании 

по Нейтронной Физике, К иев, 1971 . 

[11] G R E E B L E R , P . , H U T C H I N S , В . A . , C O W A N , C . L . , in N u c le a r Data fpr Reactors 

(P r o c .C o n f .H e l s in k i, 1970) 1, I A E A , Vienna (1970) 17. 

[12] U S A C H E V , L . N . , B O B K O V , Y . G . , Planning of an optim um set of experim ents and 

evaluations, I N D C (C C P )- 1 9 /V - V ienna, 1972 . 

[13] B A R R E , J . Y . , R A V I E R , J . , in F a st Reactor P hysic s and Related Safety P r o b le m s 

(P r o c . S y m p .K a r l s r u h e , 1967). 

[ 14] Выступление Роулэнде на англо-советском семинаре, 1 9 6 8 . 

[ 15] H Ä G G B L O M , A djustem ent of Neutron C r o s s 

Studswyk, Sw eden, 1971. 

Section Data by a L e a s t Squares Fit. 

[ 16] У С А Ч Е В , Л . H ., Б О Б К О В , Ю . Г ., Ядерные К онстанты , Вы п .1 0 , M ., А т ом и зд а т , 1 9 7 3 . 

[ 17] У С А Ч Е В , Л . Н ., Б О Б К О В , Ю .Г ., Предложение по R E N D A — всемирному списку 

запросов. Доклад на 4-ом заседании М К Я Д , В е н а , 1 9 7 2 .

142 У С А Ч Е В и д р . 

[18] C A M P B E L L , C . G . , R O W L A N D S , J . L . , Th e Relationship of M icroscopic and 

Integral D ata, in N u c le a r Data for R e acto rs, (P r o c .C o n f .H e l s in k i, 1970) 2, I A E A , 

Vienna (1970) 391. 

[19] У С А Ч Е В , Л . Н . , Б О Б К О В , Ю . Г . , О совокупном использовании результатов интег 

ральных измерений в проблеме ядерных данных для реакторов, I Совещание по 

Нейтронной Физике для Реак тор ов, К иев, 1 9 7 1 . 

[ 20] Новые Идеи Планирования Эксперимента . Под ред .В .В . Налимова, М ., Изд-во 

"Н а у к а ", 1970 . 

[ 21] P A 2 Y , U s e of Integral M e a s u r e m e n t s as Supplem entary Data in N eutro n Cross- 

Section Evaluations, (A N L - 7 3 2 0 ), 1966, 270. 

[22] H E M M E T , P . C . E . , P E N D L E B U R Y , E . D . , Optim ization of Neutron Cross- 

Section D ata. ( A N L -7320), 1966, p. 88. 

[23] B A L L A N C E , B . M . O . e t a l ., Optim ization of Neutron Cross-Section Data, 

P r o c .B N E S , L ondo n , 1969, p. 149. 

[24] D R A G T , J . B . , Statistical Consideration of Techniq ues for Adjustm ent 1970, 

(R C N - 1 2 2 ), p. 85. 


A . M. W EIN BERG: T he B r o m le y R e p o r t en titled "P h y s ic s in P e r s p e c tiv e " 

e stim a te s that u n certa in tie s in c r o s s - s e c t i o n s w ill ca u se a c o s t in cr e m e n t of 

0 .1 5 to 0. 25 US m ill/k W • h in fu e l-c y c le c o s ts o f b r e e d e r r e a c t o r s . T h is, if 

e x tra p o la te d to the y e a r 2000, w ould r e p r e s e n t a c o s t o f s e v e r a l thousand 

m illio n d o lla r s /y r . H ave you m ade any s im ila r e stim a te s o f how m uch w ould 

b e sa v e d in f a s t - r e a c t o r c o s ts by such im p ro v e m e n ts in b re e d in g ra tio as you 

su g gest, and how m uch the e x p e rim e n ts m igh t c o s t? 

G. Y AN K O V: T h e p a p e r w hich I have p rese n te d d oes not in clu d e any 

e c o n o m ic ca lcu la tio n s w h a tever. 

J. Y. B A R R E : In r e p ly to P r o f e s s o r W e in b e r g 's qu estion , I can sa y that 

in F r a n c e the e x p e rie n c e w ith fa s t-n e u tro n r e a c to r s has been that the c o s t 

o f r e a c t o r p h y s ic s stu d ies w as la r g e ly o ffs e t by the resu ltin g sa vin g s on 

this type of r e a c t o r . H ow ever, as m en tion ed in ou r p a p er (I A E A -S M -1 7 0 /69), 

th e se a re stu d ies b a sed on in te g ra l e x p e rim e n ts. T he data obtain ed in th ese 

in v e s tig a tio n s have an im p orta n t b e a rin g on the op tim iz a tio n o f the p r o je c t, 

on the sa fe ty a s p e c ts and on u n d erstan d in g o f p o w e r plant o p e ra tio n s . 

W . B . LEW IS: T h e B r o m le y R e p o r t to w hich P r o f e s s o r W ein b erg 

r e fe r r e d in clu d ed , o f c o u r s e , a p r o je c tio n o f lig h t-w a te r r e a c to r s fr o m the 

p r e s e n t tim e and, w ork in g fr o m th is, one can show what the c o s t sa vin g s 

w ould b e. T o do the sa m e thing fo r the f a s t -b r e e d e r r e a c to r , we w ould have 

to m ake a p r o je c tio n f o r the n u m ber and to ta l c a p a city o f th ese r e a c t o r s , and 

as yet I think th ere is h esita tion about m akin g any su ch p re d ic tio n fo r the 

y e a r 2000.

I A E A - S M -1 7 0 /6 9 

ROLES RESPECTIFS DES EVALUATIONS 

ET DES EXPERIENCES INTEGRALES POUR 

LA PHYSIQUE DES REACTEURS RAPIDES 

J. Y. BARRE, J.P. C H A U D A T 

CEA, Centre d'êtudes nucléaires de Cadarache, 

France 


RESPECTIVE ROLES OF EVALUATIONS A N D INTEGRAL EXPERIMENTS IN THE PHYSICS OF FAST REACTORS. 

Applications of nuclear data to the prediction of fast-power reactor parameters are described. In the 

integral approach chosen at the Commissariat à l’énergie atomique, differential measurements play, through 

evaluations, a complementary role with respect to the critical experiments which serve as references. The 

significance of differential measurements in realizing version 3 of the Cadarache multigroup effective 

cross-section sets and the most important future needs of the fast-reactor physicists are described. 

ROLES RESPECTIFS DES EVALUATIONS ET DES EXPERIENCES INTEGRALES POUR LA PHYSIQUE DES 

REACTEURS RAPIDES. 

Les applications des constantes nucléaires dans les prédictions des paramètres des réacteurs rapides de 

puissance sont décrites. Dans l'approche intégrale choisie au Commissariat à l’énergie atomique, les 

mesures différentielles, par l'intermédiaire des évaluations, jouent un r&le complémentaire par rapport 

aux expériences critiques qui servent de référence. La part donnée aux mesures différentielles dans la mise 

au point de la version 3 du jeu de sections efficaces multigroupes de Cadarache et les principaux besoins 

futurs des physiciens de réacteurs rapides sont analysés. 

IN TR O D U C TIO N 

Sur ce p r o b lè m e a u s s i la rg e m e n t tra ité [1, 2] que c o n t r o v e r s é [3] 

il n' e st pas r é a lis te de p e n s e r a p p o rte r d es arg u m en ts nouveaux s u ffis a m 

m ent fo r ts p ou r c o n v a in c re a u jo u rd ' hui le s p a rtisa n s de 1' une ou 1' autre 

d e s a p p ro c h e s u tilis é e s p ou r la d é te rm in a tio n d e s c a r a c té r is t iq u e s d 'u n 

r é a c te u r à n eu tron s ra p id e s de p u iss a n ce . En sch ém a tisa n t à 1' e x trêm e 

le s u je t, deux so lu tio n s o p p o s é e s ex iste n t su r le plan m on d ia l: 

a) U tilisa tio n d e s étu des de m é th od es de c a lc u l et d es m e s u r e s 

d iffé r e n t ie lle s « t r i é e s » dans d e s év a lu a tio n s: L e s ré su lta ts d es e x p é 

r ie n c e s c r itiq u e s se rv e n t uniquem ent à te s te r la v a lid ité d e s p a ra m è tr e s 

c a lc u lé s . C' e st plutôt 1' orie n ta tio n su iv ie aux E ta ts-U n is d 1 A m é riq u e 

et en R épubliqu e fé d é r a le d 'A lle m a g n e , p a r e x e m p le . 

b) U tilisa tio n d e s étu des de m é th od es de c a lc u l et d e s ré su lta ts des 

e x p e r ie n c e s in té g ra le s p ou r a m é lio r e r le s p r é d ic tio n s : L e s don n ées de 

b a s e , is s u e s d e s m e s u r e s d iffé r e n t ie lle s , se rv e n t e ss e n tie lle m e n t de 

poin t de d ép a rt ou d 'in t e r m é d ia ir e s . C ette a p p ro ch e e st reten u e en 

p a r t ic u lie r en G ra n d e -B re ta g n e et en F r a n c e . 

L e s p o s itio n s r e s p e c t iv e s ne sont é v id em m en t pas a u s s i tra n ch é e s 

et se situ ent e n tre c e s deux e x tr ê m e s . 

143

144 BARRE e t C H A U D A T 

Q u els sont le s argu m en ts du C E A p ou r r e te n ir la se con d e a p p ro ch e , 

c ' e s t - â - d i r e se b a s e r s u r le s e x p é r ie n c e s in té g r a le s , et dans cette 

so lu tio n , qu el r ô le in co m b e aux m e s u r e s d iffé r e n t ie lle s et aux é v a lu a tio n s? 

E n fin , au stade a ctu e l, q u els sont le s b e s o in s fu tu rs en m e s u r e s d iffé 

r e n t ie lle s d e s p r o je ts r a p id e s en F r a n c e ? 

L e m om en t e st bien c h o is i p ou r a b o r d e r c e s p r o b lè m e s , c a r la 

sy n th è se de qu atre ans de p r o g r a m m e s d 'e x p é r ie n c e s c ritiq u e s e ffe ctu é e s 

au C E A vien t de se c o n c r é t is e r dans la r é a lis a tio n , au début de cette 

an n ée, de la v e r s io n 3 du je u de s e c tio n s e ffic a c e s m u ltig rou p e s de 

C a d a ra ch e , u tilis é m aintenant p ou r le s d é fin itio n s d e s p r o je ts . C ette 

n o u v e lle v e r s io n re p ré s e n te un gain c o n s id é r a b le en p r é c is io n p a r ra p p o rt 

à la v e r s io n p r é cé d e n te [4] g r â c e aux ré su lta ts in tég ra u x obtenus su r 

M a su r ca , E rm in e et H a rm on ie. 

1. N E CESSITE DE L 'A P P R O C H E IN T E G R A L E 

1.1 . B uts de la p h ysiqu e d e s r é a c te u r s 

L ' o rie n ta tio n reten u e d é c o u le d ir e c te m e n t d e s buts p o u rs u iv is : 

o b te n ir , a v e c la p r é c is io n et dans le s d é la is r e q u is p ar le s p r o je t s , le s 

p a ra m è tr e s p rin cip a u x d es r é a c te u r s ra p id e s de p u issa n ce . La c o n n a is 

sa n ce de c e s quan tités, qui sont tou tes d e s v a le u rs in té g r a le s , est 

n é c e s s a ir e , au stade de 1' a v a n t-p r o je t p ou r la sû reté et 1' op tim isa tio n 

de la c e n tra le , au stade de 1' ex p lo ita tio n p ou r p r é v o ir et c o m p r e n d r e de 

m a n iè re sû re le co m p o rte m e n t du r é a c te u r . Il s ' agit p rin cip a le m e n t: 

- d e s e n r ic h is s e m e n ts c ritiq u e s 

- d e s d is trib u tio n s de p u issa n ce 

- d e s gain s de s u r ré g é n é r a tio n 

- d e s v a le u rs d e s b a r r e s de com m a n d e 

- d e s p r o b lè m e s lié s aux b lin d a g e s. 

1.2. C o n sé q u e n ces 

L e s buts étant d é fin is , il e st n é c e s s a ir e , p o u r c o m p r e n d r e le s 

r a is o n s d e s c h o ix fa its , de r é fu te r q u elq u es id é e s trop sou vent r e ç u e s 

et d 'in s is t e r su r le s p r o b lè m e s de p r é c is io n et de d é la i: 

- L a c o n n a is sa n ce d e s d on n ées de b a se n' e s t pas un but en s o i. Le 

fa it q u e, p a r e x e m p le , la se c tio n e ffic a c e de fis s io n du plu ton iu m -2 39 

s o it 1 ,5 ou 1 ,6 ba rn à 100 keV n' ap p orte r ie n aux in g én ieu rs de p r o je t. 

Ce qui im p o rte , c ' e st la co n n a is sa n ce de p a ra m è tr e s in té g ra u x , de taux 

de r é a c t io n s : c e son t c e s quantités qui son t m e s u r é e s dans le s e x p é r ie n c e s 

c r itiq u e s . 

- La c la s s e de p a r a m è tr e s in tég ra u x ou de r é a c te u r s à é tu d ie r est 

lim ité e à un d om ain e b ien d éfin i: dans le ca s du C E A , il s ' agit de r é a c te u rs 

à ox y d e m ixte de p lu ton iu m , r e fr o id is au so d iu m , à deux z o n e s, r é flé c h is , 

dans la g am m e de p u issa n ce c o m p r is e e n tre 250 et 2000 M W (e). P o u r le s 

b lin d a g e s du c œ u r , le s m a té ria u x et le s c o m p o s itio n s v o lu m iq u e s p o s s ib le s 

son t en n o m b re r e s tr e in t: a c ie r in o x -s o d iu m ou fe r -g r a p h ite -s o d iu m .

I A E A - S M - 1 7 0 /69 145 

L a quantité d 'in fo r m a tio n s n é c e s s a ir e s p ou r co n n a ître le s p a r a 

m è tre s p rin cip a u x dans le dom ain e c o n s id é r é e st en r é a lité t r è s in fé r ieu 

re à c e lle contenue dans le s d on n ées d iffé r e n t ie lle s . L e s e x p e r ie n c e s 

in té g ra le s son t, e lle s , c e n tré e s su r le dom ain e et le s in fo rm a tio n s 

in té r e s s a n ts . 

- La p r é c is io n d e s d on n ées de b a se é v a lu é e s , is s u e s d e s m e s u r e s 

d iffé r e n t ie lle s , e st in su ffisa n te a ctu e lle m e n t p ou r s a tis fa ir e le s dem an des 

de p r é c is io n d e s p r o je t s : ce p oin t, recon n u u n anim em en t, ne n é c e s s ite 

p a s d 1 e x e m p le su p p lé m e n ta ire , m ê m e s i la c o n v e rg e n ce e n tre la b o r a to ir e s 

a été a m é lio r é e su r c e r ta in e s d on n é e s, c e s d e r n iè r e s an n ées [2, 5 -7 ]. 

- Il e s t p o s s ib le d 'e n v is a g e r une a m é lio r a tio n d e s p r é c is io n s des 

m e s u r e s d iffé r e n t ie lle s dans le s an n ées fu tu re s , bien que p ou r p lu sie u rs 

d on n ées un c e rta in p la fon d s e m b le atteint dans 1' état a ctu e l d es tech n iq u es 

(e x e m p le : p a ra m è tr e s de r é so n a n ce du p lu to n iu m -2 3 9 ). M a is, p ou r ce 

qui c o n c e r n e le C E A , r e s p e c t e r le s d é la is d e s p r o je ts im p liq u a it pou r 

P h én ix et im p liq u e p ou r 1200 M W (e) de p a s s e r p a r le s e x p é r ie n c e s 

in té g r a le s . 

- En fa it, m ê m e dans 1' h ypoth èse utopique d 'u n e c o n n a is sa n ce p a rfa ite 

de tou tes le s d on n ées d iffé r e n t ie lle s , le te s t d e s a p p ro x im a tio n s de m é th o d e , 

ren d u es o b lig a to ir e s p a r la c o m p le x ité d e s p r o b lè m e s p o s é s p a r le d e - 

cou p a ge é n e rg é tiq u e ou le s co n d itio n s g é o m é tr iq u e s , s e r a it im p é ra tif. 

L ' e x e m p le le plu s p a rla n t e s t p roba b le m e n t le c a lc u l d e s fu ites p r é fé r e n 

t ie lle s dans le s canaux de c irc u la tio n d 'h é liu m d 'u n r é a c te u r ra p id e à g a z. 

1.3. A p p lica tio n 

P o u r a ttein d re dans le s d é la is voulu s le s p r é c is io n s d em a n d ées p ar 

le s p r o je t s , le s e x p é r ie n c e s in té g ra le s son t in d is p e n s a b le s. 

C e s e x p é r ie n c e s son t co n çu e s au C E A p ou r m e s u r e r , su r d es m ilie u x 

s im p le s , d e s g ra n d e u rs c a r a c té r is t iq u e s d e s m ilie u x é tu d iés et d ir e c t e 

m en t r e lié e s aux p a ra m è tr e s p r o je t. L e s r é su lta ts se rv e n t à la q u a lific a 

tio n de 1' e n se m b le d e s m éth od es de c a lc u l et d es d on n ées de b a se , 

cou ra m m e n t ap p elé « fo r m u la ir e » . L e seu l p r o b lè m e r é s id e dans la 

v a lid ité d e s tra n s p o s itio n s d e s ré su lta ts d e s e x p é r ie n c e s in té g ra le s au 

c a s r e e l du p r o je t. Si le s e x p é r ie n c e s son t c o r r e c t e m e n t c h o is ie s , cette 

tra n s p o s itio n c a lc u lé e e s t fa ib le et fa ite a v e c le m in im u m de r is q u e s 

d 'e r r e u r . 

L e p r o g r a m m e qui a s e r v i de b a se â la r é a lis a tio n de la v e r s io n 3 

du jeu de s e c tio n s e ffic a c e s m u ltig rou p e s de C a d a ra ch e a d é jà été p a r t ie lle 

m en t d é c r it [8, 9]. Il r e p o s e e sse n tie lle m e n t su r le s t r o is types de m e s u r e s 

in té g ra le s su iv a n tes: 

- la p la c ie n m a tiè r e ; 

- r a p p o r t p rod u ctio n to ta le su r a b so rp tio n totale dans d es e x p é r ie n c e s 

à fu ite s n u lle s; 

- r a p p o rt de taux de r é a c tio n m o y e n s: 

p a r ra p p o rt à la fis s io n 235U, fis s io n 238U, ca p tu re 238U, fis s io n 239P u, 

fis s io n 240P u , fis s io n 24IP u , 

p a r ra p p o rt à la ca p tu re 238U, captu re 235U, ca p tu re 239P u , captu re 

240P u , ca p tu re 241P u.


P o u r c e s p a r a m è tr e s , le s p r o g r è s d e s m éth od es de c a lc u l sont te ls 

que le r e c a la g e du fo r m u la ir e su r le s ré su lta ts d e s e x p é r ie n c e s in té g ra le s 

r e v ie n t uniquem ent à un aju stem en t d e s d on n ées de b a se . La m éthod e 

u tilis é e p ou r ce tte n o u v e lle v e r s io n e s t iden tiqu e dans son p r in cip e à 

c e lle u tilis é e p r é cé d e m m e n t [4]. 

Il im p o rte de p r é c i s e r que c ' e st 1' e n se m b le a p p ro x im a tio n s de 

m eth od e - don n ees a ju s té e s qui seu l conduit aux p r é d ic tio n s c o r r e c t e s 

d e s p a ra m è tr e s in té g ra u x , dans la gam m e étu d ié e , m a is que chaque 

donnée in d iv id u elle n 1 e st pas n é c e s s a ir e m e n t la v a le u r v r a ie : le s 

te n d a n ces se dégagent cep en d ant. A la lim ite , c e la n' e st pas fon d a 

m en ta lem en t im p ortan t puisque le s qu an tités in té g ra le s p ou r le s q u e lle s 

le fo r m u la ir e e st q u a lifié son t p r é d ite s a v e c la p r é c is io n r e q u is e . 

Une solu tion iden tiqu e e st a ctu e lle m e n t m is e au poin t p ou r le s p a r a 

m è tre s lie s aux p r o te c tio n s , b a sé e su r d es e x p é r ie n c e s sy sté m a tiq u e s 

de p rop a g a tio n dans d es m ilie u x de co m p o s itio n v a r ia b le en sod iu m et fe r . 

2. RO LE DES E V A L U A T IO N S DANS C E T T E A P P R O C H E 

D ans cette a p p ro ch e in té g ra le , le s m e s u r e s d iffé r e n t ie lle s , p ar 

1' in te r m é d ia ir e o b lig a to ir e d es év a lu a tio n s, jou en t un r ô le co m p lé m e n ta ire 

à qu atre niveaux: 

- fo u rn ir le s don nées n u c lé a ir e s de d ép a rt le s plus p r o b a b le s , 

- d é fin ir le s m a rg e s d 'in c e r tit u d e su r c e s v a le u rs , a d m is s ib le s p ou r la 

p h ysiqu e et la m é tro lo g ie n u c lé a ir e s , 

- d é te rm in e r ce rta in e s d on n ées p ou r le s q u e lle s la p r é c is io n d es é v a lu a 

tio n s e st su ffisa n te , 

- d e te r m in e r le s d on n ées p ou r le s q u e lle s le s e x p é r ie n c e s c ritiq u e s 

ap p orten t peu d 'in fo r m a tio n s . 

2 .1 . D onnées de d épart 

C ' e st c e rta in e m e n t le r ô le le plus im p ortan t jo u é p ar le s m e s u r e s 

d iffé r e n t ie lle s . Il e st cependant évid en t a ctu e lle m e n t que, p ou r la m a jo r ité 

d e s b e s o in s p r io r it a ir e s , le s d on n ées in itia le s sont d is p o n ib le s tant du 

poin t de vue s e c tio n s e ffic a c e s à dilu tion in fin ie que p a ra m è tr e s de 

ré s o n a n ce . 

P a r e x e m p le , au d ép a rt de la v e r s io n 3 C a d a ra ch e , le s évalu ation s 

r é c e n te s du 240Pu et du 241Pu (D FN 408 et 403) ont été u tilis é e s [10]. 

La p r é c is io n su r c e s v a le u rs a b so lu e s e st tr è s v a r ia b le suivant le s 

d o n n é e s. M a is, au stade d e s v a le u rs de d é p a rt, une con n a is sa n ce p r é c is e 

d e s fo r m e s d e s s e c tio n s e ffic a c e s en fo n ctio n de 1' é n e rg ie ou du ra p p ort 

de deux d on n ées à une é n e rg ie p e r m e t de r é d u ire le n o m b re d 1 in con n u es 

dans 1' aju stem en t. 

2.2 . In certitu d es 

La d éfin ition d es in ce rtitu d e s a d m is s ib le s su r le s d on n ées d iffé r e n 

t ie lle s e st un d e s é lé m e n ts fondam entaux de la q u a lifica tio n du fo r m u la ir e , 

s p é cia le m e n t p ou r ce rta in e s m éth od es d 'a ju s te m e n t [1]'. En e ffe t, le s 

a ju ste m e n ts d e s d on n ées de b a se su r le s ré su lta ts in tégra u x ne se font 

que dans la g a m m e p o s s ib le de v a ria tio n e s tim é e p a r 1' évalu ation à p a rtir

I A E A -S M - 1 7 0 /6 9 147 

de la d is p e r s io n d e s m e s u r e s d iffé r e n t ie lle s . Il e st im p ortan t p o u r le s 

p h y s ic ie n s de r é a c te u r s que le s in ce rtitu d e s so ie n t é v a lu é e s a v e c autant 

d 'a tte n tio n que le s v a le u rs a b so lu e s . 

L a m is e au poin t de la v e r s io n 3 C a d a ra ch e s ' e st b a sée su r le s in 

c e rtitu d e s é v a lu é e s à p a r tir d es m e s u r e s le s plu s r é c e n te s p ou r le s ré a c tio n s 

de p rod u ctio n et d 'a b s o r p tio n d e s is o to p e s 235U, 238U, 239P u , 240Pu et 

241 Pu [10 - 14]. 

2.3 . D on n ées con n u es a v e c une p r é c is io n su ffisan te 

L e niveau de p r é c is io n su ffisa n t e st sp é cifiq u e du p r o b lè m e c o n s id é r é . 

L e s s e c tio n s e ffic a c e s de captu re son t su ffis a m m e n t b ien con n u es p ou r 

le s p r o b lè m e s de b lin d a g e , a lo r s que p ou r le s b e s o in s « c o e u r » la p r é c is io n 

d o it ê tr e e n c o r e a m é lio r é e . L ' in v e r s e est v r a i p ou r le s r é a c tio n s to ta le s . 

Un e x e m p le c a r a c té r is tiq u e de c e g e n re d 'a p p o r t d e s m e s u r e s d iffe 

r e n t ie lle s e s t le p a ra m è tr e v dont 1' étude a été a p p rofon d ie dans deux 

v o ie s : 

- v a le u r du standard 252Cf, 

- v a ria tio n de v en fo n ctio n de 1' é n e rg ie . 

Etant donné le s p r é c is io n s attein tes p a r la m é tro lo g ie n u c lé a ire su r 

le s r a p p o r ts de v d e s d iv e r s is o to p e s f is s ile s au standard et le s v a ria tio n s 

de v en fo n ctio n de 1' é n e rg ie p ou r un is o to p e , c ' e st e s s e n tie lle m e n t la 

v a le u r a b solu e du Standard qui d e v ra it ê tre étu d iée p ou r le s b e s o in s d es 

r é a c te u r s . En e ffe t, p ou r le coeur 1 de P h én ix p a r e x e m p le , la v a le u r 

m oyen n e de v su r le s p e c t r e du coeur est tr è s p r o ch e de la v a le u r 

th e rm iq u e p ou r le s p rin cip a u x is o to p e s fis s ile s : 

235U v/vfr : 1 ,0 1 8 

239 Pu : 1,0 24 

241 Pu : 1,0 13 

Une e r r e u r de 0 ,5 % su r la v a le u r a b solu e th erm iq u e a la m êm e 

in flu en ce qu1 une e r r e u r de 25% su r la v a ria tio n de v a v e c 1' é n e rg ie . L e s 

p en tes de v en fo n ctio n de 1' é n e rg ie sont con n u es d 'a p r è s la m é t r o lo g ie 

à m ieu x que ±15% p ou r c e s is o to p e s . 

2 .4 . D onn ées a u x q u elles le s r é su lta ts in tégra u x son t peu s e n s ib le s 

C et a p p ort d e s évalu a tion s e st v o is in du point p r é cé d e n t. L 1 ex e m p le 

c la s s iq u e c o n c e rn e le s s e c tio n s e ffic a c e s de r a le n tis se m e n t éla stiq u e et, 

m is à p a rt 238U et F e , le s s e c tio n s e ffic a c e s de r a le n tis se m e n t in é la stiq u e . 

Au niveau de la v e r s io n 3 du je u de C a d a ra ch e , ce type d 'a p p o r t s ' e st 

c o n c r é t is é p a r un v a ste e n se m b le de d on n ées é v a lu é e s p o u r le s q u e lle s 

un bon o r d r e de g ra n d e u r e s t n é c e s s a ir e , p a r e x e m p le le s ré a c tio n s 

con cern a n t 1' o x y g è n e , le so d iu m , le p lu ton iu m -2 4 2 , le s im p u reté s des 

a c ie r s , le b o r e - 11. 

En d e h o rs d e s p r o b lè m e s lié s au c œ u r , le s évalu ation s d es r é a c tio n s 

de d is p a r itio n d 1 is o to p e s xénon ou k rypton e m p lo y é s c o m m e tr a c e u r s p ou r 

le s d é te ctio n s de ru p tu re de gain e sont d ir e c te m e n t u tilis é e s .

1 4 8 BARRE e t C H A U D A T 

3. BESOINS FU TU RS EN DONNEES E V A L U E E S 

3 .1 . G é n é ra lité s 

C e s d em an d es fu tu res doiven t te n ir com p te du p r o g r è s d e s c o n n a is 

s a n c e s et de 1' é v olu tion d es b e s o in s de la filiè r e ra p id e au C E A . 

L e s p r o g r a m m e s e x é cu té s en ph ysiqu e d es r é a c te u r s ont donné le s 

r é s u lta ts attendus. L e d e g ré de p r é c is io n atteint dans le s p r é d ic tio n s à 

p a rtir d e s e x p é r ie n c e s c r itiq u e s m et en é v id e n ce de n o u v e lle s s o u r c e s 

p o s s ib le s d 'e r r e u r qui ne peuvent plu s ê tr e n é g lig é e s : e x e m p le , captu re 

d e s a c ie r s . D ' au tre p a rt, le s p r o g r è s r é a lis é s dans le s m e s u r e s d iffé 

r e n t ie lle s d e s d on n ées de b a se p rép o n d é ra n te s ren d en t m aintenant 

d iffic ile une a m é lio r a tio n s e n sib le de la p r é c is io n : c 1 e st p robable m e n t 

le c a s , p a r e x e m p le , p ou r le s p a ra m è tr e s de r é so n a n ce de 235U, 239P u, 

24^Pu 24^ Pu 238 

L e s b e s o in s de la f iliè r e ont é v olu é v e r s d es p u iss a n ce s su p é r ie u re s 

(1200 M W (e)) et d e s p e r fo r m a n c e s plu s p o u s s é e s qui dem andent de 

m e ille u r e s p r e c is io n s . La s tra té g ie , le s p e r s p e c tiv e s et le s solu tion s 

n o u v e lle s e n v is a g é e s p o u r le s c e n tra le s fu tu res su scite n t de nouveaux 

p r o b lè m e s . On p a s s e , p a r e x e m p le , d 'u n e fréq u e n ce de r e ch a rg e m e n t 

de 56 jo u r s p o u r P h én ix à 1 an p ou r le r é a c te u r de 1200 M W (e): la 

co n n a is sa n ce d e s d on n ées co n cern a n t 1' év o lu tio n , en p a r t ic u lie r le s 

p rod u its de fis s io n (P F ), d evien t im p orta n te. 

3 .2 . E v o lu tion de la p u issa n ce d es ce n tra le s 

C ette é v olu tion donne un p o id s n ettem ent plu s im p ortan t aux b a s s e s 

é n e r g ie s (in fé r ie u r e s à 25 keV ) et aux p r o b lè m e s d 'a u to p r o te c tio n . P a r 

e x e m p le , la p a rt de ca p tu re 238U en d e s s o u s de 25 keV p a s s e de 0 ,3 7 

p ou r un e n ric h is s e m e n t de 25% (P h énix) à 0 ,5 2 pou r un e n ric h is s e m e n t 

de 12% (1200 M W (e|). 

De m ê m e , le ra p p o rt F de la se c tio n e ffic a c e m oyen n e a u top rotégée 

de ca p tu re 238U à la m ê m e se c tio n e ffic a c e à dilu tion in fin ie d é c r o ît 

a v e c 1' e n r ic h is s e m e n t E : 

E = 25% F = 0 ,8 8 

18% 0 ,8 2 

12% 0 ,7 3 

3 .3 . C aptu re d e s m a té ria u x de stru ctu re 

C 1 e st la p rin cip a le in con n ue d e s lo is de p rod u ctio n et d 'a b s o r p tio n 

qu i s u b s is te a ctu e lle m e n t au n iveau de la v e r s io n 3 du fo r m u la ir e de 

C a d a ra ch e p ou r o b te n ir le s c a r a c té r is t iq u e s d 'u n c œ u r de d é m a r ra g e . 

P o u r le s p rin cip a u x is o to p e s c o n c e r n é s (fe r , c h r o m e , n ick e l), le d om ain e 

d 'é n e r g ie p rép on d éra n t e st situ é en tre 1 et 300 k eV q u el que so it 

l'e n r ic h is s e m e n t E ( f ig .l et 2): 

P o u rcen ta g e de captu re e n tre 1 et 300 keV F e N i 

E = 25% 62% 28% 

18% 64% 35% 

12% 65% 43% 

t

I A E A - S M -1 7 0 /6 9 149 

FIG. 1. Fer: pourcentage de capture en dessous de l’énergie E. 

FIG. 2. Nickel: pourcentage de capture en dessous de l’énergie E.

1 5 0 В ARRE e t C H A U D A T 

T A B L E A U I. M A T E R IA U X DE ST R U C T U R E : B IL A N EN RE A C T IV IT E 

Enrichissement 25% 18% 12% 

f 0,967 0, 963 0,957 

dk/k («ft) 1,7 2, 3 3 ,4 

Isotope Fe Cr Ni Fe Cr Ni Fe Cr Ni 

1/f- l 0, 017 0, 004 0, 007 0, 019 0, 005 0, 008 0, 024 0, 006 0, 008 

dk/k (%) 0, 8 0, 2 0 ,4 1, 2 0,3 0, 5 1,8 0,5 0,6 

L ' im p o rta n ce r e la tiv e de c e s ca p tu res « p a r a s it e s » p a r ra p p o rt aux 

a u tres a b so rp tio n s e st d é fin ie dans le tableau I p a r 1' in te r m é d ia ir e du 

p a ra m è tr e f d é fin i c o m m e le ra p p o rt d e s a b so rp tio n s « c o m b u s t ib le » aux 

a b so r p tio n s to ta le s . Ce p a ra m è tr e ne d é c r o ît que de 1,0% quand 1' en 

r ic h is s e m e n t v a r ie de 25 à 12%. En r é a c tiv ité (d k /k ), cette captu re 

« p a r a s it e » , p r o p o rtio n n e lle à 1 - f, v a r ie de 1 ,7 à 3,4 % p ou r le s ca s 

c h o is is . 

L a p r é c is io n g lo b a le sou h aitée su r la r é a c tiv ité étant ± 0 , 5%, p ou r 

tou tes le s s o u r c e s d 'e r r e u r n eu tron iq u e, il faut con n a ître la ca p tu re des 

a c ie r s à m ieu x de ± 10%. 

L a p a ra m è tr e ( 1 / f - 1), co rre sp o n d a n t au ra p p o rt de la ca p tu re d es 

s tru c tu r e s à 1' a b sorp tio n c o m b u s tib le , m et en é v id e n ce le r ô le p r é 

pon d éra n t du fe r , puis du n ick e l (tableau I), p o u r le s a c ie r in ox c la s s iq u e s 

dans la f iliè r e ra p id e (F e 72%, C r 18%, N i 10% en v o lu m e ). 

L e s b e s o in s con cern e n t non se u le m e n t le s s e c tio n s e ffic a c e s de 

ca p tu re à dilu tion in fin ie m a is ég a le m e n t le s p a ra m è tr e s de r é s o n a n ce , 

p a r tic u liè r e m e n t d iffic ile s à d é te rm in e r p o u r le s s tru c tu re s . C e s p a r a 

m è t r e s son t u tilis é s p ou r c a lc u le r , dans un d écou p a ge m u ltig ro u p e , le 

ra p p o r t de la se c tio n e ffic a c e de captu re a u to p ro té g é e à c e lle à dilution 

in fin ie : dans le fo r m u la ir e de C a d a ra ch e a ctu e l p a r e x e m p le , c e s ra p p o rts 

n 1 ex iste n t que p ou r le f e r en tre 10 et 500 keV et v a rien t e n tre 1 et 0 ,6 

p ou r le s coeu rs u s u e ls . 

L a p r io r it é 1 d e s d em an d es e st a ctu e lle m e n t donnée aux se c tio n s 

e ffic a c e s de ca p tu re à dilu tion in fin ie et aux p a ra m è tr e s de r e son a n ce 

d e s é lé m e n ts f e r , n ick e l et c h r o m e . L e s te s ts in tégra u x com p o rte n t des 

r é s e a u x p o u r le s q u e ls 1' in flu en ce d e s s tru c tu re s v a r ie de 1 à 10% en 

r é a c tiv ité , m a is une tr a n s p o s itio n au n iveau du p r o je t ne peut se fa ir e a v ec 

g a ra n tie qu' a v e c d e s d on n ées de d ép a rt p lu s p r é c is e s . 

3 .4 . P r o d u its de fis s io n 

L a s e con d e in con n ue a ctu e lle du fo r m u la ir e v e r s io n 3 C a d arach e 

c o n c e r n e , p o u r le coeu r b r û lé , le s d on n ées d e s p roduits de fis s io n . 

Une évolu tio n c a r a c té r is tiq u e e st r e p r é s e n té e su r le tableau II p ou r 

deux v a le u r s d 'e n r ic h is s e m e n t s in itiau x, 15 et 18%. La v a ria tio n a b 

so lu e de r é a c tiv ité en tre le c œ u r « fin de v ie » et le c œ u r «d ébu t de v ie » , 

p ou r un taux de co m b u stio n de 50 000 M W j/t, e st d é c o m p o s é e en tre le s

I A E A -S M - 1 7 0 /6 9 

T A B L E A U II. E V O L U T IO N D' UN R E A C T E U R DE 1200 M W (e) 

(50 000 MW j / t ) : con trib u tion d es d iffé r e n ts is o to p e s 

dk/k (°jo) Cœur 1 (E = 15 °jo) Cœur 2 (E = 18%) 

U-235 - 0, 3 - 0, 2 

U-238 - 1,6 - 2 ,7 

Pu-239 - 0,7 - 1, 2 

Pu-240 - 0 ,0 - 0,1 

Pu-241 + 0, 6 + 0 ,6 

Produits de fission - 3,7 | - 3 . ! 1 

Divers - 1 ,3 - 2 ,2 

Total - 7 ,0 - 8 ,9 

p rin cip a u x is o to p e s . L e s p r é d ic tio n s con cern a n t le s e ffe ts d e s is o to p e s 

238u et 239pu étant a ctu e lle m e n t su ffisa m m e n t p r é c i s e s , l 1 a m é lio r a tio n 

de la c o n n a is sa n ce d e s d on n ées d es p rod u its de fis s io n d evien t p r io r it a ir e . 

L ' in ce rtitu d e su r 1' e ffe t d 'u n p s e u d o -p r o d u it de fis s io n m oy en doit 

ê tr e in fé r ie u r e à ± 1 0 % . C ette lim ite m a x im a le v a r ie en fo n ctio n in v e r s e 

du taux de com b u stio n reten u (50 000 à 100 000 M W j/t) et de la fréqu e n ce 

de r e ch a r g e m e n t (six m o is à 1 an) et s e r a plu s b a s s e p ou r d es e n r ic h is s e 

m en ts plu s fa ib le s , d on c d e s p u iss a n ce s p lu s é le v é e s d e s c e n tra le s : la 

fig u r e 3 m o n tre p a r e x e m p le 1' au gm en tation du ra p p o rt â^pp / â c u-238 

de la ca p tu re m oyen n e d e s P F à la ca p tu re m oyen n e de 238u quand 

l 1 e n r ic h is s e m e n t dim in u e. 

L e d om ain e d 1 é n e rg ie p rép on d éra n t e st situ é en tre 1 et 100 keV 

(fig .4 ): qu el que so it 1' e n ric h is s e m e n t, 65% d e s ca p tu res d e s P F ont lieu 

dans cette g am m e d 'é n e r g ie . 

L a p r in cip a le d ifficu lté p ou r s a tis fa ir e c e s d em an d es à p a rtir de la 

m é t r o lo g ie et de la p h ysiqu e n u c lé a ir e s r é s id e dans le grand n o m b re 

d 'is o t o p e s s é p a r é s à é tu d ie r: il n1 y a pas de P F p répon d é ra n t p ou r la 

f iliè r e ra p id e . En plu s d e s s e c tio n s e f f ic a c e s , il faut ég a le m e n t con n a ître 

le s re n d e m e n ts de fis s io n indépen dan ts qui v a rie n t suivant 1' é n e rg ie de 

fis s io n et l 1 is o to p e f is s ile c o n s id é r é . 

L e s d on n ées de b a se é v a lu é e s p ou r le s d iffé r e n ts p rod u its de fis s io n 

s é p a r é s s e r v ir o n t p rin cip a le m e n t de point de d ép a rt p ou r la d é te rm in a tio n 

d e s d on n ées d 'u n p s e u d o -p r o d u it de fis s io n m o y e n , ayant un e ffe t en 

r é a c tiv ité équ ivalen t â c e lu i de 1' e n sem b le d e s P F , p o u r un c œ u r à 

l'é q u ilib r e . C es d on n ées seron t a ju s té e s su r d es e x p é r ie n c e s in té g ra le s 

qu i m e su ren t d ir e c te m e n t 1' e ffe t en r é a c tiv ité de ce p s e u d o -p r o d u it de 

fis s io n . 

E tant donné le s p u is s a n ce s et le s p e r fo r m a n c e s en taux de com b u stio n 

e n v is a g é e s p ou r le s c e n tra le s r a p id e s fu tu re s , la p r io r ité 2 d es d em an d es 

e s t a ctu e lle m e n t donnée aux év alu ation s d e s p ro d u its de fis s io n . 

151

1 5 2 BARRE e t C H A U D A T 

FIG. 3. Capture des produits de fission rapportée à la capture de 238U en fonction de l’enrichissement. 

FIG. 4. Produits de fission: pourcentage de capture en dessous de l’énergie E.

3 .5 . A u tr e s d em an d es 

I A E A -S M - 1 7 0 /6 9 

Il e x is te d 1 a u tres p r o b lè m e s p ou r le s q u e ls une a m é lio r a tio n de la 

c o n n a is sa n c e d e s d on n ées de d ép a rt, sans ê tr e fon d am en tale c o m m e 

p o u r le s deu x c a s p r é c é d e n ts , s e r a it a ctu e lle m e n t u tile . Sans ê tr e 

e x h a u stif, on peut c it e r p a r e x e m p le : 

- le r a le n tis s e m e n t in é la stiq u e de 1 'u ra n iu m -2 3 8 

- la p ro d u ctio n et 1' a b sorp tio n d e s is o to p e s 242P u , 241 A m , 238P u . 

CO NCLUSIO N 

Dans 1' a p p ro ch e c h o is ie au CE A p ou r s a tis fa ir e le s d em an d es d es 

p r o je t s de r é a c te u r s à n eu tron s r a p id e s , la b a se e x p é rim e n ta le de r é 

fé r e n c e e st con stitu é e p a r le s r é su lta ts d e s p r o g r a m m e s d 'e x p é r ie n c e s 

c r it iq u e s . L e s é v a lu a tio n s, is s u e s d e s m e s u r e s d iffé r e n t ie lle s , jou en t 

un r ô le c o m p lé m e n ta ir e p a r ra p p o rt aux m e s u r e s in té g ra le s . 

L e s r é su lta ts a c c u m u lé s dans le s travau x d e s qu atre d e r n iè r e s années 

en p h ysiq u e d e s r é a c te u r s et 1' évolu tion d e s b e s o in s d es c e n tra le s ra p id e s 

lié e aux p e r fo r m a n c e s n o u v e lle s r e c h e r c h é e s se tra d u isen t, au C E A , 

d 'u n e p a rt p a r une ré d u ctio n du v olu m e de d em an d es fo n d a m en ta les de 

m e s u r e s d iffé r e n t ie lle s , d 'a u tr e p a rt p ar une é v olu tion dans la nature 

d e s d e m a n d e s, ,en fin p a r la n a issa n ce d 1 un e n se m b le de b e s o in s de 

se co n d e p r io r it é . L e s d em an d es a c tu e lle s d 'é v a lu a tio n s son t fo c a lis é e s 

su r deux p r o b lè m e s p r io r it a ir e s , dans 1' o r d r e : ca p tu re d e s m a té ria u x 

de stru c tu re F e , N i, C r et con sta n tes d e s p rod u its de fis s io n . 

L a v a lid ité de 1' a p p ro ch e reten u e, qui s ' e st c o n c r é t is é e r é ce m m e n t 

dans la v e r s io n 3 du je u de s e c tio n s e ffic a c e s m u ltig ro u p e s de C a d a ra ch e , 

va p o u v o ir ê tr e te s té e , en v ra ie g ra n d e u r, su r le s m e s u r e s p r é v u e s au 

d é m a r ra g e de P h én ix, c e n tra le de 250 M W (e), dont la d iv e r g e n c e est 

attendue p ou r le m ilie u de cette année. 


[1] CAMPBELL, C. G . , ROW LANDS, I. L. , « T h e relationship of microscopic and integral data», 

Nuclear Data for Reactors (Compt. Rend. Conf. Helsinki, 1970) 2, AIEA, Vienne (1970) 391. 

[2] BARRE, J. Y . , BOUCHARD, J ., « Rôle complémentaire des expériences intégrales par rapport aux 

mesures différentielles pour un projet de réacteur à neutrons rapides», Ibid., p. 465. 

[3] Table ronde, « The physics of fast reactor operation and design» (Compt. Rend. Conf. Londres, 1969) 

BNES (1969) 277. 

[4] BARRE, I. Y. et al., « Lessons drawn from integral experiments on a set of multigroup cross sections» , 

Ibid., p. 165. 

[5] LITTLE, W . W . et a l., «Progress in meeting cross sections needs from a fast reactor designer's 

v ie w », Neutron Cross Sections and Technology (Compt. Rend. Conf. Knoxville, 1971) 1, 

CONF-710301 (1971) 32. 

[6] FROHNER, F .H . et al., « O n shielding calculations with computer files of neutron data», 

4e Conf. Int. sur la protection des réacteurs, Paris, 1972, Compt. Rend, à paraître, mémoire D5. 

[7] DUNFORD, C. e tal., « A status report on nuclear data for shielding calculations», Ibid., 

mémoire D6. 

[8] BOUCHARD, J. e t a l., « Experimental study of burn-up in fast breeder reactors», New Developments 

in Reactor Physics and Shielding II (ANS National Meeting, Kiamesha Lake) 2, CONF-720901 (1972) 888. 

[9] BARRE, J. Y. et al., «Reactor physics and fast power breeders: M A SU RCA core R-Z program», 

Ibid., p. 822. 

153


[10] L'HERITEAU, J. P . , R1BON, P . , Examen critique des sections efficaces neutroniques du Pu 240, 

Note CEA-N-1273 - EA N D C (E) 126 A L (mars 1970). 

[11] SZABO, I. et al., «M esure absolue de la section efficace de fission de l’uranium-235 et du 

plutonium-239 entre 0, 025 et 1 M e V » , Nuclear Data for Reactors (Compt. Rend. Conf. Helsinki, 

1970) 1, AIE A, Vienne (1970) 229; 

Ibid., « z35u fission cross section from 10 keV to 200 k e V » , Neutron Cross Sections and Technology 

(Compt. Rend. Conf. Knoxville, 1971), CONF-710301 (1971) 573. 

[12] BLONS, J. et al., « Mesure et analyse des sections efficaces de fission de l'uranium-235 et du 

plutonium-241», Nuclear Data for Reactors (Compt. Rend. Conf. Helsinki, 1970) 1_, AIEA, Vienne 

(1970) 469; 

Ibid., in Neutron Cross Sections and Technology (Compt. Rend. Conf. Knoxville, 1971), 

CONF-710301 (1971) 829, 836. 

[13] RIBON, P ., LECOQ, G ., Evaluation des données neutroniques de 239Pu, Note CEA-N-1484 

(novembre 1971). 

[14] SOWERBY, M . G . , KONSHIN, V. A . , Review of the measurements of alpha for 239Pu in the energy 

range 100 eV to 1 M eV, At. Energy Rev. 10 4 (1972) 453. 


W . B. LEW IS (C h airm an ): I sh ou ld lik e to sa y on m y own b e h a lf that 

I h ave n e v e r been a d is b e lie v e r in the n eu tron p h y s ic s of f a s t -b r e e d e r r e a c t o r s . 

T h e au th ors a r e to be con g ra tu la ted on the d ev elop m en ts w hich have been 

a ch ie v e d through the com b in a tion of in te g ra l and m ic r o s c o p ic data. The 

ad va n ce lo o k s v e r y im p r e s s iv e . 

F . R U ST IC H E L L I: A s r e g a rd s data on fis s io n p rod u cts , what is m o r e 

c r it ic a l, the y ie ld s o r the n eu tron ca p tu re c r o s s - s e c t io n s ? 

J . Y. B A R R E : O ur re q u ire m e n t in r e s p e c t of fis s io n p rod u cts is to 

obtain the fo llo w in g sta rtin g data fo r the m ain is o to p e s sep a ra te d : captu re 

c r o s s - s e c t i o n s , in e la s tic slo w in g -d o w n c r o s s - s e c t i o n s and y ie ld s (e s p e c ia lly 

o f 241P u) f o r fa s t r e a c t o r s . T h e s e data w ill be u se d f o r d efin in g the con stan ts 

o f a p seu d o fis s io n p rod u ct. T h e con stan ts w ill be ad ju sted on the b a s is of 

tw o types o f in te g ra l e x p e rim e n ts: fir s t , m e a su re m e n t o f the r e a c tiv ity 

sig n a l of the total fis s io n p rod u ct obtain ed by ir ra d ia tio n and, se con d , 

ir ra d ia tio n o f c e rta in p rep on d era n t fis s io n -p r o d u c t is o to p e s w hich have been 

s e p a ra te d . In the la s t a n a ly s is, o n ly the con stan ts of this p seu d o fis s io n 

p r o d u c t a r e o f im p o rta n ce fo r the p r o je c t.

CROSS-SECTION UNCERTAINTY EFFECTS 

ON THE RATIO OF THE HIGH-ENERGY 

NEUTRON FLUX TO THE POWER 

AND RESULTING ESTIMATION 

OF THE IRRADIATION LIMIT ERRORS 

IN A FAST POWER REACTOR 

A. BOIOLI, G.P. CECCHINI 

Progettazioni Meccaniche Nucleari, Genoa, Italy 

M . COSIMI, M . S A L V A T O R E S 

Comitato Nazionale per l'Energia Nucleare, Rome, Italy 

Abstract 

I A E A - S M -1 7 0 /7 

CROSS-SECTION U N C E R TA IN TY EFFECTS O N THE RATIO OF THE HIGH-ENERGY NEUTRON FLUX T O THE 

POWER A N D RESULTING EST IM A TIO N OF THE IRRADIATION LIMIT ERRORS IN A FAST POWER REAQTOR. 

The results of some relevant cross-section uncertainty effects on the ratio н / P of the high-energy 

neutron flux to the specific power produced in different zones of a fast power reactor are presented. In 

particular, the uncertainty effects of 2S8u fission, capture and high-energy inelastic scattering cross-sections, 

prompt neutron spectrum, high-energy 239 Pu fission cross-sections, etc. are considered. The calculations 

are performed by two-dimensional generalized perturbation methods developed recently by the authors. The 

structural material swelling is essentially determined by the ratio considered, (p^/P, as a function of the total 

energy produced in the reactor. Therefore, the related irradiation limits can be investigated in terms of cross- 

section uncertainties. The results are discussed, allowing for the different correlations which can be used in 

tiie swelling calculations. 

1. IN TR O D U C TIO N 

S t a in le s s -s te e l sw e llin g w as f ir s t o b s e r v e d on fu e l-e le m e n t cla d d in g s 

by C a w torn e and F u lto n f 1 ], but now the e ffe c t s o f sw e llin g a re w e ll known 

a ls o on fu e l-e le m e n t su p p o rt and c o r e - s t r u c t u r a l c o m p o n e n ts. T h e r e fo r e , 

c o r e life -t im e has up to now b e e n c o n s id e r e d to be lim ite d on ly by the s w e llin 

g p h en om en on , w h ich is due to in te r a c tio n s o f a tom s o f the stru c tu ra l m a 

te r ia ls w ith fa s t n e u tro n s. M any in v e s tig a to rs have c o n s tr u c te d c o r r e la t io n s 

o f v o lu m e in c r e a s e a g ain st s e v e r a l im p o rta n t p a r a m e te r s , w ith p a rticu la r 

r e fe r e n c e to h ig h -e n e rg y flu e n c e s (E > 0 .1 M eV ) [ 2 - 4 ] . 

E v e n i f the u n certa in tie s o f th e se c o r r e la t io n s a re ra th e r high, it is 

n e c e s s a r y to evalu ate and, p o s s ib ly , to m in im iz e the r a tio F = fa s t flu x /p o w e r , 

in o r d e r to in c r e a s e the life o f fa s t r e a c t o r fu e l ele m e n ts tow a rd s the 

in tr in s ic b u rn -u p ca p a b ility o f h ig h -q u a lity e le m e n ts . 

F o r th is re a s o n , it se e m e d im p o rta n t to a s s e s s the u n certain ty e ffe c ts 

in trod u ce d in the F - r a t i o ca lcu la tio n . 

In p a r tic u la r , the c o n fid e n c e in the F -c a lc u la t io n ca n b e b a sed , to 

s o m e exten t, on d e ta ile d a n a ly ses o f the s e n sitiv ity to the adopted m u ltig rou p 

c r o s s - s e c t i o n s e t u n certa in tie s. 

M any s e n sitiv ity a n a ly ses a re a v a ila b le [ 5 - 7 ] , r e la te d to in te g ra l 

p a r a m e te r s , su ch as K eff, b re e d in g ra tio , i e ff, D o p p le r and so d iu m v o id 

r e a c tiv ity c o e ffic ie n t s , but n o p r e v io u s study on the F - r a t i o s e e m s to have 

b e e n p e r fo r m e d . 

155

156 B O IO U e t a l. 

T h is w o rk a im s at an alysin g the in flu en ce o f the m o r e im p orta n t c r o s s - 

s e c tio n u n certa in tie s on the F - r a t i o , in o r d e r to e sta b lis h w h eth er the c r o s s - 

s e c tio n s a r e known to su ch a p oin t as to su g g e st an e ffe c tiv e m in im iz a tio n 

o f the F . 

2. T W O -D IM E N SIO N A L G E N E R A L IZ E D P E R T U R B A T IO N M ETH ODS 

The g e n e r a liz e d U sa ch e v -G a n d in i (U -G ) [ 8, 9] p e rtu rb a tio n th e o ry w as 

u sed to c a lc u la te the a b ovem en tion ed s e n s itiv itie s . 

A s is w e ll known, w ith the U -G p e rtu rb a tio n th e o ry , it is p o s s ib le to 

evalu ate in te g ra l quantity v a r ia tio n s as lin e a r fu n ction s o f the sy s te m 

p a r a m e te r v a r ia tio n s ( c r o s s - s e c t i o n s , g e o m e t r ic a l p a r a m e te r s , e t c . ) . 

T h e p e rtu rb a tio n e x p r e s s io n s o f the lin e a r fu n ction c o e ffic ie n t s r e q u ire 

g e n e r a liz e d im p o rta n ce -fu n c tio n c a lcu la tio n s : 

Ф ■’ ■ I 

i= l,N 

■ I *. 

i= l, N 

w h e re ф{ and i//[ a r e solu tio n s o f the ite ra tiv e s y s te m s 

А* ф\ = GT 

AT ф\ = F* 

А ф1 = G 

A i//, = F ф 

1 M - l 

i = 2, . . . ,N 

A , AT r e a l and a d join t lea k a g e and a b so rp tio n m a tr ix 

F , F T r e a l and a d join t p r o d u c tio n m a tr ix 

G , G* fu n ctio n a l-d e p e n d e n t g e n e r a liz e d s o u r c e s [ 9, 1 0 ]. 

A c c o r d in g to the g e n e r a liz e d p e rtu rb a tio n th e o ry [ 8, 9 ] , fu n ction s ф? 

and i//j s a tis fy the fo llo w in g con d itio n s: 

(1) 

(2 ) 

lim ф? = 0 (5) 

lim ф. = 0 (6 ) 

In th is w o rk , the m u ltig r o u p d iffu sio n a p p ro x im a tio n w as used fo r 

the s o lu tio n o f the ite r a tiv e s y s te m s d e s c r ib e d a b ove. 

(3) 

(4)

I A E A 'S M - 1 7 0 /7 

T h e c o d e u sed [1 1 ] p r o v id e d a ca p a b ility fo r tw o -d im e n s io n a l c a lc u 

la tio n s w ith the c o r r e c t io n f o r the fu ndam en tal m od e con ta m in a tion [ 1 0 ]. 

T h e se n s itiv ity c a lc u la tio n s w e r e c a r r ie d out b y using the g e n e r a liz e d 

p e rtu rb a tio n fo r m u la s . 

G e n e r a lly , a ra tio o f r e a l flu x fu n ctio n a ls d efin ed in r e g io n s R x and Щ , 

r e s p e c tiv e ly , ca n b e e x p r e s s e d as 

dE a, (r, E)

T A B L E I. CO M POSITIO NS (IN N U CLEI X c m '3 X 1 0 24) O F TH E R E F E R E N C E F A S T P O W E R R E A C T O R 

CORE 

Inferior axial blanket Low-enrichment region Highênrichment region Radial blanket Superior axial blanket 

№ 0.01422308 0.0132773 0.01327364 0 .0 2 14229 8 0.01311882 

NFe 0.01352275 0.01352275 0.01352275 0.01442028 0.01106951 

N Cr 0.003428303 0.003428303 0.003428303 0.003655845 0.002806354 

N Ni 0.002095074 0.002095074 0.002095074 0.002234128 0.001714994 

N Na 

0.009889507 0.009889507 0.009889507 0.005994968 0.01133355 

23S 

N u 0.007090205 0.00559675 0.0052477 0.01067935 0.006539732 

235 

N u 0.0000213346 0.00003213453 0.0000196782 

N 239P u 0.000698073 0.000930713 

n 240 + 2« Pu 

0.000291732 0.000388955 

2 4 1 - 

N Pu 0.000052095 0.0000694962 

158 BOIOLI et al,

1Л 

n» 

О О 

О 'í 

16.375 

REG. 

A 

136.5 

SUPERIOR AXIAL BLANKET 

I A E A - S M -1 7 0 /7 159 

96 36.5 

LOW- ENRICHMENT ZONE 

INFERIOR AXIAL BLANKET 

FIG. 1. Axial view of the reactor (all dimensions in cm). 

T h e p o s itio n o f the tw o r e g io n s w as c h o s e n to evalu ate the F - r a t io 

se n s itiv ity to c r o s s - s e c t i o n u n certa in tie s in r e g io n s o f the c o r e w h ere 

the fa s t flu x , o r the fa s t-flu x g ra d ie n t, has a m a xim u m v a lu e . 

In the f ir s t r e g io n , th e r e fo r e , the s t a in le s s -s t e e l grow th due to the 

sw e llin g has a m a xim u m v a lu e, w h ile in the s e c o n d r e g io n w e have the 

m a xim u m f o r the d iffe r e n tia l d e fo r m a tio n o f the o p p o s ite w a lls o f the fu e l- 

e le m e n t b o x . 

4. N E U TRON C R O SS-SE C T IO N S USED AND TH EIR U N C E R T A IN TIE S 

The m u ltig rou p n eu tron c r o s s - s e c t i o n s e t used in th is w o rk w as r e c e n tly 

d e r iv e d [1 2 ] b y an o p tim iz a tio n p r o c e d u r e b a se d on E N D F /B v e r s io n -1 data 

and b y the Z P R -6 a s s e m b ly - 7 b e n ch m a rk in te g ra l e x p e rim e n ts in su p p ort 

o f the L M F B R d e m o n stra tio n p r o g r a m . 

W e c o n s id e r e d the fo llo w in g c r o s s - s e c t i o n s as the m a in s o u r c e o f 

e r r o r in the c a lc u la tio n s o f the F - r a t io : 238ц- in in e la s tic , fis s io n and 

ca p tu re c r o s s - s e c t i o n , 239pu fis s io n and in e la s tic c r o s s - s e c t i o n s , 240Pu 

38.5 

R A D IA L 

B L A N K E T

160 BOIOLI e t al, 

T A B L E II. C R O S S-S E C T IO N U N C E R T A IN T Y LIM ITS 

Reaction Energy interval 6 o/ о (in percent) 

4 ’ 

4' 

10 - 0 .1 M e V 10.0 

10 - 0 .1 M e V 10.0 

4* 100 - 1 .0 keV 20.0 

o49 

f 

49 

°in 

' 

Whole range 2 0 .0 

10 - 0 .1 M e V 10.0 

100 - 1.0 keV 15.0 

Whole range 30.0 

x49 Whole range 10.0 

«V “ 

o40 m 

10 - 0 .1 M e V 20.0 

100 - 1 .0 keV 20.0 

Whole range 3 0.0 

fis s io n and in e la s tic c r o s s - s e c t i o n s . T h e a ssu m e d e n e rg y -d e p e n d e n t unc 

e rta in ty lim its f o r the c r o s s - s e c t i o n a r e show n in T a b le II. T h e se lim its 

a r e d e r iv e d by r e c e n t w o rk s o f ev alu ation [ 1 3 -1 8 ], m a in ly p r e se n te d at 

the H e lsin k i (1970) and K n o x v ille (1971) C o n fe re n c e s on n u cle a r data fo r 

r e a c t o r s . 

A 239P u p r o m p t -fis s io n -s p e c t r u m u n certain ty w as in trod u ce d in the 

a n a ly s is, c o r r e s p o n d in g to an u n certain ty o f a few p e r c e n ts in the M a x w ellia n 

te m p e ra tu re [ 19] . 

5. R E SU L T S 

T h e se n s itiv ity c o e ffic ie n t s re la tiv e to the F - r a t io a re show n in T a b le III. 

E v id en tly , a ll v a lu e s a re v e r y lo w : on ly the tota l e ffe c t o f the u ncertain ty 

o f the 239P u fis s io n c r o s s - s e c t i o n slig h tly e x c e e d s 10% in the c e n tra l zon e, 

and th is is e s s e n tia lly due to the d ir e c t e ffe c t. 

6. CONCLUSIONS 

It fo llo w s fr o m the p r e v io u s r e s u lts that, taking into a ccou n t the v a r io u s 

c o r r e la t io n s w h ich can be used in the sw e llin g ca lcu la tio n , the m axim u m 

s e n s itiv ity v a lu e s r e la tiv e to the sw e llin g m ay b e c o n s id e r e d to be tw ice 

the v a lu e s o f th o se r e la tiv e to the F - r a t i o [ 3] .

I A E A -S M - 1 7 0 /7 161 

T A B L E III. SE N SIT IV IT Y V A L U E S R E L A T IV E TO THE F -R A T IO 

(IN P E R C E N T ) 

Varied 

parameter Energy range Direct 

o 28 

f 

28 

°C 

o28 m 

°f 

49 

o49 

in 

of‘ ° 

40 

°in 

Central zone 

Spectral Total Direct 

Peripheral zone 

Spectral Total 

Whole range -1.23 -2.18 -3.41 -0.95 - 0.0 -0.95 

10 - I M e V 

100 - 1 keV 

Whole range 

— 

-2.11 

+ 1.02 

-1.09 

-2.11 

+ 1.02 

-1.09 

... 

+ 0.13 

+ 3.60 

+ 3.73 

+ 0.13 

+ 3.60 

+ 3* 73 

Whole range ... -3.92 -3.92 ... -1.78 -1.78 

10 - 1 M e V 

100 - 1 keV 

Whole range 

-3.23 

-5.05 

- 8.28 

-2.12 

-0.74 

-2.86 

-5.35 

-5.79 

-11.14 

-3.42 

-5.08 

- 8.50 

+ 0.12 

+ 1.39 

+ 1.51 

-3.30 

-3,69 

-6.99 

Whole range — -1.23 -1.23 — -1.21 -1,21 

10 - 1 M e V 

100 - 1 keV 

Whole range 

-0.98 

-0.12 

-1.10 

-2.12 

-2.16 

-4.28 

-3.10 

-2,28 

-5.38 

-1.06 

-0.13 

-1.19 

- 0.0 

+ 0.03 

+ 0,03 

-1.06 

- 0.10 

-1.16 

Whole range — -2.26 -2.26 — -0.07 -0,07 

x 49 Whole range — -2.13 -2.13 — -0.01 -0.01 

T h is m ea n s that the e r r o r s in trod u ce d by the n e u tro n ics a re n e g lig ib le 

in c o m p a r is o n w ith th o se due to the u n certain ty in the c h o ic e o f the b e s t 

c o r r e la t io n to b e u sed. 

A n oth er c o n c lu s io n r e f e r s to the m in im iz a tio n o f the F - r a t i o : the v e r y 

lo w se n s itiv ity to the c r o s s - s e c t i o n u n certa in tie s s e e m s to in d ica te that 

m in im iz a tio n is im m e d ia te ly p o s s ib le . 

A C K N O W L E D G E M E N T 

T h e au th ors w ould lik e to thank M r . V . V io tti f o r h is h elp fu l d is c u s s io n s 

on the sw e llin g ca lc u la tio n p r o b le m s . 


[ 1] C A W T O R N E , C ., FU LT O N , E .J ., Voids in irradiated stainless steel, Nature 216 (1967) 575. 

[2] FINCH, L .M ., PETERSON, R .E ., Impact of stainless steel swelling on fast reactor core design, 

Trans. Amer. Nucl. Soc. 12 (1969) 316. 

[3] JA CK SON, R .J., SUTHERLAND, W . H . , M E TC ALF, I , L ., Swelling and creep effects upon fast reactor 

core structural design, Trans. Amer. Nucl. Soc. 13 1 (1970) 112.

162 BOIOLI e t a l. 

[4] RUSSO, S ., VIOTT1, V ., "LARA — 1 — Analisi del fenomeno del bowing térmico e per swelling 

differenziale nell'ipotesi di non-interazione tra le subassemblies", PM N Report SRV (72) 140 c. 

[5] G ANDINI, A ., SALVATORES, M , , "Sensitivity study of fast reactors using generalized perturbation 

techniques", Fast Reactors (Proc. Symp. Vienna, 1968) 1 , IAEA, Vienna (1968) 241. 

[6] BITELLI, G . , CECCHINI, G .P ., G ANDINI, A ., SALVATORES, M . , "Analysis and correlation of 

integral experiments in fast reactors with nuclear parameters”. Physics of Fast Reactor Operation 

and Design BNES (Proc, Int. Conf. London, 1969) 157. 

[7] GREEBLER, P ., H U TC H IN S, B .A ., CÍOWAN, C .L . , "Implications of nuclear data uncertainties to 

reactor design", Nuclear Data for Reactors (Proc. 2nd Int. Conf. Helsinki, 1970) 1, IAEA, Vienna 

(1970) 17. 

[8] - G ANDINI, A ., Perturbation methods in nuclear reactors from the importance conservation principle, 

Nucl. Sei. Eng. 35 (1969) 141. 

[9] GANDINI, A ., A generalized perturbation method for bi-linear functionals of the real and adjoint 

neutron fluxes, J. Nucl. Energy 21 (1967) 755. 

[10] CECCHINI, G .P ., SALVATORES, M . , Advances in the generalized perturbation theory, Nucl. Sei. 

Eng. 40 (1971) 304. 

[11] BOIOLI, A ., CECCHINI, G .P ., M E D A , N .. The GEN-P2 code (to be published). 

[ 12] SALVATORES, M . , Adjustment of multigroup neutron cross sections by a correlation method, Nucl. Sei. 

Eng. (to be published). 

[ 13] PITTERLE, T . A . , "Evaluation of 238U neutron cross-sections for the ENDF/B file", in Nuclear Data 

for Reactors (Proc. 2nd Int. Conf., Helsinki, 1970) 2, IAEA, Vienna (1970) 687. 

[14] PITTERLE, T . A . , PAIK, N . C . , DURSTON, C ., "Evaluation of modifications to ENDF/B version-II 

data”, Neutron Cross-Sections and Technology (Proc. Conf. Knoxville, 1971) _1, Knoxville, 

Tennessee (1971) 461. 

[ 15] H U M M E L, H . H . , "Sensitivity studies of the effect of uncertainty in the 238U (n, y) and in the 239 Pu (n, f) 

and (n, y) cross-sections", Neutron Cross-Sections and Technology (Proc. Conf. Knoxville, 1971) 

1, Knoxville, Tennessee (1971) 65. 

[16] OKRENT, D . , LOWENSTEIN, W . B . , ROSSIN, A . D . , SM ITH, A .B ., Z O L O TA R , B. A . , KALLFELZ, J . M . , 

Nucl. Appl, Techno1. 9 (1970) 454. 

[17] D A V E Y , W . G . , "Status of important heavy-element nuclear data above the resonance region", 

Nuclear Data for Reactors (Proc. 2nd. Int. Conf, Helsinki, 1970) 2, IAEA, Vienna (1970) 119. 

[18] SU KHOR UCHKIN , S .I ., ibid., 1 (1970) 309. 

[19] CAMPBELL, C . G . , R O W LANDS, J .L ., The energy spectrum of prompt fission neutrons, EACRP-A-143, 

14th Meeting of the European-American Committee, Stockholm (1971).

EL USO DE PARAMETROS NEUTRONICOS 

DE RESONANCIA Y SECCIONES EFICACES 

NEUTRONICAS DE CAPTURA #RADI ATI VA 

PARA LA EVALUACION DE LA INTEGRAL 

DE RESONANCIA DE ACTIVACION 

RESUELTA Y NO RESUELTA 

G.H. RICABARRA, R. TURJANSKI, M . D . RICABARRA 

Comisión Nacional de Energía Atómica, 

Buenos Aires, Argentina 

Abstract-Resumen 

I A E A - S M -1 7 0 /2 

TH E USE OF NEUTRON RESONANCE PARAMETERS A N D NEUTRON RADIATIVE CAPTURE CROSS-SECTIONS 

IN EVALUATING RESOLVED A N D UNRESOLVED A C T IV A T IO N RESONANCE INTEGRALS. 

The paper reviews the work carried out in the author's laboratory since 1968 on the calculation, evaluation 

and measurement of activation resonance integrals. The calculation methods used are described, and an 

analysis is made of the error introduced in the evaluation of the resolved resonance integral as a result of the 

current uncertainty in neutron resonance parameters. The calculation of the unresolved resonance integral is 

described, and the neutron radiative capture cross-section data in the region between 1 keV and 10 M e V 

available for its calculation are considered. The author also describes the use of experimental resonance 

integral values in evaluating neutron parameters in cases where the neutron parameters obtained by differential 

time-of-flight measurements show discrepancies. Finally, an account is given of the difficulties that arise 

in reactor physics and/or activation analysis when inexact or inadequate integral data are used. 

EL USO DE PARAMETROS NEUTRONICOS DE RESONANCIA Y SECCIONES EFICACES NEUTRONICAS DE 

CAPTU RA RADIATIVA PARA LA EVALUACION DE LA INTEGRAL DE RESONANCIA DE A C T IV A C IO N 

RESUELTA Y N O RESUELTA. 

En la memoria se pasa revista al trabajo sobre el cálculo de evaluación y medición de integrales de 

resonancia de activación que los autores realizaron en el laboratorio de la CNEA desde el año 1968. Se describen 

los métodos de cálculo usados y se analiza el error que la actual incertidumbre de los parámetros neutrónicos 

de resonancia introducen en la evaluación de la integral de resonancia resuelta. Se examina el cálculo de la 

integral de resonancia no resuelta, y la disponibilidad de las secciones eficaces neutrónicas de captura radiativa 

en la zona entre 1 keV y 10 M e V para su cálculo. Se describe igualmente el uso de los valores experimentales 

de la integral de resonancia para la evaluación de los parámetros neutrónicos en casos donde los parámetros 

neutrónicos obtenidos por la medición diferencial de tiempo de vuelo son discrepantes. Finalmente se señalan 

los inconvenientes para la física de reactores y/o análisis por activación de datos integrales evaluados de manera 

inexacta o inadecuada. 

IN TR O D U C CIO N 

L a m e d ició n de la in te g ra l de r e s o n a n c ia e s u til p a ra v e r ific a r lo s 

p a rá m e tr o s de r e s o n a n cia de n eu tron es ob te n id o s en e x p e r ie n c ia s de 

tie m p o de v u e lo y en e s e se n tid o puede c o n s id e r a r s e c o m o una té c n ica 

e x p e rim e n ta l de e v a lu a ció n . Sin e m b a rg o s i lo s d atos in te g ra le s no se 

obtien en en un e s p e c t r o bien d e fin id o la c o m p a r a c ió n e n tre lo s datos e x p e r im 

e n ta le s y ca lc u la d o s puede r e s u lta r in c ie r ta . 

L a m a y o r p a rte de la s in te g ra le s de r e s o n a n cia de a c tiv a ció n , de 

ca p tu ra y de a b s o r c ió n s e han m e d id o en e l e s p e c t r o de un r e a c to r t é r m ic o 

y s e ha su p u esto que e l e s p e c t r o es « c u a s i» l / E . L a e v id e n cia e x p e rim e n ta l 

163

164 RICABARRA e t a l. 

de e sta h ip ó te s is s e b a sa en e l a c u e rd o obten id o en tre lo s datos e x p e r im 

e n ta les y r e co m e n d a d o s de la in te g ra l de r e s o n a n cia de is ó to p o s cu yas 

p r in c ip a le s r e s o n a n cia s están en la zon a de b a ja e n e rg ía (< 100 eV . ). Sin 

e m b a rg o e l e s p e c t r o de un r e a c t o r t é r m ic o p o r e n cim a de lo s 10 keV 

puede d e s v ia r s e de la fo r m a l/E. En r e a c t o r e s c o m p a cto s de agua liv ia n a y 

u ra n io e n riq u e c id o s e a p ro x im a a l e s p e c t r o de fis ió n a la e n e rg ía de 1 M eV 

y en r e a c t o r e s m o d e ra d o s con agua p esa d a o g ra fito p o d e m o s ten er a alta 

e n e rg ía un e s p e c t r o m á s b lan d o que el e s p e c t r o l / E . 

Una h ip ó te s is g e n era lm en te a cep tada es que la a b s o r c ió n de n eu tron es 

a alta s e n e rg ía s es d e s p r e c ia b le en un r e a c to r té r m ic o y p o r e sto no es 

n e c e s a r io te n e r en cuen ta que el e s p e c t r o en la re g ió n de e n e rg ía de lo s 

M eV no e s l / E . 

C o m o s e v e r á en la s e c c ió n sigu ien te esta h ip ó te s is puede no s e r 

v á lid a p a ra un buen n ú m e ro de is ó to p o s y en algu nos c a s o s puede c o n d u cir 

a s e r io s p r o b le m a s en la in te r p r e ta c ió n de la s e x p e r ie n c ia s de m e d ició n 

de la in te g ra l de r e s o n a n cia . 

E sta s c o n s id e r a c io n e s m u estra n que p a ra h a c e r una c o m p a ra ció n 

c o r r e c t a de lo s d a to s.e x p e rim e n ta le s y ca lcu la d o s de la in te g ra l de 

r e s o n a n cia e s im p orta n te e v a lu a r y c a lc u la r no sola m e n te la a b s o r c ió n 

de n eu tron es de la p a rte re su e lta , sin o tam bién de la p a rte no re su e lta . 

C A L C U L O DE L A IN T E G R A L E P IT E R M IC A Y D E L A IN T E G R A L 

DE RESO N AN CIA 

In te g ra l e p ité r m ic a e in te g ra l de r e so n a n cia resu e lta 

Si se co n o ce n lo s p a rá m e tr o s de re s o n a n cia en e l in te rv a lo de e n e rg ía 

de in te r é s e s p o s ib le , usando la e cu a ció n de B r e it-W ig n e r y e l e s p e c t r o 

n e u tró n ico, c a lc u la r la in te g ra l de ca p tu ra o a b s o r c ió n e p ité r m ic a re su e lta , 

que puede s e r d efin id a co m o : 

El 

I e(R) = f стА(Е) фер1(Е) d E /E (1) 

eg 

donde фер!(E) e stá n o rm a liz a d o a la e n e rg ía de la re s o n a n cia d el «sta n d a r d » 

Au (4, 5 eV ), epi(E) = E ф(E ) /4 , 5 ф(4, 5), s i s e supone que e l e s p e c t r o es 

l / E , $epi(E) = 1 y te n d rem o s la in te g ra l de re s o n a n cia en la zon a re su e lta : 

el 

I (R) = J o a(E) d E /E (2) 

eg 

Eg es la e n e rg ía de e m p a lm e del flu jo té r m ic o y e p ité r m ic o ; en la 

e x p e r ie n c ia la e n e rg ía de c o r te , E l, d ep en d erá d e l filt r o e le g id o , p e r o 

una ap rop ia d a c o r r e c c ió n p e r m ite una c o m p a ra ció n con s iste n te e n tre e l 

c á lc u lo y la e x p e r ie n c ia . E l e s la e n e rg ía de re s o n a n cia m á xim a 

c o n o c id a d el is ó to p o de in te r é s , ста es la s e c c ió n e fic a z de a b s o r c ió n , 

ca p tu ra o a ctiv a ció n .

IAE A - S M - 1 7 0 /2 165 

En un r e a c t o r té r m ic o en g e n e ra l s e supone que e l e s p e c t r o es 

a p ro x im a d a m e n te l / E a b a ja s e n e rg ía s , p e r o p a ra altas e n e rg ía s se 

d e s v ía de la fo r m a l / E y s e a p ro x im a a l e s p e c t r o de fis ió n en la re g ió n de 

lo s M eV. 

L a in te g ra l r e s u e lta de a b s o r c ió n e p ité r m ic a o de re s o n a n cia in clu y e 

la co n trib u c ió n de: a) re s o n a n cia s de e n e rg ía p o s itiv a s y b) n iv e le s 

n e g a tiv o s que con trib u y en a la s ca p tu ra s 1 /v . 

E s u su al s u b s tr a e r la co n trib u ció n 1 /v de la in te g ra l e p ité r m ic a o de 

la in te g ra l de r e s o n a n c ia y ten em os: 

У - 

El 

lé(R) = J (°a,(E) - g Сто ■J E o /E )


T A B L A I. C O M P A R A C IO N D E D ATO S IN T E G R A L E S CA LCU LA D O S Y 

E X P E R IM E N T A L E S DE ISOTOPOS CON E S P A C IA M IE N T O DE NIVELES 

D E L O RDEN DE LOS keV 

Elemento 

Г a 

(barn) 

I ¿ b 

(barn) 

Observaciones 

5 1 y 0,15 0 ,48 [23] 0 Cálculo parámetros ref. [27]. 

Fe 0,2 6 [24] 

0,32 [ 4] 

1 ,1 [25] d Medidas de oscilación, los au 

tores suponen espectro l/E. 

Ni 0,1 6 [ 4] 1 [25] d Medidas de oscilación, los au 

“ Zn 0 ,5 9 [26] 0 ,9 6 [26] 

7íGe 0 ,2 2 [ 3] 0,67 [ 3] 

e0Se 0 ,5 6 [ 7] 1.62 [ 7] 

130Te 0,17 [ 6] 0,48 [ 7] 

a Cálculo Breit-Wigner. 

k Intégral epitérmica experimental. 

tores suponen espectro l/E. 

° Corregido por desviación espectral a 4 keV (espectro de un acelerador). Por lo tanto el autor supone 

I¿ = Г [ 2 3 ] . 

d Medido en el centro de un reactor tipo piscina de uranio enriquecido al 20%, 0 £pi/©th - 0 ,1 [25]. Los 

autores suponen I¿ = I ' . 

T A B L A II. P A R A M E T R O S DE RESO N AN CIA N EUTRO N ICA 

DE LAS DOS RESO NAN CIAS MAS IM P O R T A N T E S D E L 148Nd 

e r 

(eV) 

Г7 

(m eV) 

r n 

(m eV) 

Г 

(m eV) 

Referencias 

100± 15 1610±240 1710 [19] 

155 70± 8 2000 2070 [20] 

40 a 2460±200 2500±200 [21] 

250±283 a 1850±200 2100±200 [22] 

96 ± 14 2600±200 2696 [19] 

285 58± 6 1980±100 2083 [20] 

3700±370 [21] 

50± 224 a 3130±100 3180±200 [22] 

a Obtenido sólo por transmisión, el ancho radiativo tiene un error muy grande debido a que es obtenido por 

diferencia de magnitudes del mismo orden.

I A E A - S M -1 7 0 /2 1 6 7 

E STIM A C IO N DE L A P A R T E NO R E S U E L T A DE L A IN T E G R A L E P IT E R M IC A 

Y D E L A IN T E G R A L DE RESO N AN CIA 

L a in te g ra l e p ité r m ic a no resu e lta puede d e fin ir s e : 

em a x 

i;(N R ) = J (aA (E) - g oo\fE0/E ) 0epi(E) d E /E (5) 

El 

donde E max = 10 M eV p a ra n u e s tros c á lc u lo s y s i e l e s p e c t r o e s l / E 

te n e m o s la in te g ra l de re s o n a n cia no re su e lta : 

em a x 

I1 (NR) = J (cta (E) - g ct0nTEo/E ) d E /E (6) 

el 

E sta p a rte d el c á lc u lo tien e en cuenta la co n trib u ció n a la in te g ra l 

e p it é r m ic a o de re s o n a n cia de la s a b s o r c io n e s n e u tró n ica s en la re g ió n no 

r e s u e lta de alta e n e rg ía . 

En la m a y o r p a rte de lo s tr a b a jo s a n te r io r e s cuando lo s p a rá m e tr o s de 

r e s o n a n cia a b a ja e n e rg ía se co n o c ía n con exactitu d , s e ha su p u esto 

d e s p r e c ia b le la con trib u ció n de la p a rte n o re s u e lta en c o m p a ra ció n con 

la s a b s o r c io n e s en la zon a r e su e lta [4 ] o se ha c a lc u la d o u san do la a p r o x im 

a ció n s [ 5, 6] . En algu nos e stu d io s de la s ca p tu ra s n e u tró n ica s en la 

re g ió n no re s u e lta en un e s p e c t r o de un r e a c t o r rá p id o s e ha u sad o la 

a p ro x im a ció n js.y £ [ 8 ]. 

Sin e m b a r g o s i la in te g ra l e p ité r m ic a no r e su e lta se e stim a d e sd e unos 

p o c o s keV (Е МдХ~ keV) la a p ro x im a ció n j3 o ^ m á s £ puede su b e s tim a r 

se r ia m e n te la s ca p tu ra s n e u tró n ica s a alta e n e rg ía en e l e s p e c t r o de un 

r e a c t o r . 

En la tabla III se m u e stra la in te g ra l e p ité r m ic a no re s u e lta estim a d a 

p a ra e l 74G e, 100 M o y v a r io s is ó to p o s d el z ir c o n io y d e l n e o d im io , u san do 

la s e c c ió n e fic a z de ca p tu ra obten id a p o r aju ste s e m ie m p ír ic o d el m o d e lo 

e s ta d ís tic o [ 10]. Se puede v e r que la a p ro x im a ció n £ puede su b e s tim a r 

s e r ia m e n te la in te g ra l e p ité r m ic a o de re s o n a n cia no r e s u e lta s . 

L a s a p ro x im a cio n e s j3 o ¿ m á s £ no s ó lo su b estim a n la s ca p tu ra s a 

a lta s e n e rg ía s sin o que a l d e s c r ib ir in co r r e cta m e n te la fo r m a de la 

d is tr ib u c ió n de a b s o r c io n e s en fu n ción de la e n e rg ía pueden e n m a s ca ra r e l 

e fe c to d el a p a rta m ien to de l / E d el e s p e c t r o a altas e n e rg ía s . 

P a r a algu nos is ó to p o s e s to a fe c ta no s ó lo e l c á lc u lo de la in te g ra l 

e p ité r m ic a que p e rm ite una c o m p a r a c ió n sig n ific a tiv a con lo s d atos e x p e r im 

e n ta le s, sin o tam bién e l c á lc u lo d e l fa c to r de c o r r e c c ió n e s p e c t r a l 

n e c e s a r io p a ra o b te n e r la in te g ra l de re s o n a n cia a p a rtir de lo s datos 

e x p e rim e n ta le s. 

En la tabla IV m o s tr a m o s e je m p lo s de is ó to p o s en que la co n trib u ció n 

de la a b s o r c ió n n e u tró n ica a e n e rg ía s d el o rd e n 'd e lo s M eV es sig n ific a tiv a 

p a ra e l e s p e c t r o de n u e s tro r e a c t o r [ 7, 12]. En r e a c t o r e s de agua p esa d a ' 

y / o g ra fito c o m o m o d e ra d o r e sta fr a c c ió n puede s e r sig n ifica tiv a m e n te 

m e n o r. 

P o r lo tanto a fin de e s tim a r c o r r e c ta m e n te (d en tro de un 50%) las 

ca p tu ra s o a b s o r c io n e s n e u tró n ica s en la p a rte no re s u e lta d e b e m o s u sa r 

s e c c io n e s e fic a c e s de ca p tu ra o a b s o r c ió n e x p e rim e n ta le s o en su d e fe c to 

s e c c io n e s e fic a c e s ca lcu la d a s con un m o d e lo e s ta d ís tic o s e m ie m p ír ic o . 

E sta s s e c c io n e s e fic a c e s deben s e r in teg ra d a s n u m é rica m e n te en e l e s p e c t r o

T A B L A III. C A L C U L O DE L A IN T E G R A L DE R E SO N AN CIA Y D E L A IN T E G R A L E P IT E R M IC A 

NO R E SU E L T A S DE VARIOS ISOTO PO S . 

isótopo 

e l 

Г (NR) I¿(NR) a 

sr Aproximación s Modelo estadístico 

semiempírico 

Modelo estadístico 

semiempírico 

(keV) (x l O 3) (barn) (barn) (barn) 

14 Ge 60 0, 0471 0,0032 0,058 0,161 

90Zr 70 0, 0160 0,0009 0, 041 0,151 

91 Zr 10 0,3672 0,1502 0,296 0,537 

52 Zr 50 0, 0396 0,0032 0, 070 0,203 

54 Zr 40 0,0326 0,0033 0, 065 0,161 

96Zr 60 0, 0291 0,0020 0,054 0,148 

100 Mo 2 0,0865 0,1769 0,650 0,942 

I46Nd 7 0, 181 0,106 0,640 1,16 

148Nd 9 0,231 0,105 0,560 1,03 

150Nd 4 0,672 0,687 1,21 1,9 1 

a Espectro de nuestro reactor (2 0 % uranio enriquecido y agua liviana) [ 7 ,1 2 ] , calculado con 54 grupos. 

1 6 8 RICABARRA et al.

I A E A - S M -1 7 0 /2 169 

T A B L A IV. CO N TRIB U C IO N DE L A A B SO R C IO N N E U TRO N IC A A A L T A 

E N E R G IA 3 A L A IN T E G R A L E P IT E R M IC A 

Elemento 

Д а 

Ni 0 ,859 b 

(barn) (barn) 

(0,798+0,061) 

(A /I¿ ) x 100 

1 86 

64 Zn 0,350 0,96 36 

74Ge 0, 108 0,681 16 

94 Zi 0, 123 0,417 30 

80Se 0, 088 1,62 5 

iooMo 0,222 4 ,2 0 5 

146Nd 0,47 2 ,5 8 18 

L48Nd 0 ,48 11,7 4 

a Д = ^200keV ® ° 0 VE0/E > ®epi(E) dE/ E ( В Д ° rápido de nuestro reactor (2 0 % uranio enriquecido 

y agua liviana) [ 7 ,1 2 ], calculado con 54 grupoS). 

b Captura (n, p) = 0, 798 b, más captura (n, y) = 0,061 b. 

d el r e a c to r c a lc u la d o a m u ltig ru p o s. E l e s p e c t r o ca lcu la d o puede v e r ific a r s e 

en algu nas r e g io n e s de e n e rg ía im p o rta n te s m ed ian te d e te c to r e s de u m b ra l 

y de re s o n a n cia . 

A p a r e c e e l p r o b le m a de cuánta ex actitu d p o d e m o s a sig n a r a la s s e c c io n e s 

e fic a c e s ca lcu la d a s con e l m o d e lo e s ta d ís tic o s e m ie m p ír ic o . 

C o m o ha o b s e r v a d o B en zi [ 9] la s s e c c io n e s e fic a c e s de captu ra 

ca lcu la d a s co n e l m o d e lo e s t a d ís tic o son p o c o s e n s ib le s a la s fu n cio n e s de 

fu e rz a n e u tró n ica su p u esta p e r o son fu e rte m e n te d ep en d ien tes de la 

«fu n c ió n de fu e rz a ra d ia tiv a ». 

P o r o tr o la d o es de d e s ta c a r que p a ra m u ch os is ó to p o s la s e c c ió n 

e fic a z de ca p tu ra o a c tiv a ció n a alta s e n e rg ía s se c o n o c e sola m e n te en 

algu n os puntos (p or e je m p lo a 25 k eV y a 1 M eV ) y a v e c e s se p resen ta n 

d is c r e p a n c ia s n o ta b le s e n tre lo s r e su lta d o s de d istin to s la b o r a to r io s y p or 

lo tanto lo s c á lc u lo s s e m ie m p ír ic o s a ju sta d os c o n e s t o s datos pueden te n e r 

la m ism a in ce r tid u m b r e . 

P o r e s ta s r a z o n e s e s n e c e s a r io ev a lu a r la s s e c c io n e s e fic a c e s e x p e r im 

e n ta le s d is p o n ib le s en la r e g ió n de e n e rg ía m a y o r de 10 k eV e igualm en te 

e l an ch o ra d ia tiv o y e l e sp a c ia m ie n to p r o m e d io a b a ja s e n e rg ía s obten id os 

p o r m e d icio n e s de tie m p o de v u e lo . 

Si la s s e c c io n e s e fic a c e s y e l v a lo r de la fu n ción de fu e rz a ra d ia tiv a 

con cu e rd a n ra z o n a b le m e n te b ie n con lo s v a lo r e s obten id os o su p u estos p o r 

e l c á lc u lo co n e l m o d e lo e s ta d ís tic o , s e p od rán u tiliz a r en fo r m a con fia b le 

p a ra la e s tim a c ió n de la in te g ra l e p ité r m ic a y de re s o n a n cia no re su e lta . 

E je m p lo s de e ste tip o de estu d io pueden e n co n tr a r s e en n u e s tr o s tr a b a jo s 

a n te r io r e s [ 3 , 11]. 

F in a lm e n te , la s c o n s id e r a c io n e s a n te r io r e s s e r e su m e n en la fig u r a 1, 

donde se m u e stra e sq u e m á tica m e n te e l tr a b a jo de e v a lu a ció n y c á lc u lo 

n e c e s a r io p a ra que la c o m p a r a c ió n con lo s datos e x p e rim e n ta le s tenga 

se n tid o .


CALCULO A M U IT IG RU PO S 

D EL ESPECTRO NEUTRONICO 

M ED ID A DEL IN DICE E S - 

PECTRAL DE NEUTRONES 

GRADIENTE D EL INDICE E S 

PECTRAL Y FLUJO TERMICO 

F IG .l. Diagrama de cálculo de la intégral epitérmica. 

SELECCION DEL LUGAR 

DE IR R A DIA CIO N 

PREPARACION DE SOLUCIONES PREPARACION Y A N A LISIS POR 

INCLUIDO EL « S T A N D A R D » ACTIVACION DE LAS MUESTRAS 

IcontrolI 

COMPUTADORA DE 16 К 

DE M EM ORIA 

Z Z .... 

REDUCCION DATOS 

«ON L IN E » INTEGRALES 

E 

(I p /б0), le 

CONVERTIDOR ANALOGICO 

DIGITAL DE 100 Me 

IRRADIACION DE MUESTRAS 

« B A R E » Y BAJO CADMIO 

O EN D O S ESPECTRO S 

MEDICION Y REDUCCION 

DE OATOS 

DETECTOR G e -L i 

DE 30 cm3 

P REAM PLIFIC ADOR Y 

AM PLIFICADOR 

F IG .2. Esquema del sistema experimental usado para determinar la integral epitérmica.

I A E A - S M -1 7 0 /2 1 7 1 

A d e m á s , en la fig u r a 2 se m u e stra e l s iste m a e x p e rim e n ta l se g u id o p o r 

n o s o tr o s en la d e te rm in a ció n de la in te g ra l de re s o n a n cia e in te g ra l e p ité 

r m ic a y e l p r o ce d im ie n to de evalu a ció n y c á lc u lo a p lica d o p a ra o b ten er 

la in te g ra l de r e s o n a n cia e x p e rim e n ta l. L o s d e ta lle s e x p e rim e n ta le s se 

han d e s c r ip to en tr a b a jo s a n te r io r e s [ 7, 2 ] . 

P a r a c o m p a r a r lo s r e s u lta d o s e x p e rim e n ta le s obten id os en d istin tos 

r e a c t o r e s e s p o r lo tanto im p orta n te d is p o n e r de una adecu ada d e s c r ip c ió n 

d el e s p e c t r o n e u tró n ico y d el ín d ice e s p e c t r a l de n e u tro n e s. Sin e m b a rg o , 

e x ce p to p a ra u nos p o c o s is ó to p o s , e s to s datos n o son d e s c r ip to s en la 

m a y o r ía de lo s e x p e rim e n to s . 

USO D E LOS D ATO S IN T E G R A L E S E P IT E R M IC O S EN L A E V A L U A C IO N 

DE LOS P A R A M E T R O S DE RESO N AN CIA 

En e sta p a rte n os lim ita r e m o s a d a r algu n os e je m p lo s tom a d o s en su 

m a y o r ía de n u e s tr o s tr a b a jo s en e ste te m a , que d em u estra n c ó m o lo s 

d atos de e x p e r ie n c ia s in te g ra le s pueden s e r ú tile s en la e v a lu a ción . 

1) Is ó to p o s d e l z ir c o n io 

E l 94Z r y e l 96 Z r s o n de in te r é s en f ís ic a de r e a c t o r e s . A m b o s is ó to p o s 

tienen p r im e r a p r io r id a d en R en da 1972; d e sd e e l punto de v is ta de la f ís ic a 

n u c le a r son ta m b ién in te resa n te s p o r e s ta r en la r e g ió n de m a sa de m á xim a 

fu n ción fu e r z a £ y m ín im a fu n ción fu e r z a s^. L a in te g ra l de r e so n a n cia 

m ed id a p o r n o s o tr o s m o s tr ó que la s ca p tu ra s £ son c a s i e l 100% d el 

to ta l [ 12] . En p a rticu la r la r e s o n a n c ia de 302 e V e s una r e s o n a n c ia £ 

100 v e c e s m á s in ten sa de lo s e s p e ra d o s p o r la s is te m á tic a n u c le a r [ 13]. 

E ste r e su lta d o no se h abía p r e v is to ni te ó r ic a m e n te ni de la s m ed id a s 

d ife r e n c ia le s y a r r o ja una s o m b r a de duda en la a s ig n a ció n £ o £ de 

re s o n a n cia s de is ó to p o s p a r d e l z ir c o n io , b a sa d a s sola m e n te en la c o m p a r a 

c ió n de lo s an ch os n e u tró n ic o s con lo s p r e v is to s p o r la s is te m á tic a n u c le a r [14]. 

2) E je m p lo de is ó to p o s con e sp a c ia m ie n to s de re s o n a n cia d el o rd e n de lo s keV 

L a s m e d id a s de la in te g ra l de r e s o n a n c ia de a c tiv a c ió n m u estra n 

c o n s iste n te m e n te que e x iste una s e r ia d is c r e p a n c ia en tre lo s v a lo r e s 

e x p e rim e n ta le s y lo s c a lc u la d o s co n la fo r m u la c ió n de B r e it-W ig n e r . L a 

m is m a d is c r e p a n c ia s e o b s e r v a en la in te g ra l de r e s o n a n cia e p ité r m ic a 

de a b s o r c ió n d eterm in a d a con té c n ica s de o s c ila c ió n en e l e s p e c t r o de un 

r e a c t o r (tabla II). 

D e b id o a que p a ra e l 74Ge se d isp on e de p a rá m e tr o s de r e so n a n cia 

n e u tró n ica ob te n id o s p o r té c n ic a s de tie m p o de v u e lo de tr a n sm isió n y 

ca p tu ra en m u e stra s e n riq u e cid a s [15] y ta m b ién de m e d id a s de a c tiv a ció n 

de b a ja r e s o lu c ió n en tre 10 k eV y 2 M eV [ 16, 17], h e m o s p od id o c a lc u la r 

d a tos in te g ra le s de ca p tu ra en la r e g ió n de e n e rg ía m a y o r que 10 k eV p o r 

d ife r e n te s p r o c e d im ie n to s y c o m p a r a r lo s [ 3 ]. 

N o s o tr o s lle g a m o s a d o s re su lta d o s: 1) Una e s tim a ció n c o r r e c t a de la 

in te g ra l e p ité r m ic a n o r e s u e lta d ebe te n e r en cu en ta que la d is tr ib u c ió n de 

s e c c io n e s e fic a c e s a alta e n e rg ía no puede s e r r e p re s e n ta d a p o r la a p r o x im 

a ció n en p a rticu la r, s i e l e sp a cia m ie n to p r o m e d io de la s re s o n a n cia s 

e s d el ord e n de lo s k eV . 2) E l c á lc u lo de la in te g ra l e p ité r m ic a y de la


in te g ra l de r e s o n a n cia en la zon a en tre 10 keV y 60 k eV a p a r tir de 

s e c c io n e s e fic a c e s de a c tiv a ció n con b a ja r e s o lu c ió n (ДЕ = 10 keV ) da 

re s u lta d o s que con cu e rd a n con la in te g ra l e p ité rm ic a de a c tiv a ció n y d is crep a n 

co n lo s obten id os con lo s p a rá m e tr o s de r e s o n a n cia n e u tró n ica que a p a ren te 

m ente su b estim a n en e sta zon a la s ca p tu ra s n e u tró n ica s. 

3) E je m p lo de lo s is ó to p o s d el n e o d im io 

L o s p a rá m e tr o s de r e s o n a n c ia d el 146Nd, 148 Nd y 150Nd son de in te rés 

en la f ís ic a d el qu em ado [ 18] y han sid o in v e stig a d o s p o r cu a tro e x p e r ie n c ia s 

de tie m p o de v u e lo [ 19-22]. 

A p e s a r de e ste e s fu e r z o hay tod avía una c o n s id e r a b le in ce rtid u m b re en 

lo s v a lo r e s del ancho ra d ia tiv o d e l 148Nd y d el 150Nd p resen tá n d o se 

d ife r e n c ia s d el d ob le o m á s en tre lo s r e su lta d o s p a ra la s re s o n a n cia s m ás 

im p o rta n te s de e s to s is ó to p o s . 

N o s o tr o s r e a liz a m o s una m ed id a de la in te g ra l e p ité r m ic a y de r e so n a n cia 

d el 146Nd, 148 Nd y 150Nd con un e s p e c t r ó m e t r o gam m a de alta r e s o lu c ió n , lo 

que es e s p e cia lm e n te im p ortan te p a ra e s to s is ó to p o s d eb id o al c o m p le jo 

e s p e c t r o gam m a obten id o p o r a c tiv a ció n con n eu tron es en una m u e stra de 

n e o d im io . A d e m á s s e r e a liz ó un c á lc u lo y evalu a ció n d etalla d os de a c u e rd o 

a lo s p r o c e d im ie n to s d e s c r ip to s en la fig u ra 1 [11]. 

H e m o s lle g a d o a la co n c lu s ió n de que e l v a lo r de la in te g ra l de 

r e s o n a n cia d el 148Nd es ap roxim a d a m en te la m itad d e l reco m e n d a d o 

a n te rio rm e n te y en c o n s e c u e n c ia e l an cho ra d ia tiv o es tam bién la m itad 

d el v a lo r p re v ia m e n te a cep ta d o. 

P o r o tr o la d o s e obtuvo un buen a c u e rd o en tre lo s v a lo r e s e x p e r im 

e n ta le s y ca lc u la d o s d e l 146Nd y d e l 150Nd. Cabe se ñ a la r que la m agnitud 

r^Ty/rde la s p r in c ip a le s reson a n cia s d el 14eNd y 150Nd p resen ta un buen 

a c u e r d o en tre d istin ta s d e te rm in a cio n e s de tie m p o de v u e lo . 

ALG U N AS O BSE RVA CIO N ES SO BRE L A U T IL IZA C IO N DE LAS IN T E G R A L E S 

E P IT E R M IC A S Y DE RE SO N AN CIA EN E L ANALISIS P O R A C T IV A C IO N 

E x is te a ctu alm en te una ex ten sa in fo rm a c ió n s o b r e p a rá m e tr o s de 

r e s o n a n c ia n e u tró n ica p a ra c a lc u la r la in te g ra l e p ité r m ic a de m u ch os 

is ó to p o s (CIN DA 72). Un p r o ce d im ie n to p a ra h a c e r lo está d e s c r ip to en 

la fig u ra 1. 

Una pregu n ta que ca b e h a c e r s e es s i la gran can tid a d .d e in fo rm a c ió n 

d isp o n ib le e s u tiliza d a en a n á lisis p o r a c tiv a ció n y s i e sta in fo rm a c ió n 

e stá p rese n ta d a de m a n e ra s ig n ific a tiv a y u tiliz a b le p a ra fin e s p r á c tic o s . 

Si e sta in fo rm a c ió n e s tu v ie r a d isp o n ib le p e r m it ir ía r e a liz a r un a n á lisis 

sem icu a n tita tiv o u san do m u e stra s c u b ie rta s con d ife ren te s filt r o s n e u tró n icos. 

E s to su m a d o a una adecu ada d e s c r ip c ió n d el e s p e c t r o de n eu tron es en la 

fa c ilid a d de ir r a d ia c ió n e v ita r ía la in n e c e s a r ia d e te rm in a ció n de s e c c io n e s 

e fic a c e s e fe c tiv a s p a ra ca d a ca m p o n e u tró n ico p a rticu la r. 

L a c o m b in a ció n de e s t o s p r o ce d im ie n to s co n un a n á lisis d e l e s p e c t r o 

gam m a c o n un e s p e c t r ó m e t r o de alta r e s o lu c ió n trabajan d o « o n lin e » con 

una com p u ta d o ra d a ría la p o s ib lid a d d el a n á lis is sim u ltá n eo de m u ch os 

is ó to p o s en té r m in o s se m icu a n tita tiv o s. 

L a p o s ib ilid a d de u sa r d ife r e n te s filt r o s c o m o Rh o r В con e n e rg ía de 

c o r t e e le v a d a e s ta m b ién m u y a tra ctiv a p a ra e l a n á lisis p o r a ctiv a ció n .

I A E A - S M -1 7 0 /2 173 

P a r ticu la rm e n te e l u so de filt r o s g ru e s o s de b o r o e n riq u e c id o 

(500 m g /c m 2) d a ría la p o s ib ilid a d de m e d ir en la r e g ió n de alta e n e rg ía 

d el e s p e c t r o de un r e a c to r , donde la s d ife r e n te s a c tiv a c io n e s s e r ía n 

a p ro x im a d a m e n te p r o p o r c io n a le s a la fu n ción fu e r z a ra d ia tiv a , m in im iza n d o 

e l e fe c to de a ctiv id a d e s de con ta m in a ció n con r e s o n a n c ia s in ten sa s de b a ja 

e n e rg ía , que p roducen una fu e rte a ctiv id a d que d ificu lta la d e te rm in a ció n 

de is ó to p o s con r e s o n a n c ia s de ca p tu ra d é b ile s. 

L o s p a rá m e tr o s de re s o n a n cia s evalu ados y s e c c io n e s e fic a c e s de 

ca p tu ra a alta e n e rg ía p o d ría n u s a r s e p a ra c a lc u la r la in te g ra l e p ité rm ic a 

y e s t o s d atos p od ría n s e r d e s c r ip to s en ta bla s de f á c il u s o p a ra a n á lisis 

p o r a ctiv a ció n . 

L a s ta bla s de que s e d isp on e p a ra a n á lisis p o r a c tiv a c ió n son 

in co m p le ta s y no s ie m p r e b a sa d a s en una ad ecu ada evalu a ció n ; ad em ás, 

en g e n e r a l con sta n lo s datos e x p e rim e n ta le s de la in te g ra l de r e so n a n cia 

y n o u san la in fo r m a c ió n que puede o b te n e r se de lo s p a rá m e tr o s de 

r e s o n a n c ia n e u tró n ica . Aunque e x iste n algu nas ta bla s que sigu en la s lín e a s 

s u g e rid a s [6], no se extien d en a tod os lo s is ó to p o s de in te r é s en e l a n á lisis 

p o r a ctiv a ció n . 

CONCLUSIONES 

D e b e m o s s e ñ a la r fin a lm en te que un c á lc u lo y e v a lu a ció n de la s 

a b s o r c io n e s y ca p tu ra s n e u tró n ica s en fu n ción de la e n e rg ía debe s e r h ech a 

en la zon a r e s u e lta y no re su e lta , s i s e d e s e a c o m p a r a r lo s datos ca lcu la d o s 

co n lo s datos e x p e rim e n ta le s de la in te g ra l e p ité r m ic a obten ida en e l 

e s p e c t r o de un r e a c t o r . 

L o s p a rá m e tr o s de r e s o n a n cia deben s e r e v a lu a d os p a ra c a lc u la r 

la p a rte re s u e lta de la in te g ra l de re s o n a n cia y la in te g ra l de re s o n a n cia en 

la re g ió n de alta e n e rg ía d el e s p e c t r o d el r e a c t o r d ebe s e r estim a d a usando 

la s s e c c io n e s e fic a c e s de ca p tu ra e x p e rim e n ta le s o ca lcu la d a s con e l m o d e lo 

e s t a d ís tic o s e m ie m p ír ic o . 

Una c o m p a ra ció n de d atos c a lc u la d o s con lo s e x p e rim e n to s puede 

r e s o lv e r d is c r e p a n c ia s en lo s p a rá m e tr o s n e u tró n icos ob te n id o s en la s 

m e d ic io n e s de tie m p o de v u e lo c o m o lo m u estra n algu n os re su lta d o s 

p re se n ta d o s en e ste tr a b a jo . 

D e sd e e l punto de v is ta d e l a n á lisis p o r a c tiv a ció n la p o s ib ilid a d de u sa r 

filt r o s de alta e n e rg ía p o d r ía exten d er la a p lica b ilid a d d e l a n á lisis p o r a c t iv 

a ció n . 

Sin e m b a r g o p a ra que e l a n á lisis p o r a c tiv a ció n pueda h a c e r s e en fo r m a 

sem icu a n tita tiv a , s e n e c e s ita r ía m e jo r a r e l c o n o c im ie n to de la s s e c c io n e s 

e fic a c e s de ca p tu ra ra d ia tiv a p a ra la m a y o r ía de lo s is ó to p o s . 

R E F E R E N C IA S 

[1] HARVEY, J . A . , Reactor Physics in the Resonance and Thermal Region (GOODJOHN, A. J ., 

POM RANING, G . G . . EdS) II, M IT Press, England (1966) 103. 

[2] RICABARRA, G . H ., TURJANSKI, R ., RICABARRA, M . D ., Nuclear Data for Reactors (Actas Conf. 

Helsinki, 1970) Ц, OIEA, Viena(1970) 589. 

[3] RICABARRA, M . D . , TURJANSKI, R ., RICABARRA, G . H . , Can. J. Phys. 50 (1972) 1978. 

[4] S C H M ID T, J .J ., Neutron Cross Sections for Fast Reactors Materials. Parti: Evaluation, KFK-120, 

Karlsruhe ( 1966).

174 R IC AB ARRA e t a l. 

[5] PERSIANI, P .J ., Reactors Physics Constants, P. 163, ANL-5800, Argonne (1963). 

[6] WALKER, W . H . , Fission Product Data for Thermal Reactors. Parti: Cross Sections, AECL-3037, 

Chalk River (1969). 

[7] RICABARRA, M . D . , TURJANSKI, R . , RICABARRA, G . H . , CanJ. Phys. 46 (1968) 2473. 

[8] C O N N O L L Y , T . J ., KRUIJF, F ., An Analysis of Twenty-Four Isotopes for Use in Multiple Foil Measurements 

of Neutron Spectra below 10 keV, KFK-718, Karlsruhe (1968). 

[9] BENZI, V ., Nuclear Data for Reactors (Actas Conf. Helsinki, 1970) П, OIEA, Viena(1970) 379. 

[10] BENZI, V ., REFFO, G ., Newsletter Bulletin 10, C CDN- N W /10, Neutron Data Compilation Centre, 

France (1969). 

[11] RICABARRA, M . D . , TURJANSKI, R ., RICABARRA, G . H . , Measurement and Evaluation of Activation 

Resonance Integral of 146Nd, 148Nd and 150Nd (presentado al Can. J. Phys.). 

[12] RICABARRA, M . D . , TURJANSKI, R ., RICABARRA, G . H . , Can. J. Phys. 48 (1970) 2362. 

[13] RICABARRA, M . D . , TURJANSKI, R ., RICABARRA, G . H . , Nucl. Sei. Eng. 48 (1972) 370. 

[14] BARTOLOM E. J .R ., HOCKENBURY, R .W ., MOYER. W .R ., T A T A R C Z U K , J .R ., BLOCK, R . C . , 

Nucl. Sei. Eng. 37 (1969) 137. 

[15] M A LETZKI, K h .t PIKELNER, L .B ., SA LA M A TIN , I . M . , SHARAPOV, E .I ., Energie atomique 24 

(trad, franc, rev. rusa Atomnaya Energiya) (1968) 80. 

[16] D O V B E N K O , A. G . , KOLESOV. V . E . , KOROLEVA, V .P ., TOLST IK O V , B .A ., Energie atomique 27 

(1969) 41. 

[17] TOLST IK O V , В. A ., KOROLEVA, V .P ., KOLESOV, V .E ., D O V BEN KO, A. G ., Energie atomique 23 

(1967) 114. 

[18] Reactor Burn-up Physics (Actas Grupo expertos, Viena, 1971)»OIEA, Viena(l973). 

[19] K A R Z H A V IN A , E .N ., NGU EN NGUEN FON G , POPOV, A .B ., TA SK A E V , A .I ., USSR State Commitee on 

Utilization of Atomic Energy, Nuclear Data Information Centre, INDC-260 E (1969). 

[20] M IG N EC O , E ., THEOBALD, J .M ., PERLMAN, I.J , J. Nucl. Energy 23 (1969) 369. 

[21] ALVES, R .N ., DE BARROS, S ., CHE VILLON, P .L ., JULIEN, J ., MORGENSTERN, J.. SAMOUR, C ., 

Nucl. Phys. A134 (1969) 118. 

[22] TELLIER, H ., Propriétés des niveaux induits par les neutrons de résonance dans les Isotopes stables du 

néodyme, CEA-N-1459, Saclay (1971). 

[23] RYVES, T . B . , J. Nucl. Energy 24 (1970) 35. 

[24] STORY, J .S ., Nuclear Data for Reactors (Actas Conf. Helsinki, 1970) 11, OIEA, Viena (1970) 721. 

[25] CARRE, J . C . , VIDAL, R . , Nuclear Data for Reactors (Actas Conf. Paris, 1966) 1, OIEA, Viena (1967) 479. 

[26] RICABARRA, M . D . , TURJANSKI, R . , RICABARRA, G . H . , Can. J. Phys. 47 (1969) 19. 

[27] M O X O N , M . C . , Nuclear Data for Reactors (Actas Conf. Helsinki, 1970) П, OIEA, Viena, (1970) 815.

I A E A - S M -1 7 0 /1 8 

ASSESSMENT OF METHODS AND DATA 

FOR PREDICTING INTEGRAL PROPERTIES 

FOR URANIUM-FUELLED THERMAL- 

REACTOR PHYSICS EXPERIMENTS" 

R. C H A W L A 

Indian Institute of Technology, 

Kanpur, India 

Abstract 

ASSESSMENT OF M E T H O D S A N D D A T A FOR PREDICTING INTEGRAL PROPERTIES FOR URANIUM-FUELLED 

THERMAL-REACTOR PHYSICS EXPERIMENTS. 

The performance of "best" available theoretical methods and differential nuclear data for predicting 

integral thermal-reactor properties, such as reactivity and reaction rate ratios, is assessed in the light of 

evidence from a broad range of clean, benchmark experiments. It is shown in the present study that for 

improving the consistency of calculated integral parameters for D 20 , H 20 and graphite moderated systems, 

significant modifications to certain currently used nuclear data are desirable. Along with changes in moderator 

scattering cross-sections, 238 U resonance data and the 23SU fission energy spectrum, some modification of 235U 

thermal data has been made which lies within the experimental uncertainties of differential measurements. 

The "new " data options have been used in various analyses with the W IM S lattice code, and results are 

presented for the benchmark studies and also for some lattices with more complicated geometries. It is 

shown that the preferred data generally give more consistent results, for both reactivities and reaction rates 

over a wide range of conditions, than any previously considered data combinations. 

1. INTRODUCTION 

In recent years, a high degree of sophistication in representing 

the {iiysics of thermal reactors has been achieved through the development 

of detailed computer codes, such as WIMS in the United Kingdom [1] 

and HAMMEB in the United States [2] » Application of these detailed methods 

and associated nuclear data has been expected to provide a consistent picture 

for the calculation of integral parameters, such as reactivity and 

reaction rate ratios, for a wide range of theimal reactor lattices, i.e. 

for various moderators and fuel enrichments. 

Several separate assessments have previously been reported for 

the performance of WIMS - based methods in analysing simple-geometry lattices 

moderated by graphite [3] , light water [4] and heavy water [5, 6] . 

These studies have demonstrated how for experiments where errors due to 

theoretical approximations are small, it becomes possible to make quantitative 

inferences on the adequacy of fundamental nuclear data. Thus, for 

example, earlier analyses hasre prompted corrections to epithemal data for 

both 23 % [7] and 235u [в] . 

In a recent study, Kemshell [9] showed that in spite of the improved 

differential data embodied in WIMS there have remained certain 

outstanding inconsistencies in calculations for clean experimental assemblies. 

For example : 

(i) reactivity predictions for DgO lattices are 1-1.5$ lew 

while those for light water end graphite moderated aesem- 

_______ ' bliee appear to be correct to within ~ 0.55? 

* Work carried out while author was Research Fellow at Atomic Energy Establishment, 

Winfrith, Dorchester, Dorset, United Kingdom 

175

176 C H A W L A 

(ii) fast fission ratios are signific&ntly ( ~ 10$ ) 

underpredioted for most lattices. 

The present study, following these earlier findings, describes 

an investigation of WIMS methods and data, carried out in the light of 

evidence from a variety of uranium - fuelled reactor physics experiments. 

By choosing lattices with simple geometry end accurately documented experimental 

information, errors of representation in the theoretical methods 

have been minimised in an effort to focus attention on the effects of existing 

uncertainties in differential nuclear data. Further, in order to 

arrive at a consistent set of recommendations, a sufficiently broad range 

of experiments, in both composition and type, have been considered. These 

include exponential and critical single-rod assemblies with the three 

principal moderators, homogeneous experiments with 93$ 235jj fuel, and 

British end Canadian heavy-water cluster lattices. 

2. METHODS AND DATA 

2.1 Résumé of WIMS Methods 

Description and earlier validations of the physics methods embodied 

in the WIMS code have been given by Askew et al [1] and Payers et 

al [4] . A brief résumé is presented here. 

The basic WIMS library is in 69 energy groups, 14 of these 

spanning the h igh energy region from 10 MeV to 9.118 keV, 13 in the resonance 

region above 4 eV, and 42 themal groups. In most cases, the group 

constants are foimed from the UKAEA Nuclear Data File [10] using suitable 

weighting spectra in the G A U X Y code [11] . An exception to this rule is 

the thennal energy transfer matrices which are produced by PIXSE [12] 

from a variety of thennal scattering laws including the Nelkin model for 

H 2O, the Effective Width model for DjO end an improved Egelstaff model 

for graphite. 

Treatment of the resonance region in WIKS is based cn the use 

of equivalence theorems to relate a group resonance integral for the 

heterogeneous cell to group resonance integrals for various homogeneous 

mixtures of moderator and resonance absorber. The library of resonance 

integrals has been compiled via the SDR Code [13] which solves the slowing 

down equations using some 120,000 energy points. The various procedures 

embodied in tiie WBCS resonance treatment have been shown to yield 

results which compare very favourably with more detailed methods of calculation 

such as the MOCTJP Monte Carlo Code [14"J , and it has been concluded 

that the probable error for^ßü captures, for example, is better 

than 1$ at all pitches [4] . 

Although solution of the transport equation is possible in the 

full 69 - group structure, such calculations tend to be unnecessarily 

elaborate. A special procedure is therefore embodied in WIMS for group 

condensation. This is based on the use of the "Spectrox" method [15] 

for producing in the full 69 groups, a condensation flux spectrum for each 

of the principal regions of the lattice cell, coupled together through 

collision probability expressions. Following the generation of condensed 

group cross-sections, a more accurate solution is obtained using either 

differential (discrete ordinate, DSN) or integral (collision probability) 

transport theory methods. 

Calculations for leakage in WIMS are performed on the homogenised 

cell in the same group structure as used for the main transport

I A E A -S M -1 7 0 /1 8 177 

routine. Allowance for asymmetric diffusion is made using methods due 

to Benoist [16] . übe leakage flux solution is obtained by either 

diffusion theory or the method, the latter employing explicit P-j 

scattering data for the principal moderating nuclei, viz. hydrogen 

denterium, oxygen and carbon. 

Details of the editing and operating instructions for the 

VflMS code have been given by Roth et al 1.171 • 

2.2 Bata Used 

There has been considerable uncertainty in tile last few years 

about the accuracy of epithemal 41 capture data. The original WBtS 

resonance integral tabulations for were based on differential measurements. 

Initial comparison of predicted and experimental reaction 

rate ratios for light water and graphite lattices, however, indicated 

that these resonance tabulations were too high and a uniform reduction 

of the microscopic cross-eecticn by 0.2 b a m jn the resonance region 

was proposed by Askew L7] • More recently, fresh assessments have been 

carried out by Kemsihell [6, 9] for a wider range of lattices with more 

accurately documented reaction rate measurements, and it has been concluded 

that the Askew correction is more than is required for optimum 

agreement with experiment. An intermediate value of 0.1 barn has been 

recommended aß a suitable uniform adjustment of the o r i g i n a l 

nance cross-section. This is in line with tiie results of a recent 

American study recommending modifications to ENDF/B resonance data 

[18]. 

Some uncertainty has also existed on the epiiiieimal data for 

2350. The resonance integrals originally contained in the WIMS libraiy 

for 235U were based on the measurements of Brookes which suggest a value 

of 0.67 forOC25, the infinite dilution ratio of capture to fission above 

0.5 eV L4] . As a result of more recent studies [8, 19] , however, opinion 

has hardened on a much lower ¿5 value of 0.50, and the presently 

recommended 235u resonance data in WIMS meets this criterion. 

The 235a fission spectrum is another item of data on vtfiich 

considerable doubt has been cast recently. The usual representation in 

the WIMS library is based on the measurements of Bonner and may be approximated 

by a Maxwellian spectrum with an averse temperature of 1.30 MeV. 

Several different types of integral measurements, however, indicate that 

the mean energy of the fission spectrum should be 5-1C$ higher than 

indicated by the differential measurements. Thus, for example, integral 

reaction rate measurements by Grundl [20] suggest a Maxwellian temperature 

as high as 1.5 MeV. Data adjustment studies for fast reactor 

benchmark experiments have suggested that a 10$ increase in the 235jj 

fission temperature is plausible \2Í) . The use of a fission temperature 

of 1.43 MeV in the WIMS libraiy has been recently advocated for HTR 

(High Temperature Reactor) studies, as it leads to considerable improvement 

in tte calculated age of fission neutrons in graphite (Section 3.3). 

In the light of the áx>ve evidence, this hardened fission spectrum 

has been used for the present study. 

The other important recent changes in WIMS data have been those 

in moderator cross-sections. For deuterium, for example, there have been 

two alternative UKAEA data files in the past, viz DPH 218 with a cross- 

section in the slowing down region (

178 C H A W LA 

Similarly, for hydrogen, a recommended value of 20.3 b a m s has been used 

for C p instead of the earlier 20.0 bams. For carbon, the presently used 

WIMS library has revised high energy cross-sections and a 0"p value of 4.74 

bams, 

3. EXPERIMENTS C ŒSIDEHED 

3.1 Natural U/D20 single-rod lattices 

As mentioned in Section 1, an important discrepancy in Ше analysis 

of experimental reactor lattices has been the underprediction of 

reactivity for D_0 systems [6, 22] . As the first stage of the present 

investigation , WIMS methods and data were applied to two sets of single, 

natural-uranium rod/DgO lattices, viz. 

(i) a series of exponential experiments carried out in tile subcritical 

assembly MINOS at Wttrenlingen [23] • The lattices 

were regular arrays of 10 mm diameter natural uranium 

metal rods, with square pitches of between 80 and 160 mm. 

and (ii) critical lattice studies performed in ttie Process Development 

Pile of the Savannah River Laboratory [24] . These 

were hexagonal lattices with higher moderator-to-fuel 

volume ratios (v /V.). 

Q Г 

WB!S calculations were initially carriedcut with a view to 

assessing the effects of simple changes in data and numerical treatment. 

Most of the calculations were performed in 18 transport groups with 15-20 

spatial points. Effects of further reducing the numerical approximations — 

e.g. using 36 energy groups, doubling the spatial mesh points or using 

n = 8 instead of n = 4 for the DSN routine - were all found to giveÛI^ 

in reactivity. 

Despite the systematic differeacts between the TOrenlimgen 

and Savannah River experimsnts, the conclusions from the WIMS analyses 

were similar, viz. 

(i) underprediction o f ke -f was -» 1.0% even itóien using the 

best numerical approximations and latest recommended 

moderator data. 

238 

(ii) tile Kemshell modification to TJ resonance data (Section 

2,2) caisiderably reduced earlier reported trends 

with lattice pitch. 

and (iii) use of the hardened 2^ U fission spectrum (l.43 MeV 

temperature) increased fast fissions by 7 - 8$. 

3.2 HgO and graphite moderated single-rod lattices 

The reactivity underprediction for DgO lattices cannot be 

considered in isolation as any recommended changes in basic nuclear data 

should be generally applicable, i.e. to H?0 and graphite moderated systems 

aß well. In order to assess the effects of the latest WIMS library data 

on predictions for light water lattices, the critical single-rod assemblies 

VlOCH [_4] , were reanalysed. Calculations were carried out in 25 

transport groups, more detailed high energy treatment being Important for 

these lattices from the standpoint ef slowing shown in HgO. The main conclusion 

drawn from these analyses was that while predictions for R1

I A E A - S M -1 7 0 /1 8 179 

TABLE I. "BEST-VAXUE" WIMS REACTIVITY ESTIMATES POE SINGIB-ROD LATTICES 

Lattice I Fuel/Moderator í < w 

i 

! 

к во I I keff 

ÏÏÜr 8 Hat. U/D20 19.4 1.143 0.991 

WÍir 12 Nat. U/DgO 44.e 1.221 0.987 

i&r 16 Nat. U/DgO 80.5 1.211 0.985 

SEL 1-7-1 Nat. D/DgO 53.1 1.229 0.989 

SRL 1-8-1 Nat. U/DgO 71.1 1.230 0.990 

SEL 1-9-II Nat. U/DgO 95.2 1.222 0.993 

SRL 1-12-î1 Nat. 0/D20 161.5 1.182 0.991 

R1/100 H 3$ en. U/H20 1.00 1.260 1.000 

E2/100 H 3$ en. U/H20 3.16 1.328 0.993 

S3/100 H Ъ1° en. D/HgO 0.78 1.212 1.000 

BICEP 76 Nat. U/С 76.7 1.059 0.994 

BICEP EMR 24/5 1.2# en. U/С 26.8 1.172 0.997 

E n e rg y -------► 

F IG .l. Thermal neutron spectra comparison for some single-rod lattices.

180 C H A W L A 

TAB IE II . ENERGY DISTRIBUTION OF CELL ABSORPTIONS FOR SOME SINGLE-ROD 

LATTICES 

Lattice 

t Absorptions (normalised to total of 1000 ) 

10 MeV- 

5.5KeV Í5.5KeV- 4.0 - Í0.625- Í0.100- Î0.050- Î0.030- Î0.015 

Í4.0 eV 0.625eVl0.100eVÏ0.050eV{0.030eV50.015eV|o.OeV 

Ops. 1-15 [ 16-27 28-45 i 46-56 i 57-60 : 61-63 i 64-66 467-69 

Wiir 8 52 126 18 103 206 187 181 127 

Wiir 16 32 33 5 73 235 229 228 165 

SRL 1-7-1 42 44 7 81 337 225 216 148 

SRL 1-12-F 38 20 3 69 243 235 230 162 

R2/100H 45 124 21 112 201 184 179 134 

R3/100H 120 323 46 154 127 93 81 56 

BICEP 76 54 81 16 110 238 202 180 119 

BICEP 24/5 93 197 39 170 203 136 103 59 

TABLE III . AGE PREDICTIONS (CM2 ) FOR THE PRINCIPAL MODERATORS 

I 

Moderator î 

H 2° 

V 

Present 

WIMS Value 

1 Value with 

Ï Earlier Data 

i 

К Experiment 

27.3 26 .6 27. 8 ± 0.2 125] 

26. 6 + 0.3 

[26] 

112 110 (DIN 218) 112+2 [27] 

Graphite 311 298 311 + 2 Ш 

TABLE I V . "BEST-VAHJE" WIMS RESULTS FOR OAK R U G E и/й20 SPHERES 

T- . i Sphere 

* ÏRadius (nrm ) Г * 5* « , i 

к 00 

i ï 

keff 

1 346.0 1378 1.206 0.987 

2 346 .0 1177 1.202 0.987 

3 346.0 1023 1.195 0.985 

4 346.0 972 1.196 0.986 

10 610.1 1835 1.065 0.988

I A E A - S M -1 7 0 /1 8 181 

and НЗ/10Ш were satisfactory, that for R2/100H was low by-jO.1?#. As discussed 

later, this can be attributed to the fact that tiie neutron energy 

spectrum for R2/10CH is radically different from the spectra for the other 

lattices. 

Calculations for some of the BICEP single-rod assemblies [3] 

were repeated using the latest recommended WIMS libraiy data to see the 

effects on graphite moderated systems with simple geometry. It was found 

that к values were generally underpredicted,though not as much as for 

the lattices. Further, the degree of underprediction varied with 

neutron spectrum for the lattice. 

Table I summarises "best-value" WIMS reactivity estimates for 

the various types of single-rod lattices considered. It is seen that к 

is underpredicted in all cases except for the two low (Vm/V.,) H^Q lattices 

R and R,/10CH. Fig. 1 compares thermal, cell-averaged neutron energy 

spectra of some of 1fae lattices for whicfa к is underestimated with toat 

of R,/ 10СЙ. The differences indicate that thermal events are much less 

important in ttie latter case. A better comparison may be made by considering 

the energy distribution of neutron absorptions in the various lattice 

cells. This has been done in Table II, the normalisation being to a total 

cell absorption of 1000 neutrons. Considering Wiir 8, B2/100 H and BICEP 

76, it is seen that although the moderator is different in each case, the 

distribution of absorption events is quite similar over the entire neutron 

energy range. One then gets a very consistent picture viiile noting that 

WIMS ke££ predictions for these single-red lattices are 0.991, 0.993 and 

0.994, respectively. These results indicate that the underprediction of 

reactivity is a moderator - independent deficiency. The most significant 

feature appears to be the energy distribution of neutron events, the 

discrepancies in к being greater for the more themalised lattieee. 

There are no significant trends with resonance capture or with leakage 

(i.e. кQQ ). 

3.3 Neutron Age Measurements 

Experimental determination of the age of fission neutrons te 

the 1.45 eV indium resonance is valuable evidence fer testing methods fend 

data effecting the calculation of leakage. The present study has involved 

the use of a considerably hardened fission spectrum, and there have also 

been significant modifications to moderator cross-sections. It is important 

to assess the effects of -tiiese changes on calculated values of the 

neutron age in graphite, H_0 and DgO. Table III summarises WIMS results 

for the three moderators, obtained using the 1.43 MeV fission spectrum 

and the latest data files for hydrogen, deuterium and oxygen. Comparisons 

are made with earlier calculated values and also wi1h tile more recent 

experimental values [1, 25, 26, 27} . It is seen feat the present predictions 

for DgO and graphite agree very well with experiment but that for 

H O, the large spread in the experimental values prevents any definite conclusion 

being drawn. 

3.4 Oak Ridge 255U/&20 Spheres 

Hie series of critical homogeneous U/H„0 sphere experiments carried 

out at OENL [28] is a particularly useful set for the present study, 

in that the geometry is simp le, leakage effects are relatively small, the 

fuel is highly enriched (~93$ U) so that data effects are negligible, 

and finally, the neutron spectra are well theimalised so that 

any shortcomings in thermal data would be highlighted. Detailed experimental 

consideration of these OEÍÍL criticáis has been given by Stsub et

182 C H A W L A 

TABLE V. ENERGY DISTRIBUTION OF FISSION YIEED FOR SOME OF THE EXPERIMENTS 

Г ! 7 I ORNL 5 Ш г î SRI I B2/100H { R3/10CH 

Bxperm ent jExpt. ■, 12 f w 

I 1.206 j 1.221 I 1.229 I 1,328 I 1.212 

keff________ f 0.987 f 0.987 ï 0.989 ï 0.993 î 1.000 

(noim. to 10005 

0.625 - 0.35 eV 5 5 4 15 37 

0.35 - 0.22 eV 8 9 7 23 52 

0.22 - 0.10 eV 54 67 68 84 114 

0.10 - 0.05 eV 207 233 239 223 173 

0.05 - 0.03 eV 221 230 233 205 127 

0.03 - 0.015 eV 248 229 227 198 110 

0.015 - 0.0 eV 236 165 155 143 77 

Net Thermal 

Í / r\ СОЕ лИЛ 

a 

979 938 933 891 690 

a 975, 972, 970 and 983 for Expts. 2, 3» 4 and 10, respectively. 

al [29^ . Recently three of the experiments (Hos. 1, 4 and 10) were analysed 

by Slaggie [30] using ENDF/B data, Versions I and II, and к . values 

were found to be consistently underpredicted, by ~ 0.7$ with Version I and 

~1.2$ with Version II. 

235 

In applying W M S to the analysis of the five ORNI U/HÔ 

spheres, several checks were first carried out on the adequacy of tfie 

methods. Final "best-value" reactivity estimates obtained using the recommended 

data options are summarised in Table IV. The к values are 

seen to agree well with the ENDF/B-II results reported byalaggie, there 

being a consistent underprediction by ~ 1.4$ for the four small spheres 

and by ~1.2$ for the large one. 

From 1iie values, it is seen that leakage is ~22$ for Experiments 

1-4 and cnly -8$ for Experiment 10. This difference provides a 

useful check on the adequacy of tile leakage calculations for these H„0 

moderated experiments. In any event, it is clear that the underpredictinn 

of by 1.2$ for the large sphere cannot be explained by any discrepancy 

that may exist between theory and experiment for the age in H„0 

(Section 3.3). 

The use of ^ B as poison in three of the ОШЪ experiments 

enables a practical check on the adequacy of moderator absorption cross- 

sections, absorptions in hydrogen varying between 28$ for Experiment 4 

and 48$ for Experiment 10. The consistent underprediction of k ^ ^ for 

the spheres thus points at shortcomings in fuel cross-sections.

I A E A - S M -1 7 0 /1 8 183 

WIMS results for the experiments considered in Sections 3.1 

and 3.2 have shown that the only type of single-rod lattice for which 

eigenvalues are low by more than 1$, is 1iie DgO moderated assembly, 

characterised by a well-themalised neutron spectrum. Table V compares 

the energy distribution of fission yield, ?E(, for OBNL Experiment 1 

with those for some of the single-rod lattices and shows that neutron 

spectra for the OHNIi spheres are even more thermalised than for the DgO 

lattices. The present results for the spheres thus strengthen the 

argument presented earlier,viz. that the underprediction of reactivity 

by WIMS is a moderator-independent deficiency which seems to be linked 

to shortcomings in theimal data. 

235 

4. MODIFICATION OF ÏÏ THEHMAb DATA AKP ITS EFFECTS 

4.1 Discussion of Differential Data and Modifications Considered 

The justification end the effects on WIMS predictions of certain 

simple cbanges in 235ц theimal data are discussed in this section. 

These have been considered in the light of a recent synopsis, by 

Westcott [31] i of tiie various differential measurements at thennal 

energies of Г , , Г and W for the fissile nuclides. Although an assessment 

of üie relative merits of the different sets of experimental peints 

has not presently been made, it is realised that a le est-squares fit is 

not necessarily the "best" curve especially «hen there is relatively 

large scatter among -tile data points, as is indeed seen to be the case 

from Figs. 2 and 3. föie experimental points for C. are seen to have the 

least spread. This follows from the fact that absolute values are better 

defined for flj., than for either ** or 0^, as systematic еггогв are smaller 

in measurements of the foimer. In comparing different data sets, renormalisation 

can therefore be justified more easily for

Ё -(1 0 0 -2 0 0 Е ) 

16.0 

14.0 

,< 12.0 

x ORL 160] 

♦ MTR 160) 

» HANI55) 

i HAN (58) 

• MISC 

+ * + T + ♦ * 

10.0 

0.0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 

E (eV) 

17.0 

16:0 

_ 150 

ш 

g 14.0 

1Л 

со 

T 13.0 

SÜ 

о . j j 

° * х„ 0 

0x »*4 Хх 

i T v а , 

< + 

FIG. 3. од and of for 235U between 0 .0 and 0.1 2 eV. 

IT 12.0 

11.0 

10.0 

9.0 

* LRL(66) 

♦ MOU68) 

A HANÍ57) 

▼ COL (58) 

в MISC. 

------ ENDF/B-H 

------ WIMS (DFN ¿8) 

------WIMS WITH 

NEW d ( 8) 

0.0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 

E(eV) 

184 C H A W LA

IAEA-SM-170/18 185 

For the discrepancies that have been shown to exist In WIMS 

reactivity predictions, modifications are sought to the theimal eta for 

Zii)U, and the simplest change would be to vary « with absorptions remaining 

the same. As mentioned above, the measurements of e\ are more 

reliable than those of and « . Hence, considering that tne present 

WIMS data is a fairly good fit to the experimental cr points, it is appropriate 

to assume constancy of 235fj absorptions in WIKS and to modify

186 C H A W L A 

5. FURTHER VALIDATIONS 

The satisfactoiy prediction of reactivity for simple, benchmark 

experiments is the most important basic criterion in testing a reactor 

physics code and its associated nuclear data libraqr. However, it 

is in the analysis of systems with more complicated geometries aid under 

power reactor conditions that a design code finds ultimate application. 

It was therefore decided to examine the validity of the presently recommended 

data modifications in the light of experimental evidence from 

Ц) lattices with more complex geometries, e.g. clusters, and (ii) actual 

power reactor studies. 

In view of the fact that earlier reported discrepancies have been 

largest for heavy water systems, particular attention was given to British 

and Canadian DgO - moderated experiments [5, 6] . It was found that, with 

the presently recommended data modifications, a significant overall improvement 

is obtained in reactivity predictions for cluster lattices. Fur- 

ttiemore, agreement between theory and experimsnt was found to be considerably 

better for reaction rate ratios. Relative conversion ratio (e.C.R) 

predictions were within 2$ of experimental values for a wide range of 

lattices, and fast fission ratios were underpredicted only by ~(3 ± 2)% 

compared with earlier errors of over 10$. 

As an application to reactors under power conditions, an assessment 

was made of certain information f готп the Steam Generating Heavy Water 

Reactor (SGHWR) Prototype at Winfrith [32] . It was found that reactivity 

changes with bumup are predicted quite satisfactorily using the modified 

data in WIMS. However, evidence on the isotopic composition of irradiated 

fuel was inconclusive. Overall, the presently recommended data,being a 

more consistent interpretation of available differential and integral information, 

was thought to be quite acceptable as an interim iapprovement for 

reactor design computations. 

6. SUMMARY AND С0НС1ЛSIGNS 

The main aim of this study has been to present a comprehensive 

comparison between -theoretical predictions and integral evidence from 

the m a l reactor physics experiments, in order that a consistent set of 

recommendations can be made to resolve a range of earlier reported discrepancies. 

For the most part, the Winfrith-developed code WIMS, has been 

used. However, reference has been made in places to American methods and 

data, thereby providing a check on theoretical treatment. 

Following Kemshell's recent survey of relative conversion ratio 

measurements [9] , the recommended modifications to 238p data have been incorporated 

into the WIMS libraiy, together with the latest changes in 

moderator scattering cross-sections. Present calculations have confirmed 

that 238[j capture rates are now predicted satisfactorily for various types 

of reactor lattices. Further, a 2^5u fission energy spectrum with a temperature 

of 1.43 MeV has been used Jn the present analyses, which implies 

~ 10% hardening of -tiie earlier used Bonner spectium. This modification 

has significantly improved the prediction of fast fission ratios. The 

calculation of age in graphite m d DgO has also been improved, but the evidence 

for HgO remains somewhat inconclusive. 

Using the ebove m odifications in nuclear data, analysis of a 

range of single-rod uranium lattices with each of the three principal 

moderators - DgO, HgO and graphite - indicated a trend to undeipredict 

reactivity which was found to be related to the energy distribution of 

thermal neutron events in tie fuel, rather than to the type of moderator 

used.By analysing a series of well thermalised, homogeneous critical sphere

I A E A - S M -1 7 0 /1 8 187 

experiments with highly enriched fuel (~93$ г35п), any possible residual 

errors due to uncertainties in 238ц data were completely eliminated and 

attention strongly focused on_thermal 235u cross-sections. An energy - 

dependent variation of the U thermal ot , based on keeping the more 

reliably Known absorption cross-section unchanged, has been considered 

within the spread of differential measurements, and it has been shown that 

this produces considerable improvement in the consistency of reactivity 

results for 1he different types of benchmark experiments analysed, the 

various predicted mean values lying in tiie range 0.996 - 1.003. 

Finally, a limited survey of cluster lattice experiments and 

power reactor studies has been used to provide some direct evidence of the 

improvement obtained in reactor design calculations with adoption of the 

presently recommended data modifications. 

ACKNOWLEDGEMENTS 

This study was carried out under a Research Fellowship with the 

United Kingdom Atomic Eneigy Authority. The author would like to express 

his gratitude to several people at the Atomic Energy Establishment, 

Winfrith, in particular to Dr. F.J. Fayers and Dr. D. Hicks, of the 

S.&.H.W.R. Development Division, for their guidance, advice and encouragement. 

HEEEHENCES 

1. ASKEW, J.R., FAYERS, F.J., KEMSHELL, P.B., J. Bilt. Nucl. Eneigy 

Soc. 5 (1966) 564. 

2. SÖICH, J.E., HOHECK, H.C., Rep. DP - 1064 (1967). 

3. BARCLAY, F.R., Rep. AEEW - R4 73 (1966) 

4. FAYERS, F.J.. KEMSHELL, P.B., TERRY, M.J., J . Brit. Nucl. Energy 

Soc. 6 (1967) 161 

5. BRIGGS, A.J., JOHNSTONE, I., KEMSHELL, P.B., NEWARCE, D.A., J.Brit. 

Nucl. Energy Soc. 7 (1968) 61 

6. KEMSHELL, P.E., Rep. AEEW - R549 (l96 9) 

7. ASKEW, J.R., Rep. AEEW - M602 (l965) 

8. FOX, W.N., KING, D.C., PITCHER, H.H.W., SANDERS, J.E., J. Brit. Nucl. 

Energy Soc. 9 (1970) 15. 

9. KEMSHELL, P.B., Rep. AEEW - R 786 (1972) 

10. STORY, J.S., et. al., Proe. Int. Conf. Peaceful Uses Atom.Energy, 

Geneva (l 964 ) 168. 

11. BELL, V.J., et. al., Rep. AEEW - R37 9 (1964) 

12. MACDOUGÁLL, J.D., Rep. AEEW - M318 (1963) 

13. BRISSENDEN, R.J., DÜRST0N, C., Rep. ANL - 7050 (1965) 51.

1 8 8 CHAWLA 

14. BANNISTER, G.W., BASHER, J.C., PULL, I.C., Rep. AEEW - R 243 (1968) 

15. LESLIE, B.C., J. Nucl. Energy J7 ( 196-3) 293 

16. BENOIST, P., AERE Trans. 842 (1959) 

17. ROTH, M .J ., MACDOUGALL, J.D., KEMSHELL, P.B., Rep. AEEW-R538 (1967) 

18. HARDING, R.S., GAVIN, P.H., HE ELENS, R.L., ANS Trans. 1969 Winter 

Meeting 12 2 744. 

19. FEINER, P., ESCH, L.J., Reactor Physics jn the Resonenœ and Thermal 

Regions, Vol. II, M.I.T. Prese (1S66) 299. 

20. GEUNDL, J.A., Nucl. Sei. Engng» 31 (1968) 191. 

21. CAMPBELL, C.G.. ROWLANDS, J.L., Proc. IAEA Conf. Nucl. data Reactors, 

Helsinki (l 970 ) IAEA - CN - 26/116. 

22. HCTHENSTEIN, Vi., Rep. RNL - ЯР - 1001 (1969) 

23. LUTZ, H.R., et al., Proc. IAEA Conf. Exponential and Crit 

Expts. Vol. II (1964) 85 

24. HURLEY, T.J. Jnr., FIKE, H.R., O'NEILL,G.F., Nucl. Sei., 

Engg. 12 (1962) 341. 

25. DO EBNER, ll.C., et al., Nucl. Sei. Engng. 9 (l96l) 221 

26. PASCHALL, IUC., Nucl. Sei. Engng. 20 (1964) 436 

27. GRAVES, W.E., Nucl. Sei. Engng. 12 (1962) 439 

2S. G’VIN, P.., MAGNUSON, D.W., Nucl. Sei. Engng. 12 (1962) 364 

29. STAUB, A., et. al., Nucl. Sei. Engng. 34 (1968) 263 

30. SLAGGIE, E.L., Rep. Gulf - ET - 10337 (l97l) 

31. ’.VSSTCOTT, C.H., lie p. AECL - 3255 (1969) 

32. FAYEHS, F.J., J . Brit. Nucl. Energy Soc. 11 (1972) 29

IAEA -S M -1 7 0 /6 7 

UTILISATION DE RESULTATS DE MESURES 

INTEGRALES POUR PRECISER LES VALEURS 

DES CONSTANTES NUCLEAIRES NEUTRONIQUES 

P. REUSS 

CEA, Centre d'études nucléaires 

de Saclay, 

France 


U S E O F R ESU LTS O F IN T E G R A L M E A S U R E M E N T S IN D E T E R M IN IN G M O R E PR EC IS E LY T H E V A LU E S O F 

N E U T R O N N U C L E A R C O N S T A N T S . 

In teg ra l neutron m easurem ents m ay — sin ce w e now h ave very p recise codes - p ro v id e sig n ific a n t 

in fo rm a tio n on n u cle a r constants. T h e ir analysis perform ed in th is sp irit is the lo g ic a l o u tco m e o f im portant 

e x p e rim e n ta l research done on reactors. It does not a llo w testing a ll data o f the c a lc u la t io n , but o n ly those 

q u a n tities w h ic h are already o f a g lo b a l nature. T h e analysis d e a lt w ith in the present paper, concern in g 

m easurem ents o f the L a p la c ia n re la tin g to a l l th e rm a l-n e u tro n -re a cto r types, has, above a ll, co n firm e d the 

new n o rm a liz a tio n o f the 235U fission cross-section and g iv en rise to a decrease o f the Z38U e ffe c tiv e resonance 

in te g ra l. 

U T IL IS A T IO N DE R E S U L T A T S D E M ESURES IN T E G R A LES P O U R PRECISER LES V A LE U R S DES C O N S T A N T E S 

N U C LE A IR E S N E U T R O N IQ U E S . 

Les mesures neutroniques in tégrales peuvent conduire, m ain tenan t q u 'o n dispose de codes très précis, 

à des renseignem ents s ig n ific a tifs sur les constantes n u clé a ires. Leu r analyse, fa ite dans ce t esprit, est 

l ’ aboutissem ent lo g iq u e de l'im p o r ta n t tr a v a il e x p é rim e n ta l fa it sur les p ile s . E lle ne p erm et pas de tester 

toutes les données du c a lc u l m ais des grandeurs i caractère synthétique. C e lle dont le m é m o ire rend com pte, 

entreprise sur des mesures de la p la c ie n rela tiv es à l ’ ensem ble des filiè re s à neutrons th erm iques, a co n d u it, 

p rin c ip a le m e n t, à c o n firm e r la n o u v e lle n o rm a lisatio n de la section de fission de l ' u ra n iu m -235 et à proposer 

une d im in u tio n de l ’ in té g ra le e ffe c tiv e de résonance de l'u ra n iu m -2 3 8 . 

1. INTERET DES MESURES INTEGRALES 

1. 1. M esu res intégrales 

L es quantités intégrales qu'on m esu re dans un m a ssif ou une e x 

p érien ce critiqu e sont souvent obtenues avec une très grande p récision . 

Cette seule rem arque in cite à pen ser que ce s m esu res pourraient être 

utilem ent con sid érées par ceux qui se préoccupent du problèm e des 

constantes n u cléaires. 

L es résultats qu'on obtient ne sont pas des constantes n ucléaires : ils 

en dépendent d irectem en t m ais de façon com plexe. On peut dire qu'on 

m esu re des fonctionnelles des section s effica ces. 

Inversem ent, ce qui in téresse en p rem ier lieu le physicien des réa cteu rs 

n 'est pas tant les section s e ffica ce s des différen ts noyaux que les valeu rs 

de quelques p aram ètres très globaux, tel un facteur de m ultiplication. On 

sera it logiquem ent amené à m esu rer les quantités in tégrales auxquelles 

on s'in té re s s e , m ais, à cause d 'im p éra tifs expérim entaux, ce ne sont, 

généralem ent, pas exactem ent le s m êm es : par exem ple on s 'in té re sse au 

facteur de con version m ais on m esu re un indice captures 238U /fissio n s 235U 

relatif. L es définitions en sont cependant toujours voisin es. 

189

190 REUSS 

1.2 . Interm édiaire du calcu l 

Que ce soit pour p a sser des grandeurs m esu rées aux grandeurs intéressa 

n tes, ou pour tester les constantes de base à partir des m esu res 

in tégrales, il y aura un in term édiaire indispensable : le calcu l de la 

fonctionnelle reliant le s section s e ffica ce s à la grandeur con sid érée. Il est 

donc cla ir que, si ce calcu l n 'est pas extrêm em ent p ré cis et fiable, la p ré 

cision expérim entale qu'on a au niveau de la m esure devient totalem ent 

illu so ire , surtout quand on passe au niveau du test des données de base. 

1.3. Situation ancienne des codes de calcul 

Jusque dans un passé récen t le schém a trop sim p liste des calcu ls 

rendait très critiquable l'u tilisation des m esu res intégrales pour le test 

des section s e ffica ce s, à tel point qu'on a souvent adopté une dém arche de 

pensée différente. 

La m ise au point du code COREGRAF [ 1] (calcul des réseaux de la 

filiè re uranium n atu rel-graphite-gaz) peut serv ir d 'exem p le. On a, a p riori, 

la issé indéterm inés quelques p aram ètres (en l'o c c u r r e n c e les constantes A 

et B de l 'e x p ression classiqu e de l'in tégra le effective de 238 U : I eff = A 

+ B n/S/M ). En interprétant systém atiquem ent un grand nom bre d 'exp érien ces 

(m esures de laplacien) on a déterm iné ces param ètres. On voit que 

l'aju stem en t fait a eu en réa lité deux ob jectifs: non seulem ent p a llier une 

m éconnaissance des section s e ffica ce s dans le dom aine des réson an ces, 

m ais en core c o r r ig e r les approxim ations faites par a illeu rs dans le schém a 

de calcu l. Ce deuxièm e ob jectif était bien présent com m e le m ontre le fait 

qu 'il a fallu ajuster deux intégrales effectiv es : l'u n e pour les calcu ls 

critiq u es, l'a u tre pour les ca lcu ls d'évolution. On a rem éd ié de la sorte, 

entre autres, à l'hypothèse trop sim p liste consistant à n égliger la rép a rtition 

non uniform e au sein du barreau des captures de 238u donc de la fo r 

m ation de 239 Pu. 

1.4. Situation présente des codes de calcu ls 

Depuis quelques années des outils beaucoup plus perfection nés ont été 

m is au point. On peut prendre com m e exem ple le code APO LLO [2] 

résolvan t dans un grand nom bre de groupes (186 ou 99) l'équation de 

Boltzm ann en géom étrie à une dim ension par la m éthode des probabilités 

de p rem ier ch oc. On peut penser que maintenant le passage des section s 

e ffica ce s m icroscop iq u es aux quantités intégrales auxquelles on s'in té re sse 

est beaucoup m oins hasardeux, au m oins dans les cas sim ples (par exem ple, 

réseau régu lier de cellu les contenant un barreau cylindrique de 

com bustible). 

Une autre rem arque très im portante doit être faite : non seulem ent 

l'o u til de calcu l s 'e s t perfection né, m ais il s 'e s t aussi gén éralisé. A insi, 

alors que COREGRAF ne pouvait être u tilisé que pour les ca lcu ls de r é a c 

teu rs de la filiè re UNGG (parce que l'aju stem ent n'était valable que pour 

cette gamme étroite de situations), APO LLO peut serv ir au calcu l des 

réseau x des réa cteu rs de n 'im p orte quelle filiè re .

1. 5. Nouvel intérêt des m esures intégrales 

IA EA -SM - 170/67 191 

L 'u tilisation des m esu res intégrales pour tester le s section s e ffica ce s 

devient maintenant intéressante. D'une part les im p récision s dues au calcu l 

n é ce ssa ire pour faire la transposition sem blent maintenant suffisam m ent 

faibles pour ne pas ren dre illu soire cette dém arche (au sens indiqué et non 

au sens «ajustem ent du code de ca lcu l»). D 'autre part le fait qu'un m êm e 

code devient u tilisable pour in terp réter une bien plus large gam m e de 

situations va ren dre ce test beaucoup intéressant : par exem ple il est bien 

évident que c 'e s t le m êm e uranium qu'on m et dans tous les réa cteu rs. Si 

on u tilise des quantités in tégrales (qui dépendent de ses section s) m esu rées 

dans des situations très d ifféren tes, on aura une inform ation beaucoup 

plus p ré cise. 

1. 6. D ifficulté de m ise en œ uvre 

L es section s e ffica ce s sont des fonctions, donc sont rep résen tées par 

une infinité de valeu rs num ériques. Même si on se lim ite à un schém a 

m ultigroupe, com m e dans APO LLO , ce sont des m illie rs de valeurs 

num ériques qu'on u tilise dans le s calcu ls. 

D 'autre part, m êm e en considérant toutes les m esu res intégrales 

faites dans le m onde, il est bien cla ir que le nom bre de renseignem ents de 

ce type est bien m oindre. 

Il n 'est, par conséquent, pas question de tester toutes le s sections 

e ffica ce s par les m esu res in tégrales. C ela signifie q u 'il y a un préalable 

à ce genre d'études : il faut synthétiser l'in form ation que représentent les 

m illie rs de section s e ffica ce s en un petit nom bre de grandeurs les c a r a c 

térisant de façon globale. 

On a là une étape in term édiaire nécessitant un choix délicat à faire : 

ces grandeurs doivent d'une part rep résen ter de façon co r r e c te les sections 

e ffica ce s qu'on veut tester, d'autre part jou er un rô le non n égligeable dans 

le calcu l des quantités intégrales qu'on exam ine et de ce lle s auxquelles 

s 'in té re s s e le physicien des réa cteu rs. P our prendre des exem ples 

extrêm es : la valeur m oyenne de la section effica ce de 235U dans le domaine 

des réson an ces ca ra cté rise m ieux cette fonction que le m axim um dans le 

m êm e domaine ; la section à 2200 m /s de 241 Am joue un rôle m oins im p ortant 

que celle de 235 U. 

2. E XE M PLE DE MISE EN OEUVRE 

2. 1. P rin cip es de l'étu de qui a été faite 

On a ch erch é à appliquer les id ées évoquées plus haut à l'étu de critiqu e 

du codé A PO LLO . Dans une p rem ière étape on s 'e s t lim ité aux réseaux 

à com bustible en uranium fra is, appartenant aux différentes filiè re s à 

neutrons therm iques. En effet, dans un réacteu r à neutrons rapides la 

situation neutronique est vraim ent trop différente et ce serait d'autres 

grandeurs synthétiques qu'on pourrait tester (et non les m êm es dans un 

rôle différent).

192 REUSS 

On est parti des données de la bibliothèque UKAEA [3]. On a ca ra ctérisé 

l'en sem b le des section s qu 'elle contient par douze grandeurs seu lement. 

En examinant les d ivergen ces entre calcu l et ex p érien ce sur un 

certain nom bre de m esu res in tégrales soigneusem ent ch oisies on a cherché 

à dégager des tendances à m od ifier l'une ou l'a u tre de ces grandeurs. Ces 

tendances pourront ensuite être u tilisées dans deux optiques : soit le choix, 

pour chaque noyau, de la bibliothèque la m ieux en a ccord avec ces tendances 

obtenues; soit l'aju stem ent de la bibliothèque dont on est parti. 

2 .2 . Méthode u tilisée pour la rech erch e de tendances 

D ésignons par Un l'une des grandeurs synthétiques retenues et Q ¡ 

l'u n e des quantités in tégrales exam inées. Au p rem ier ord re, pour une 

petite m odification des Un, on peut é c r ir e 

Si on peut trou ver un jeu de m odification s 6Un tel que les é ca rts entre expérien 

ce et ca lcu l c o r r ig é par ( 1) soient sensiblem ent réduits, on aura 

dégagé le s tendances à ces m odification s. 

Pratiquem ent on a procéd é de la façon suivante : 

— On a évalué les coefficien ts d'influence o?in par des form ules 

sim p les, ce qui a p erm is d 'é v ite r de p a sser un grand nom bre de fois le 

code APO LLO . 

— Considérant le s variations m axim ales des Un qu'on peut adm ettre 

com pte tenu des im p récision s sur les m esu res des section s, on a élim iné 

de l'étu de le s Un conduisant à des m odification s trop petites des Q ¡ (une 

tendance dégagée su r une telle grandeur n'aurait pas été sign ificative). 

— P our les Un restants on a ch erch é les m odification s am éliorant de 

façon cla ire la coh éren ce entre ca lcu l et ex p érien ce sans conduire à des 

variations proh ibitives des Un. P our ce la on a ajusté le s 6Un de (1) par 

m oindres c a rré s en m inim isant l'é c a r t quadratique m oyen entre m esu re et 

calcu l des Q ¡, tout en donnant un certain poids aux m esu res des sections 

e ffica ce s (ce qui sign ifie qu'on suppose plus probable que |êUn | soit petit 

que grand). 

2. 3. M esu res u tilisées 

n 

Deux types de m esu res ont été u tilisées : 

— des m esu res de l'â g e pour les tro is principaux m odérateu rs (graphite, 

eau ord in aire, eau lou rde), 

— des m esu res de laplacien et de taux de réaction dans des réseaux 

appartenant à toutes les filiè res à neutrons therm iques : 

RHT (m esu res fran çaises) 

UNGG (m esures fran çaises) 

D2 O (m esures fra n ça ises) 

H2 O (m esures am éricain es). 

(1)

IA E A -SM -17 0 / 67 193 

P ar ailleu rs on a u tilisé la valeur de la section de fission de 235U tenant 

com pte de la n ouvelle évaluation de la p ériod e de 234U et les valeu rs r e c o m 

m andées dans [4] pour les section s de diffusion des m odérateu rs dans le 

domaine des réson an ces des noyaux lourds. 

2 .4 . Grandeurs synthétiques con serv ées dans l'étude et tendances obtenues 

A près élim ination des grandeurs peu effica ce s on a con servé pour la 

rech erch e de tendances le s Un suivants : 

Ofg — section m oyenne de fission de 238U 

Ieffg — intégrale effectiv e de réson an ce de 238U 

cTf5 — section m oyenne de fission de 235U 

r — âge dans le m odérateur 

D — coefficien t de diffusion therm ique m oyen du m odérateur. 

L 'étude a conduit à p rop oser les m odification s suivantes (de la b ib lio 

thèque UKAEA) : 

— prendre pour т le s valeu rs m esu rées qui sont un peu su p érieu res aux 

valeu rs qu'on obtient en utilisant la bibliothèque ; 

— ne pas m od ifier en plus des fuites (r et D), ou alors très légèrem ent si 

on veut re cen trer au m ieux les résultats ; 

— pren dre la valeur de cr f 5 n orm a lisée avec la nouvelle évaluation de la 

périod e de 234U. Il est intéressant de noter que la rech erch e de 

tendances qui a été faite a con firm é cette nouvelle valeur. 

— dim inuer I eff8 de 0, 8 barn. 

Ce dern ier point est sans doute le plus im portant. On sait que cette 

con clu sion est cla ssiqu e: e lle avait déjà été notée lo r s de l'aju stem ent de 

COREGRAF; elle a égalem ent été obtenue par d'autres auteurs. 

CONCLUSION 

Une fois adm is qu'on peut fa ire confiance au code de calcu l on ne peut 

guère douter de l'in té rê t de prendre en com pte les m esu res in tégrales pour 

p r é c is e r le s constantes neutroniques. P ar contre la m ise en œ uvre peut 

être revue : on peut critiq u er le choix des grandeurs synthétiques retenues, 

le choix des m esu res intégrales u tilisées et la m éthode de rech erch e des 

tendances. L 'a p plication a été faite dans un cadre restrein t. On pourrait 

l'éten d re, en p a rticu lier, à l'étu d e du plutonium. 

Il nous sem ble que ce n 'est que par une étude critique rem ontant 

jusqu'au test des données de base qu'on peut pleinem ent ju stifier et v a lo r ise 

r le tra vail expérim ental de longue haleine qui a été accom p li et est 

p ou rsuivi sur le s m aquettes ou les p iles. Un sim ple constat des divergen ces 

entre ca lcu l et ex p érien ce est p eu t-être un renseignem ent suffisant pour 

l'exploitan t des réa cteu rs, m ais certainem ent pas pour le physicien qui a 

b esoin de sa v o ir le s expliquer.

194 REUSS 

[1] C O G N E , F . , H O F F M A N N , A . , REUSS, P . , C O R E G R A F 2, code de c a lc u ls de réseaux et d 'é v o lu t io n des 

réseaux â graph ite, C E A - N -1 3 4 4 (1970). 

[2] H O F F M A N N , A . , JEANPIERRE, F . , K A V E N O K Y , A . , L I V O LA N T , M . , L O R A IN , H . , A P O L L O , code 

m u ltig ro u p e de résolu tion de 1' équation du transport pour les neutrons therm iques et rapides, 

C E A - N -1610 (1972). 

REFERENCES 

[3] N O R T O N , S . , T h e U K A E A N u cle a r Data L ib ra ry , A E E W -M 8 2 4 (1968). 

[4] K E M S H E LL , P . B . , Som e Integ ral Properties o f N u c le a r D ata D educed from W IM S A n alyses o f W e ll 

T h e rm a lise d U ra n iu m La ttice s, AE EW -R 786 (1972). 


J. BOUCHARD: My question is addressed to M r. R euss and a lso to 

M r. B arré: what, from your point of view , are the m ost im portant integral 

m easurem ents? 

P . REUSS: A s fa r as therm al neutron reactors are con cern ed, the 

m ost im portant m easurem ents are the follow ing: buckling (or k eff ); the ratio 

238U fis s io n s /235U fission s; con version fa ctor, i . e . 238U captu res/ 235U 

fission s; also, analyses on irradiated fu els. 

J. Y. BARRE: In the case of fast neutron re a cto rs, among the m ost 

im portant integral experim ents, i . e . m easurem ents of neutron balance 

param eters which can be ca rried out v e ry ea sily (one might say "a sym p totica 

lly "), m ention shoüld be made of the follow ing: m aterial buckling; ratio of 

production to total absorption, o r the "K«, para m eter"; ratio of average 

reaction rates, either of fissio n o r capture, esp ecia lly the average ratio 

238U ca p tu re s /239Pu fission s, which is at p resen t m easured with a p recision 

of ± 2 by our techniques and enables us to have v e ry good confidence in the 

calculated breeding gain. 

G. CASINI: I should like to com m ent on integral experim ents, in p articular, 

those relating to burnt lattices. A s has been pointed out in the 

preced in g d iscu ssion , there are a num ber of ben ch-m ark experim ents with 

which the relia b ility of nuclear data can be checked — esp ecia lly in the case 

of unirradiated la ttices. An effort has been made in the United States to 

sele ct 12 ben ch -m ark experim ents fo r fast b reed ers and a sim ila r program 

fo r therm al lattices is being undertaken by the E uropean -A m erican R eactor 

P h ysics C om m ittee. H ow ever, I fe e l that it would be d esirable to devise 

a num ber of ben ch -m ark experim ents fo r the case of irradiated lattices, 

coverin g in particular isotop ic concentrations and, if p ossible, reactivity 

values as w ell. I think an international effort along these lines would be 

w elcom e.

Section III 

SAFEGUARDS

Chairman 

. EDER (Austria)

THE ROLE OF NUCLEAR DATA 

IN NUCLEAR MATERIAL SAFEGUARDS 

C. WEITKAMP, A. v. BAECKMANN, K. BÖHNEL, M. KÜCHLE 

Gesellschaft für Kernforschung, Karlsruhe 

L. KOCH 

European Institute for Transuranium Elements, 

Karlsruhe, Federal Republic o f Germany 

Abstract 

T H E R O LE O F N U C L E A R D A T A IN N U C L E A R M A T E R I A L S A FEG U A R D S . 

For the tim e ly d e te ction o f a d iversion o f fissio n a b le m a te ria l from the n u cle a r fu e l c y c le the 

safeguards system uses m a te ria l b alances based on m easurem ents o f m a te ria l flo w and in ven tory. 

In add itio n to c la s s ic a l a n a ly tic a l tech n iq u es, various n u cle a r m ethods have been developed for this 

IA E A -S M -1 70/78 

purpose. T h e g e n e ra l procedure for m ost o f these m ethods consists in the d e te rm in a tio n o f the mass o f 

the fis s ile sp ecim en re la tiv e to a known standard. T h e w ay in w h ic h n u cle a r data are req u ired for the 

d e v e lo p m e n t or e ffic ie n t use o f the m ethods can be d iv id e d in to four categories. (A) T h e very fe a s ib ility 

o f the m eth od or its d e ve lo p m e n t depend upon data in s u ffic ie n tly known. (B) D ata are d ire c tly needed 

for th e conversion o f m easured values in to m a te ria l mass; no standard specim ens are used. (C) T h e 

use o f a s u ffic ie n tly la rg e set o f standards is im p o ssib le or im p ra c tic a l; th erefore n u cle a r data are needed 

for c a lib ra tio n or in te rp o la tio n . (D) T h e use o f standards provid es fu ll c a lib ra tio n p o ssib ilitie s , or 

e x istin g data are adequate. 

For purposes o f illu s tra tio n a few m ethods are discussed. A n extrem e e x a m p le for category A is 

g a m m a resonance flu o re sce n ce w here the a ccu ra cy req uired for the le v e l and tra n sitio n energies is far 

b eyond presen t-d ay ca p a b ilitie s . C a lo rim e try and o-sp ectrom etry are d ire c tly based upon h a lf- liv e s and 

energies some o f w h ic h are in a d e q u a te ly know n (case B). T y p ic a l m ethods for w h ic h the num ber o f 

standards c a n b e g re a tly red u ced b y c a lc u la t io n are neutron c o in c id e n c e d e te rm in a tio n o f plu to n iu m , a ll 

techn iqu es that use th erm a l neutron in te rro g a tio n and d iffe re n t kinds o f a c tiv a tio n analysis; som e o f the 

req u ire d n u cle a r data need im p rov em ent (case C). Passive y-assay and fast-neutron in terro g atio n 

b e lo n g to categ o ry D. Spent fu e l is g e n e ra lly not am enab le to d ire ct m easurem ent o f fissile m a te ria l 

content. H ere isotope co rre la tio n s as now determ in ed e m p ir ic a lly for a num ber o f th e rm a l reactors and 

w it h in th e b u rn -u p range p resen tly o b ta in a b le le n d them selves to th e in d ire c t d e te rm in a tio n o f burn-up 

param eters in c lu d in g fis s ile m a te ria l content. T h is co rre la tio n te ch n iq u e has proved rem a rk a b ly universal. 

A n extended general a p p lic a tio n requires qu a n tita tiv e th e o re tic a l e x p la n a tio n w h ic h is o n ly possible i f the 

in te g ra l neutron re a c tio n cross-sections o f heavy isotopes and se le cte d fission products are im prov ed. 

1. I N T R O D U C T I O N 

I n o r d e r t o d e t e c t a n d p r e v e n t t h e d i v e r s i o n o f f i s s i o n a b l e 

m a t e r i a l f r o m t h e n u c l e a r f u e l c y c l e , a w o r l d w i d e s y s t e m h a s 

b e e n d e v e l o p e d t h a t i s g e n e r a l l y r e f e r r e d t o a s n u c l e a r m a t e r i 

a l s a f e g u a r d s . T h i s s y s t e m i s b a s e d t o a l a r g e e x t e n t o n t h e 

c l o s u r e o f m a t e r i a l b a l a n c e s . I n o r d e r t o s e t u p t h e b a l a n c e 

a c c u r a t e m e a s u r e m e n t s o f i n v e n t o r y a n d a l l i n p u t a n d o u t p u t o f 

t h e p a r t i c u l a r m a t e r i a l b a l a n c e a r e a a r e n e c e s s a r y . T h e s e 

m e a s u r e m e n t s c a n n o t a l w a y s b e p e r f o r m e d , o r a r e i m p r a c t i c a l t o 

p e r f o r m , b y c l a s s i c a l ( i . e . , n o n - n u c l e a r ) m e a n s . S o m e t h o d s 

f o r t h e d e t e r m i n a t i o n o f r e a c t o r f u e l h a v e b e e n d e v e l o p e d t h a t 

m a k e u s e o f i t s n u c l e a r p r o p e r t i e s . I t i s t h e p u r p o s e o f t h i s 

p a p e r t o s h o w i n w h i c h w a y t h e a s s a y o f n u c l e a r f u e l d e p e n d s 

u p o n t h e a v a i l a b i l i t y a n d a c c u r a c y o f n u c l e a r d a t a . 

197

TABLE I. CATEGORIES O F METHODS GROUPED ACCORDING TO THEIR 

DEPENDENCE UPON NUCLEAR DATA 

Category Dependence upon Data Examples 

A The feasibility of the method or its development 

depend upon data insufficiently known. 

В 

С 

D 

Data are directly needed for the conversion of measured 

values into physical quantities (isotopic ratio, 

material m a s s ) ; no standard specimens are used. 

Measurements are made relative to standard samples, 

but the proper application of corrections requires 

nuclear data. 

The use of standards provides full calibration possibilities, 

or existing data are adequate. 

Y -Ray Resonance Flurescence 

Neutron Capture y Spectroscopy 

a Spectrometry 

Calorimetry 

Thermal Neutron Interrogation 

Activation Analysis 

Neutron Coincidence Techniques 

Passive y Assay 

Fast Neutron Interrogation

IA E A -S M -1 70/7 8 199 

I n s t e a d o f p r e s e n t i n g a l i s t a r r a n g e d s i m i l a r l y t o t h e 

w e l l - k n o w n I N D C n u c l e a r d a t a r e q u e s t c o m p i l a t i o n / 1_ 7 w e d i s 

c u s s a f e w i n d i v i d u a l m e t h o d s w i t h r e s p e c t t o t h e i r d e p e n d e n c e 

u p o n n u c l e a r d a t a , t r y i n g t o g r o u p t h e m i n t o f o u r c a t e g o r i e s 

a s s h o w n i n T a b l e I. 

2. G A M M A - R A Y R E S O N A N C E F L U O R E S C E N C E 

A n e x a m p l e f o r a m e t h o d t h a t i s o n l y n o w b e i n g i n v e s t i g a t e d 

f o r i t s u s e i n t h e a s s a y o f n u c l e a r m a t e r i a l i s y - r a y r e s o n a n c e 

f l u o r e s c e n c e . I n t h i s m e t h o d t h e s a m p l e i s i r r a d i a t e d w i t h у 

r a y s , a n d t h e r e s o n a n c e - s c a t t e r e d p h o t o n s a r e m e a s u r e d w i t h a 

w e l l - s h i e l d e d d e t e c t o r . T h e m e t h o d u t i l i z e s t h e f a c t t h a t t h e 

e l a s t i c s c a t t e r i n g c r o s s s e c t i o n w h i c h , a t a y - r a y e n e r g y a r o u n d 

1 M e V , i s 1 b a r n f o r i s o t o p e s o f u r a n i u m a n d p l u t o n i u m , i n 

c r e a s e s b y o r d e r s o f m a g n i t u d e i f t h e e n e r g y o f t h e y - r a y is 

v e r y c l o s e t o t h e e n e r g y o f a l e v e l o f t h e n u c l i d e o f i n t e r e s t , 

e . g . 2 3 5 U. E m i s s i o n b y a n i d e n t i c a l s y s t e m d o e s u s u a l l y n o t , a s 

i t d o e s i n o p t i c a l s p e c t r o s c o p y , f u l f i l l t h e e n e r g y r e q u i r e m e n t 

b e c a u s e t h e e n e r g y l o s s o f t h e y - r a y d u e t o r e c o i l o f t h e r e s i 

d u a l n u c l e u s e x c e e d s t h e w i d t h o f t h e y l i n e b y a f a c t o r o f t e n . 

E v e n i f i n t e n s e s o u r c e s o f r a d i a t i o n t h a t d e e x c i t e a p p r o p r i a t e 

l e v e l s i n 2 3 5 U w e r e a v a i l a b l e ( w h i c h is n o t t h e c a s e ) , o t h e r 

s o u r c e s o f у r a d i a t i o n w o u l d t h e r e f o r e h a v e t o b e u s e d . 

_ T h e c r o s s s e c t i o n f o r y r e s o n a n c e f l u o r e s c e n c e c a n b e s h o w n 

/ 2 _ 7 t o b e g i v e n b y 

a = 1 . 4 g y 2 ( E 2 т 6) 1 e x p { — (АЕ/6 ) 2 } b a r n (1) 

w h e r e E i s t h e e n e r g y o f t h e y r a y o r o f t h e l e v e l i n M e V , т 

i t s l i f e t i m e i n p i c o s e c o n d s , g = ( 2 J i + l ) / ( 2 J o + l ) t h e s t a t i s t i 

c a l f a c t o r w h i c h a c c o u n t s f o r t h e a n g u l a r m o m e n t a J о a n d Ji o f 

t h e g r o u n d a n d e x c i t e d s t a t e s , a n d у = Г о/Г t h e b r a n c h i n g r a t i o 

f o r d e e x c i t a t i o n o f t h e e x c i t e d s t a t e i n t o t h e g r o u n d s t a t e . 

ДЕ= | E _ - E e +R| i s t h e e n e r g y m i s m a t c h , i . e . t h e d i f f e r e n c e b e t 

w e e n t n e l e v e l e n e r g y E a a n d t h e y - r a y e n e r g y £ e m i n u s r e c o i l R 

(in e V ) , a n d 6 ( a l s o i n eV) i s a w i d t h p a r a m e t e r w h i c h , i f l i n e 

s h a p e s a r e a p p r o x i m a t e d b y G a u s s i a n s , is g i v e n b y 6 2 = Дд+Де, 

Да a n d Де b e i n g t h e l e v e l w i d t h o f t h e a b s o r b e r a n d l i n e w i d t h 

o f t h e e m i t t e r , r e s p e c t i v e l y . 

I n o r d e r t o p r e d i c t t h e f e a s i b i l i t y o f a n e x p e r i m e n t d e s i g n e d 

t o p r o d u c e a s i z e a b l e e n h a n c e m e n t o f t h e e l a s t i c s c a t t e r i n g c r o s s 

s e c t i o n , a n a t t e m p t h a s r e c e n t l y b e e n u n d e r t a k e n J_ 3 _ / t o c o m 

p a r e e n e r g i e s o f k n o w n s t a t e s o f 2 3 5U w i t h t a b l e s o f y - r a y e n e r 

g i e s f r o m r a d i o a c t i v e s o u r c e s a n d t o c o m p u t e t h e r e s o n a n c e c o n 

t r i b u t i o n t o t h e c r o s s s e c t i o n v i a e q . (1). T h i s w o r k c o u l d o n l y 

y i e l d c a n d i d a t e s ( p a i r s o f m a t c h i n g у s o u r c e s a n d 2 3 5U n u c l e a r 

s t a t e s ) f o r a n e x p e r i m e n t ; e x a c t c r o s s s e c t i o n s c o u l d n o t b e o b 

t a i n e d d u e t o l a c k o f s u f f i c i e n t a n d s u f f i c i e n t l y a c c u r a t e n u 

c l e a r d a t a f o r v a r i o u s q u a n t i t i e s , i n p a r t i c u l a r 

(1) E n e r g y : s t a t e - o f - t h e - a r t m e a s u r e m e n t s o f y - r a y a n d l e v e l 

e n e r g i e s a r o u n d 1 M e V a r e a c c u r a t e t o a b o u t 25 e V , w i t h 

t h e m a i n c o n t r i b u t i o n o f 2 2 e V f r o m t h e r e f e r e n c e e n e r g i e s 

a n d o n l y 13 e V f r o m a l l e x p e r i m e n t a l e r r o r s ¡_ 4 _ / . A s y - r a y 

w i d t h s i n e x c e s s o f 1 0 e V c a n b e o b t a i n e d b y u s e o f s p e c i a l 

t e c h n i q u e s l i k e C o u l o m b f r a g m e n t a t i o n ¡_ 5 _ / , t h e p r e s e n t

TABLE И. ENERGY Е AND PARTIAL PRODUCTION CROSS - SECTION a FOR THE 

MOST INTENSE y-LIN ES FOLLOWING THERMAL NEUTRON CAPTURE 

Isotope E, keV a, barn Reference Element E, keV ст, barn Reference 

235u 6395.5 ± 0.3 0.32 ± 0.05 Г n 7 Cr 8881 0.22 

238 

/~15_Z 

4059.4 ± 2.0 0.30 ± 0.04 

239 

L 12 / Fe 7646, 7632 0.55 + 0.55 / 15 / 

5123.2 ± 0.4 2.05 ± 0.40 / 10, 13 / Ni 8996 1.20 / 15 / 

241PU 

Pu 5476.9 ± 0.5 7.60 ± 1.90 / 14 / Cu 7917 1.52 / 15 / 

со 

о

IA E A -S M -1 70/78 201 

s t a t e o f d e v e l o p m e n t o f e n e r g y m e a s u r e m e n t s is n o t i n a d e 

q u a t e . H o w e v e r , f e w a u t h o r s g o t h r o u g h t h e t e d i o u s p r o c e d u r e 

o f a n a l y z i n g t h e i r m e a s u r e d d a t a t o t h a t d e g r e e o f a c c u r a c y , 

o r if t h e y d o , f a i l t o p u b l i s h i m p o r t a n t d e t a i l s o f t h e i r 

w o r k a s , e . g . , t h e s e t o f r e f e r e n c e e n e r g i e s u s e d . S o a c o n 

s i s t e n t c o m p a r i s o n o f d a t a f r o m d i f f e r e n t a u t h o r s i s s e l d o m 

p o s s i b l e . 

I n t h e c a s e o f 2 3 5 U, e n e r g i e s o f l e v e l s a r o u n d 1 M e V a r e 

a c c u r a t e t o 1 0 0 - 3 0 0 e V i f m e a s u r e d b y y - r a y s p e c t r o s c o p y 

( f o l l o w i n g t h e r e a c t i o n 2 3 * U ( n , y ) 2 3 5U) o r a b o u t 2 k e V f r o m 

c h a r g e d - p a r t i c l e s p e c t r o s c o p y . F o r t h e m o s t p r o m i s i n g l e v e l , 

h o w e v e r , a n e n e r g y o f ( 1 1 1 6 . 2 ± 0 . 2 ) k e V h a s b e e n q u o t e d 

( c o m p u t e d f r o m c a s c a d e d e e x c i t a t i o n ) w h e r e a s t h e g r o u n d s t a t e 

t r a n s i t i o n e n e r g y i s g i v e n a s ( 1 1 1 5 . 6 ± 0 . 3 ) k e V J_ 6 _ / . A 

s o u r c e o f 2 4 5 d - 6 S Z n w i t h i t s s t r o n g ( 1 1 1 5 . 5 1 8 ± 0 . 0 2 5 ) 

k e V y - r a y m a y p r o v i d e s o m e c h a n c e f o r r e s o n a n c e e x c i t a t i o n 

o n l y i f t h e l a t t e r o f t h e t w o l e v e l e n e r g i e s i s c o r r e c t . 

(2) O t h e r p r o p e r t i e s o f e x c i t e d s t a t e s : f o r t h e c o m p u t a t i o n o f 

t h e c r o s s s e c t i o n f r o m e q . (1) t h e s p i n , d e e x c i t a t i o n b r a n 

c h i n g r a t i o a n d h a l f l i f e o f t h e l e v e l o f i n t e r e s t a r e a l s o 

r e q u i r e d . O n e o f t h e v i r t u e s o f t h e 1 1 1 6 k e V s t a t e o f 2 3 5 U 

i s t h a t i t s v a l u e s f o r J a n d Го/ Г a r e k n o w n ; t h e h a l f - l i f e , 

a l t h o u g h n o t m e a s u r e d , c a n b e c o m p u t e d t h e o r e t i c a l l y w i t h i n 

a f a c t o r o f 1 0 o r s o f r o m t h e s p i n , p a r i t y , a n d К q u a n t u m 

n u m b e r w h i c h a r e a l l k n o w n . 

T h e n u m b e r o f c a n d i d a t e s f o r a s s a y b y у r e s o n a n c e f l u o r e s 

c e n c e c o u l d b e g r e a t l y i n c r e a s e d i f m o r e d e t a i l s w e r e k n o w n 

a b o u t t h e l e v e l s c h e m e o f 2 3 5 U. O n l y t h e n w o u l d t h e s t a r t o f a n 

e x p e r i m e n t a l p r o g r a m b e j u s t i f i e d i n w h i c h t h e f e a s i b i l i t y o f 

t h e m e t h o d i s p r o v e d . S o у r a y r e s o n a n c e f l u o r e s c e n c e w h i c h c o u l d 

o f f e r c o n s i d e r a b l e a d v a n t a g e s o v e r e x i s t i n g m e t h o d s o f 2 3 5 u a s s a y 

i s a n e x a m p l e h o w l a c k o f d a t a c a n a f f e c t a m e t h o d i n i t s v e r y 

f i r s t s t a g e o f d e v e l o p m e n t . 

3. N E U T R O N C A P T U R E G A M M A - R A Y S P E C T R O S C O P Y 

A n o t h e r m e t h o d f o r w h i c h d a t a d e p e n d e n c e h a s a l s o b e e n c r i t i 

c a l a t a n e a r l y s t a g e i s y - r a y s p e c t r o s c o p y f o l l o w i n g n e u t r o n 

c a p t u r e . T h e r e a s o n f o r t h i s h a s b e e n t h e f a c t t h a t , a f t e r a 

f e a s i b i l i t y s t u d y o f t h e m e t h o d h a d s h o w n i t s p o t e n t i a l a p p l i 

c a b i l i t y t o t h e a s s a y o f i n d i v i d u a l i s o t o p e s i n n u c l e a r f u e l 

/ 7 _ 7 , у r a y s f r o m c a p t u r e h a d t o b e i d e n t i f i e d a s s u c h , a n d 

p a r t i a l c a p t u r e y - r a y p r o d u c t i o n c r o s s s e c t i o n s h a d t o b e 

m e a s u r e d . T h e f i r s t p r o b l e m w a s s o l v e d u s i n g d i f f e r e n t a p p r o a c h e s 

/ 8 - 1 0 _ 7 , a n d i t t u r n e d o u t t h a t , i n a g r e e m e n t w i t h e x p e c t a 

t i o n s , o n l y f e w l o w - e n e r g y y r a y s c a n b e d e f i n i t e l y a s s i g n e d t o 

c a p t u r e , b u t i n t h e h i g h - e n e r g y p a r t o f t h e s p e c t r a (E > 4 M e V ) 

m o s t o f t h e l i n e s o b s e r v e d a r e i n d e e d p r i m a r y c a p t u r e у r a y s . 

I n t e n s i t y m e a s u r e m e n t s , h o w e v e r , h a d t h e s o m e w h a t d i s a p p o i n t i n g 

r e s u l t t h a t p a r t i a l p r o d u c t i o n c r o s s s e c t i o n s f o r t h e s t r o n g e s t 

p r i m a r y у r a y s a r e a f a c t o r o f 10 t o 3 0 s m a l l e r t h a n e x p e c t e d . 

T h e m o s t i n t e n s e c a p t u r e у r a y o f s o m e i s o t o p e s o f u r a n i u m a n d 

p l u t o n i u m a n d t h e c o r r e s p o n d i n g p r o d u c t i o n c r o s s s e c t i o n f o r 

t h e r m a l n e u t r o n s a r e l i s t e d i n T a b l e II. F o r c o m p a r i s o n t h e s a m e 

d a t a a r e a l s o g i v e n f o r a n u m b e r o f m e t a l s t h a t o c c u r i n a l l o y s 

f o r s t r u c t u r a l a n d c l a d d i n g m a t e r i a l s . A s T a b l e I I s h o w s , y - r a y

202 WEITKAMP et al. 

e n e r g i e s f r o m c a p t u r e i n f u e l a r e u s u a l l y l o w e r a n d p r o d u c t i o n 

c r o s s s e c t i o n s o n l y o f t h e s a m e o r d e r o f m a g n i t u d e a s f o r o t h e r 

m a t e r i a l s . T h e r e f o r e v e r y g o o d s t a t i s t i c s i s r e q u i r e d w h i c h c a n 

o n l y b e o b t a i n e d b y u s i n g a r e a c t o r n e u t r o n b e a m ; d u e t o t h i s 

f a c t t h e m e t h o d h a s n o t m a t u r e d i n t o a w i d e l y - u s e d p r o c e d u r e f o r 

i n - p l a n t a p p l i c a t i o n . I f p h o t o n p r o d u c t i o n c r o s s s e c t i o n s h a d 

b e e n a t h a n d i n a n e a r l y s t a g e a m u c h m o r e d e t a i l e d p r e d i c t i o n 

o f t h e p o t e n t i a l a n d l i m i t a t i o n s o f t h e m e t h o d w o u l d h a v e b e e n 

p o s s i b l e . 

4. A L P H A S P E C T R O M E T R Y 

T h e m e a s u r e m e n t o f 2 3 8 P u w h i c h i s o f g r e a t i m p o r t a n c e f o r 

t h e a s s a y o f r e a c t o r p l u t o n i u m b y c a l o r i m e t r y (cf. c h a p t e r 5) o r 

c o i n c i d e n c e c o u n t i n g i s u s u a l l y d o n e b y a s p e c t r o m e t r y o r m a s s 

s p e c t r o m e t r y . B e c a u s e m a s s - 2 3 8 c o n t a m i n a t i o n s f r o m u r a n i u m a r e 

h a r d t o a v o i d , a s p e c t r o m e t r y i s t h e p r e f e r r e d m e t h o d , p a r t i c u 

l a r l y f o r c o n c e n t r a t i o n s < 0 . 3 %, a n d i n s o m e l a b o r a t o r i e s i n c l u 

d i n g o u r o w n t h e c r o s s c h e c k o f m a s s s p e c t r o m e t r i c 2 3 8 P u 

m e a s u r e m e n t s b y a s p e c t r o m e t r y is c u r r e n t p r a c t i c e . 

F o r t h e c o m p u t a t i o n o f t h e a t o m i c r a t i o Рв/Рэ o f 2 3 e P u a n d 

2 3 9 P u f r o m t h e m e a s u r e d r a t i o a o f 2 3 8 P u a c t i v i t y a n d t h e s u m 

o f t h e a c t i v i t i e s o f 2 3 9P u a n d 21,0P u f r o m t h e r e l a t i o n 

V p , ■ “ т ,/г 1 TV , 

t h e p r e c i s e k n o w l e d g e o f t h e h a l f l i v e s T 1 /2 o f 2 3 8 P u , 2 3 9 P u a n d 

2 "°Pu i s r e q u i r e d , a n d g e o m e t r i c a l f a c t o r s f o r t h e d e t e c t i o n o f 

a p a r t i c l e s f r o m 2 3 e P u a n d 2 3 9 ' 21,0p u m u s t b e e q u a l . W h e r e a s a 

s p e c t r a o f t h e t h r e e i s o t o p e s s e e m t o b e k n o w n w i t h a d e q u a t e 

a c c u r a c y a n d t h e v a l u e s o f t h e h a l f l i v e s o f 2 3 9 P u a n d P u h a v e 

n o t c h a n g e d m u c h i n r e c e n t y e a r s , n e w m e a s u r e m e n t s o f T i y 2 (2 3 8 Pu) 

c h a n g e d i t s v a l u e f r o m 8 6 . 4 y e a r s / ! 6 _ 7 t o 8 7 . 8 y e a r s j_ 1 7 _ 7 , 

i . e . b y 1 . 6 %. T h i s a c c o u n t s p e r f e c t l y f o r t h e s y s t e m a t i c d e v i 

a t i o n o f t h e r e s u l t s o f a s p e c t r o m e t r i c 2 3 8 P u d e t e r m i n a t i o n s 

w h i c h w e r e s y s t e m a t i c a l l y l o w a s l o n g a s t h e o l d e r h a l f l i f e 

w a s u s e d . T h e r e f o r e a n i n d e p e n d e n t r e i n v e s t i g a t i o n o f a l l t h r e e 

h a l f l i v e s a p p e a r s v a l u a b l e . 

5. C A L O R I M E T R Y 

H a l f l i v e s o f p l u t o n i u m i s o t o p e s a r e s u f f i c i e n t l y s h o r t so 

t h i s m a t e r i a l c a n b e d e t e r m i n e d n o n d e s t r u c t i v e l y b y m e a s u r e m e n t 

o f t h e d e c a y h e a t 

H = (I s i p i ) M = i M (2) 

H is r e l a t e d t o t h e p l u t o n i u m m a s s M b y a p r o p o r t i o n a l i t y f a c t o r 

i g i v e n b y t h e s u m o f t h e p r o d u c t s o f t h e s p e c i f i c p o w e r c o n s t a n t s 

§i a n d p e r c e n t a g e s p ^ o f t h e i s o t o p e s i n v o l v e d . U n l i k e m o s t o t h e r 

m e t h o d s , c a l o r i m e t r y r e l i e s h e a v i l y o n p r e c i s e n u c l e a r d a t a 

b e c a u s e t h e d e t e r m i n a t i o n i s u s u a l l y d o n e b y a b s o l u t e m e a s u r e 

m e n t o f e l e c t r i c q u a n t i t i e s w i t h o u t r e f e r e n c e t o a s e t o f s t a n 

d a r d s a m p l e s . T h e u s e o f s t a n d a r d s w o u l d b e i m p r a c t i c a l b e c a u s e 

t o o m a n y p a r a m e t e r s w o u l d h a v e t o b e v a r i e d . J u s t a s a

IA E A -S M -1 70/78 203 

s p e c t r o m e t r y c a n b e c o n s i d e r e d a n a b s o l u t e m e t h o d f o r t h e d e t e r 

m i n a t i o n o f i s o t o p e ra tio s, c a l o r i m e t r y i s o f t e n r e f e r r e d t o a s 

a n a b s o l u t e m e t h o d f o r t h e m e a s u r e m e n t o f p l u t o n i u m quantities. 

T h e c o n v e r s i o n o f h e a t o u t p u t i n t o p l u t o n i u m m a s s v i a e q . (2) 

i s c o m p l i c a t e d b y t h e f a c t t h a t t h e i s o t o p i c c o m p o s i t i o n is 

u s u a l l y n o t m e a s u r e d a t t h e s a m e t i m e . T h e a c t u a l p e r c e n t a g e s 

p ^ t o b e u s e d i n e q . (2) a r e t h e r e f o r e f u n c t i o n s o f t h e m e a s u r e d 

v a l u e s o f p ¿ , o f t h e h a l f l i v e s a n d o f t h e t i m e t b e t w e e n i s o t o p i c 

a n a l y s i s a n d c a l o r i m e t r i c m e a s u r e m e n t . 

T h i s m e a n s t h a t t h e e r r o r o f t h e p l u t o n i u m m a s s M d e p e n d s 

d ir e c tly u p o n t h e a c c u r a c y o f t h e m e a s u r e d p o w e r H, o f t h e c o n 

s t a n t s s, o f t h e m e a s u r e d p e r c e n t a g e s p, o f t h e t i m e l a g t 

a n d o f t h e h a l f l i v e s T 1/2 (2 3 8 Pu) a n d T i / 2 (2Ц' P u ) . I n a d d i t i o n 

e r r o r s o f t h e h a l f l i v e s e n t e r i n t o t h e a c c u r a c y o f s o m e o f t h e 

m e a s u r e d v a l u e s o f p a s d i s c u s s e d i n t h e p r e c e d i n g s e c t i o n a n d 

i n t o s o m e o f t h e s a s w i l l b e s h o w n b e l o w a n d t h u s in d irectly i n 

f l u e n c e t h e a c c u r a c y o f t h e r e s u l t . 

A d e t a i l e d e r r o r a n a l y s i s h a s b e e n m a d e j_ I 8 _ / w h i c h s h o w s 

t h a t t h e i m p o r t a n c e o f t h e d i f f e r e n t p a r a m e t e r s d e p e n d s i n a 

c o m p l i c a t e d w a y u p o n t h e c o m p o s i t i o n o f t h e m a t e r i a l . I n s t e a d 

o f g i v i n g t h e l e n g t h y f o r m u l a e r e s u l t s w i l l b e d i s c u s s e d t h a t 

h a v e b e e n o b t a i n e d f o r t h r e e t y p i c a l c a s e s ( T a b l e I I I ) . O f t h e 

v a r i a b l e s t h a t d e t e r m i n e t h e p r o p o r t i o n a l i t y f a c t o r e a l l b u t 

f i v e c o n t r i b u t e n e g l i g i b l y ( < 0 . 0 5 %) t o t h e t o t a l e r r o r o f t h e 

p l u t o n i u m m a s s M. I n T a b l e I V t h e a s s u m e d r e l a t i v e u n c e r t a i n 

t i e s S o f t h o s e f i v e q u a n t i t i e s a n d t h e i r c o n t r i b u t i o n s a t o 

t h e t o t a l r e l a t i v e e r r o r 6 M a r e s h o w n ; f o r c o m p a r i s o n t h e s t a t e - 

o f - t h e - a r t p r e c i s i o n o f t h e h e a t m e a s u r e m e n t H i s a l s o i n c l u d e d . 

T h e l a r g e s t f r a c t i o n o f t h e t o t a l e r r o r i s c l e a r l y d u e t o t h e 

e r r o r o f t h e p e r c e n t a g e o f 2 3 e P u f o r w h i c h s o m e i m p r o v e m e n t c a n 

b e e x p e c t e d f r o m b e t t e r h a l f - l i f e v a l u e s ( s e e s e c t i o n 4 ) . F o r 

m a t e r i a l w i t h l o w c o n t e n t o f 2 3 e P u t h e s p e c i f i c p o w e r c o n s t a n t s 

o f 2 3 9P u a n d 2l,0P u p l a y a c e r t a i n p a r t ; t h e d e t e r m i n a t i o n o f p l u 

t o n i u m w i t h h i g h c o n t e n t s i n 2l,1P u s u f f e r s t o s o m e e x t e n t f r o m 

t h e p o o r k n o w l e d g e o f t h e s p e c i f i c p o w e r o f 21,1P u . A s u r v e y o f 

t h e l a t e s t v a l u e s o f s a s d e t e r m i n e d d i r e c t l y (by c a l o r i m e t r y ) 

o r i n d i r e c t l y ( f r o m e n e r g y a n d h a l f - l i f e m e a s u r e m e n t s ) i s g i v e n 

i n T a b l e V . W h e r e c o m p u t e d a n d m e a s u r e d v a l u e s e x i s t , t h e t w o 

v a l u e s h a v e b e e n c o m p a r e d w i t h e a c h o t h e r a n d w i t h t h e e r r o r s o f 

t h e i n d i v i d u a l d e t e r m i n a t i o n . F o r 2 3 9 P u t h e a g r e e m e n t i s q u i t e 

g o o d . F o r 21,0P u t h e d i f f e r e n c e i s l a r g e r t h a n t h e s u m o f t h e 

e r r o r s ; t h e r e f o r e t h e l a r g e r o f t h e t w o e r r o r s ( 0 . 7 6 %) s e e m s t o 

b e m o r e r e a l i s t i c a n d h a s b e e n a d o p t e d f o r t h e c a l c u l a t i o n o f t h e 

m a s s e r r o r i n T a b l e IV. F o r 21,1A m t h e t w o e r r o r s j u s t o v e r l a p , 

a n d t h e s m a l l e r o f t h e t w o h a s b e e n u s e d . 

T h e q u e s t i o n o f i n d e p e n d e n c e o f t h e e r r o r s o f t h e q u a n t i t i e s 

l i s t e d i n T a b l e I V a n d o f t h e i r i n f l u e n c e o r m u t u a l c a n c e l l a t i o n 

f o r t h e a c c u r a c y o f t h e v a l u e o f e, i . e . o f t h e c a l o r i m e t r i c 

p l u t o n i u m d e t e r m i n a t i o n , i s n o t a t r i v i a l p r o b l e m b e c a u s e o f t h e 

f o l l o w i n g r e a s o n s : 

(1) F e w h a l f - l i f e m e a s u r e m e n t s a r e a b s o l u t e , o r if t h e y a r e , 

i m p u r e s a m p l e s a r e u s e d . T h e r e f o r e c o r r e c t i o n s f o r t h e i m 

p u r i t y h a l f l i v e s h a v e t o b e a p p l i e d w h i c h h a v e m o s t l y 

b e e n d e t e r m i n e d b y t h e s a m e p r o c e d u r e a s t h e o n e m e n t i o n e d . 

T h i s f e e d b a c k e f f e c t h a s s e l d o m b e e n p r o p e r l y t a k e n i n t o 

a c c o u n t .

T A B L E III. COM POSITIO N O F T H R E E B A T C H E S O F P L U T O N IU M 

Isotope 

238. 

Pu 

239: 

24o; i 

Pu 

Pu 

241 

Pu 

242 

Pu 

ALKEM 1968 Yankee V+VI,1 Yankee V+VI,16 

0.041 % 0.289 % 1.228 % 

90.517 % 85.050 % 69.309 % 

8.265 % 10.294 % 16.337 % 

1.113 % 4.011 % 10.853 % 

0.064 % 0.356 % 2.274 % 

TABLE IV. ADOPTED RELATIVE ERRORS 6 AND ERROR CONTRIBUTION 

a OF THE MOST IM PORTANT PARAM ETERS TO THE T O T A L ERROR 

OF THE CALORIMETRIC DETERMINATION OF THREE BATCHES OF 

R EACTOR-G RADE PLUTONIUM 180 D A F T E R ISOTOPIC COMPOSITION 

MEASUREMENT 

Batch 

Quantity 

ALKEM 1968 

S a 

Yankee V+VI,1 

6 a 

Yankee V+VI,16 

6 a 

Heat Output 0.25 % 0.25 % 0.25 % 0.25 % 0.25 % 0.25 % 

Percentage of 23®Pu 2.00 % 0.18 % 1.00 % 0.39 % 0.75 % 0.52 % 

■t ii 2l+0pu 0.30 % 0.07 % 0.26 % 0.05 % 0.18 % 0.02 % 

Specific Power of 23^Pu 0.20 % 0.13 % 0.20 % 0.08 % 0.20 % 0.03 % 

и n u 24 0pu 0.76 % 0.17 % 0.76 % 0.13 % 0.76 % 0.09 % 

и и и 2^1 pu 5.00 % 0.08 % 5.00 % 0.17 % 5.00 % 0.19 % 

Total Error of Pu Mass 0.40 % 0.52 % 0.62 % 

204 W EITKAM P et al,

TABLE V . DECAY ENERGY Q, H A L F-LIF E T i AND CALCU LATED SPECIFIC 

POWER s AS W E LL AS CALORIMETRIC VALUE OF s FOR FIVE ISOTOPES 

OF PLUTONIUM AND 241A m . ERRORS OF THE s ALSO GIVEN IN PERCENT AND 

COMPARED WITH THE DIFFERENCE BETW EEN THE CALCU LATED (FROM 

Q AND T i ) AND MEASURED (CALORIM ETRIC) VALUE 

Isotope Decay Energy3 

Q, keV 

238 

239*“ 

240Û 

2 4 llU 

2 4 2 f 

24l!U 

Am 

5593.40 ± 0.20d 

5243.6 ± 0.8? 

5255.5 + 0.73 

not applicable 

4982.5 ± 1.2f 

5638.05 ± 0.12 

Half Lifeb 

T l/2' years 

87.80 ± 0.028 

24401 ± 40? 

6620 ± 50 . 

15.10 ± 0.14 

386900 ± 1600n 

436.6 ± 3.0° 

Specific Powe r s, mW/g 

from Q and T^ 2 by Calorimetry 

567.17 ± 0.13 

1.9052 ± 0.0032 

7.0088 ± 0.0530 

0 . 11277± 0.00050 

113.53 ± 0.80 

1.9142 ± o.olccf 

7.1046 ± 0.0150 

3.62 ± 0 . 18m 

114.50 ± 0.17P 

Difference 

0.52% 

1.37% 

0.85% 

Percent 

Errors of s 

0.023 - 

0.17 0.47 

0.76 0.21 

5.00 

0.44 

0.70 0.15 

Decay energies not updated or corrected for consistent standards. 

b Half lives as determined by calorimetric and decay energy measurement not considered. 

c Values computed from the relation s = 2119.338 (Q/MeV) / { (A/amu) J[T years) } where A is the 

mass number_ on the 12C scale as given, e.g., in Ref. ¡_ 19_/. 

From Ref. / 20 /. 

e From Ref. / 17 /. 

From Ref. / 21 /. _ 

9 From Ref. j_ 22, 23_/. 

h , . _ _ 

From a réévaluation of the data published in Ref. 2 4 using (original values in parentheses) 

T i / 2 ( Pu) =_87.80 (87.60) y, T i /2 (21,1Pu) = 15.10 (14.03) y, si = 3.62 (4.24) mW/g and of 

the data of_ /_ 50_/ by use of si = 567.17 (567.00) mW/g, so = 7.105 (7.097) mW/g. Results are 

(for / 24 / ) s g = 1.9054 ± 0.0040 mW/g, so = 7.1046 ± 0.0150 mW/g and (for two samples measured 

in /_ 50_/) S9 = 1 .9235 ± 0.0039 mW/g, S9 = 1.9136 ± 0.0039 mW/g. For so the value so determined 

has been adopted, for S9 the average of the three values has been taken. Clearly, the prob- 

. able sg error is_ larger than the uncertainties quoted. 

' From Ref. / 25 /■ 

¿ From Ref. /_22_/. 

From Ref. / 2 6 / . Note that the new value_was_added in proof and does not appear in the abstract 

of / 26 / nor in the older paper J_ 21_ / . 

From Ref. /_28_/. 

n From Ref. / 5 1 / . 

° From Ref. / 29 /. 

P From Ref. / 30_/.


(2) T h e i n f l u e n c e o f e r r o r s o f n u c l e a r c o n s t a n t s u p o n t h e 

a m o u n t o f p l u t o n i u m t o b e m e a s u r e d d i f f e r s w i t h t h e a p p l i 

c a t i o n o f d i f f e r e n t m e a s u r e m e n t a n d e v a l u a t i o n t e c h n i q u e s . 

A n e x a m p l e is t h e m e a s u r e m e n t o f t h e 2 3 e P u p e r c e n t a g e , p 8 . 

I f p e i s d e t e r m i n e d b y a s p e c t r o m e t r y , t h e e r r o r o f 

T i / 2 (2 3 8 Pu) e n t e r s i n b o t h pe a n d se a n d w i l l p a r t i a l l y 

c a n c e l , p r o v i d e d t h e a s p e c t r o m ê t r i s t a n d c a l o r i m e t r i s t 

u s e t h e s a m e h a l f - l i f e v a l u e . If, o n t h e o t h e r h a n d , pa 

i s l a r g e s o t h a t m a s s s p e c t r o m e t r y i s a p p l i e d f o r i t s d e 

t e r m i n a t i o n , T 1/2 (2 3 8 Pu) e n t e r s o n l y i n sg p r o d u c i n g a 

q u a l i t a t i v e l y d i f f e r e n t e f f e c t . 

T h e r e f o r e m o r e p r e c i s e m e a s u r e m e n t s o f i n d i v i d u a l n u c l e a r d a t a 

i n v o l v e d i n t h e c o n v e r s i o n o f h e a t i n t o p l u t o n i u m m a s s m u s t b e 

a c c o m p a n i e d b y a c o m p r e h e n s i v e e v a l u a t i o n o r r é é v a l u a t i o n o f 

p u b l i s h e d m e a s u r e m e n t s w i t h t h e a i m o f o b t a i n i n g a con sisten t set 

o f data , a n d a s y s t e m s a n a l y t i c a l s t u d y o f t h e m e t h o d w i t h a l l 

i t s a n c i l l a r y m e a s u r e m e n t s t h a t c o u l d g o a s f a r a s t o p r e s e n t 

a r e c i p e f o r t h e procedure to follow i n t h e a s s a y o f r e a c t o r p l u 

t o n i u m b y c a l o r i m e t r y . 

6. A S S A Y T E C H N I Q U E S U S I N G N E U T R O N I N T E R R O G A T I O N 

A w i d e l y u s e d n o n d e s t r u c t i v e t e c h n i q u e f o r t h e a s s a y o f 

n u c l e a r m a t e r i a l c o n s i s t s o f i r r a d i a t i n g t h e s a m p l e w i t h n e u t r o n s 

a n d c o u n t i n g o f t h e e m i t t e d f i s s i o n n e u t r o n s . T h e i r i n t e n s i t y 

i s a m e a s u r e o f t h e a m o u n t o f f i s s i l e m a t e r i a l p r e s e n t . D i s 

c r i m i n a t i o n b e t w e e n s o u r c e n e u t r o n s a n d f i s s i o n n e u t r o n s i s d o n e 

e i t h e r b y u s i n g a p u l s e d s o u r c e a n d d e t e c t i n g d e l a y e d f i s s i o n 

n e u t r o n s , b y u s i n g a s t a t i o n a r y s o u r c e o f r e l a t i v e l y l o w e n e r g y 

n e u t r o n s t o g e t h e r w i t h a t h r e s h o l d d e t e c t o r , o r b y u t i l i z i n g 

t h e m u l t i p l i c i t y o f f i s s i o n n e u t r o n e m i s s i o n . 

I n a n y c a s e r e a c t i o n s a n d m a t e r i a l s a r e u s e d w h i c h a l s o 

o c c u r i n a n u c l e a r r e a c t o r a n d f o r w h i c h a l l r e l e v a n t n u c l e a r 

d a t a a r e a v a i l a b l e . T h e y a r e u s e d f o r i n s t r u m e n t d e s i g n c a l c u 

l a t i o n s , o p t i m i z a t i o n s t u d i e s , a n d f o r t h e d e t e r m i n a t i o n o f 

c o r r e c t i o n s s u c h a s n e u t r o n m u l t i p l i c a t i o n i n t h e s a m p l e . B e c a u s e 

c a l c u l a t i o n s d o n o t g i v e t h e r e q u i r e d a c c u r a c y t h e c a l i b r a t i o n 

o f t h e i n s t r u m e n t i s u s u a l l y d o n e w i t h a s e t o f s t a n d a r d s a m p l e s . 

G o o d c a l i b r a t i o n i s r e l a t i v e l y e a s y t o o b t a i n f o r c l e a n 

m a t e r i a l l i k e f r e s h f u e l r o d s , b u t i s d i f f i c u l t f o r s c r a p a n d 

w a s t e w h e r e t h e d e t e c t o r r e s p o n s e d e p e n d s g r e a t l y u p o n t h e m a 

t r i x m a t e r i a l a n d t h e l o c a t i o n o f t h e f i s s i l e m a t e r i a l i n t h e 

s a m p l é . E x t e n s i v e s t u d i e s o f t h i s e f f e c t w e r e m a d e , a n d 

m e t h o d s f o r i t s r e d u c t i o n p r o p o s e d / 3 1 _ 7 . N e v e r t h e l e s s u n c e r 

t a i n t i e s i n s a m p l e c o m p o s i t i o n , e . g . t h e p r e s e n c e o f h y d r o g e n , 

a r e s t i l l a m a j o r s o u r c e o f e r r o r . T h i s e f f e c t is p r o b a b l y 

m u c h l a r g e r t h a n t h e i n f l u e n c e o f n u c l e a r d a t a u n c e r t a i n t i e s 

i n s u p p l e m e n t a r y c a l c u l a t i o n s . 

A n a r e a i n w h i c h n u c l e a r d a t a a r e o f i m m e d i a t e i m p o r t a n c e 

i s t h e d e t e r m i n a t i o n o f f i s s i o n a b l e m a t e r i a l i n s a m p l e s c o n 

t a i n i n g m i x t u r e s o f d i f f e r e n t f i s s i l e a n d f e r t i l e s p e c i e s . 

T h e p r e p a r a t i o n o f s t a n d a r d s o f a l a r g e n u m b e r o f c o m p o s i t i o n s 

i s n o t e c o n o m i c . T h e r e f o r e c a l c u l a t e d v a l u e s a r e n e e d e d f o r i n 

t e r p o l a t i o n . E r r o r s m a y r e s u l t f r o m i n t e r a c t i o n e f f e c t s ; i t w a s ,

IA E A -S M -170/78 207 

e . g . , o b s e r v e d t h a t p r e d i c t i o n s o f r e s o n a n c e s e l f s h i e l d i n g o f 

2 3 5ц _ 2 3 9 p u m i x t u r e s i n t h e s l o w i n g - d o w n s p e c t r o m e t e r w e r e in 

e r r o r b y 15 %. E r r o r s c a n a l s o r e s u l t f r o m f a s t f i s s i o n a n d i n 

e l a s t i c s c a t t e r i n g i n 2 3 8 U. A s t u d y o f t h e i n f l u e n c e o f n u c l e a r 

d a t a u p o n t h e s e e f f e c t s h a s s o f a r n o t b e e n m a d e . 

7. A C T I V A T I O N A N A L Y S I S 

A n e x a m p l e f o r a c t i v a t i o n a n a l y s i s i s t h e d e t e r m i n a t i o n o f 

c o n c e n t r a t i o n s o f 2 3 5U a n d 2 3 9 P u i n w a s t e s o l u t i o n s o f r e p r o c e s 

s i n g p l a n t s a s p r e s e n t l y u n d e r i n v e s t i g a t i o n /13, 14, 3 2 _ / . T h e 

m e t h o d i s b a s e d o n t h e s e p a r a t i o n o f t h e f i s s i o n p r o d u i s 8 8 K r 

a n d 1 3 8 X e a n d y s p e c t r o m e t r y o f t h e d a u g h t e r n u c l i d e s R b a n d 

1 3 8 C s . B e c a u s e o f t h e l a r g e d i f f e r e n c e s i n y i e l d f o r t h e i s o 

b a r s 88 a n d 1 3 8 i n f i s s i o n o f 2 3 5 U a n d 2 3 9 P u t h e m e t h o d i s s u i 

t e d f o r t h e d e t e r m i n a t i o n o f t h e a b s o l u t e q u a n t i t y a n d o f t h e 

r a t i o o f t h e t w o f i s s i o n a b l e n u c l i d e s . F o r t h e r e d u c t i o n o f m e a 

s u r e d d a t a t h e f o l l o w i n g n u c l e a r c o n s t a n t s a r e r e l e v a n t : 

- h a l f l i v e s o f 8 8 K r , e e R b , 1 3 8 X e , 1 3 8 C s ; 

e m i s s i o n p r o b a b i l i t i e s f o r t h e 1 4 2 6 a n d 1 8 3 7 k e V 

y r a y s o f 1 3 6 C s a n d 8 8 Rb, r e s p e c t i v e l y ; 

f i s s i o n c r o s s s e c t i o n s o f 2 3 5 U a n d 23 Pu; 

- c u m u l a t i v e y i e l d s o f 8 8 K r a n d 1 3 8 X e . 

I f t h e s y s t e m i s c a r e f u l l y c a l i b r a t e d w i t h s t a n d a r d s o l u t i o n s 

t h e k n o w l e d g e o f t h e n u c l e a r d a t a l i s t e d i s o f l i t t l e i m p o r t a n c e 

a s l o n g a s a l l e x p e r i m e n t a l c o n d i t i o n s r e m a i n u n c h a n g e d . T h e 

e x p e r i e n c e s h o w s , h o w e v e r , t h a t t h i s r e q u i r e m e n t i s i m p o s s i b l e 

t o f u l f i l l , a n d c o r r e c t i o n s h a v e t o b e a p p l i e d t h a t d e p e n d m o s t 

c r i t i c a l l y u p o n t h e h a l f l i v e s a n d t o a l e s s e r e x t e n t u p o n t h e 

o t h e r d a t a l i s t e d . W h e r e a s c r o s s s e c t i o n s a n d y i n t e n s i t i e s a r e 

a c c u r a t e l y k n o w n , n o s a t i s f a c t o r y v a l u e s f o r c u m u l a t i v e y i e l d s 

o f 8 8 K r a n d 1 3 8 X e h a v e s o f a r b e e n p u b l i s h e d . 

8. C O I N C I D E N C E T E C H N I Q U E S 

A c h a r a c t e r i s t i c o f n u c l e a r f i s s i o n i s t h e f a c t t h a t i n m o s t 

o f t h e i n d i v i d u a l e v e n t s a n u m b e r o f n e u t r o n s a n d p h o t o n s a r e 

e m i t t e d s i m u l t a n e o u s l y . T o u s e t h i s e f f e c t f o r a s s a y , p u r p o s e s 

s e v e r a l c o i n c i d e n c e t e c h n i q u e s h a v e b e e n d e v e l o p e d £ ~ Í3 -J 9 _ J 

t h a t e s s e n t i a l l y a l l o w t o d e t e r m i n e t h e n u m b e r o f p a i r s , 

t r i p l e s , o r h i g h e r m u l t i p l e s o f c o r r e l a t e d p a r t i c l e s a n d t h e r e 

f r o m t h e n u m b e r o f f i s s i o n s i n t h e s a m p l e t o b e a s s a y e d . 

T h e m e a s u r e m e n t o f p a i r c o i n c i d e n c e s h a s p r o v e n p a r t i c u l a r l y 

u s e f u l i n t h e d e t e r m i n a t i o n o f i s o t o p e s t h a t u n d e r g o s p o n t a n e o u s 

f i s s i o n , e . g . i n t h e n o n d e s t r u c t i v e a s s a y o f p l u t o n i u m . 

T h e n e t c o u n t r a t e С o f t w o - f o l d c o i n c i d e n c e s i s r e l a t e d t o 

t h e m a s s e s пк o f t h e f i s s i o n i n g i s o t o p e s i b y t h e r e l a t i o n 

С = I m ±x ( L / A ±) x ( I n 2 / T i /2 , ±) x { V p ( V p - D / 2 x I = m J у±к± I (3) 

w h e r e L i s A v o g a d r o ' s n u m b e r , A t h e m a s s n u m b e r , a n d I is c h a r a c 

t e r i s t i c o f t h e i n s t r u m e n t u s e d a n d t h e m e t h o d a p p l i e d . N u c l e a r 

d a t a o f i n t e r e s t a r e t h e p a r t i a l h a l f l i f e f o r s p o n t a n e o u s f i s - 

s i o n T i / 2 a n d t h e a v e r a g e n u m b e r o f p r o m p t n e u t r o n p a i r s 

V p (V p - 1 ) /2 w h i c h m a y b e d e t e r m i n e d f r o m t h e f i r s t a n d s e c o n d 

m o m e n t o f t h e p r o b a b i l i t y d i s t r i b u t i o n p ( V p ) t h a t V p n e u t r o n s a r e


e m i t t e d i n a f i s s i o n e v e n t . E q . (3) c a n _ b e ^ h o w n t o h o l d f o r i n 

s t r u m e n t s w i t h s m a l l d e a d t i m e l o s s e s / 4 0 _ / . S o m e t i m e s , h o w e v e r , 

c o r r e c t i o n t e r m s m u s t b e a d d e d w h i c h c o n t a i n h i g h e r m o m e n t s o f 

P ( V p ) . W h e t h e r t h e a c c u r a c y o f t h e s e d a t a i s s u f f i c i e n t f o r 

p r a c t i c a l p u r p o s e s h a s n e v e r b e e n i n v e s t i g a t e d . 

I n t h e f o l l o w i n g t h e d e p e n d e n c e o f t h e m e t h o d o n t h e n u c l e a r 

c o n s t a n t s a s d e f i n e d i n eq. (3) is d i s c u s s e d u n d e r t h e a s s u m p 

t i o n t h a t I i n e q . (3) i s d e t e r m i n e d b y c a l i b r a t i o n w i t h o n e o r 

m o r e s t a n d a r d s . = m i / m d e n o t e s t h e a b u n d a n c e o f i s o t o p e i 

r e l a t i v e t o t h e s u m o f a l l spontaneously fission in g i s o t o p e s , -i.e. 

t = 1, a n d m = £ m ^ i s t h e t o t a l m a s s o f spontaneously fission in g 

m a t e r i a l . I t i s s h o w n t h a t t h e d a t a d e p e n d e n c e d i f f e r s w i d e l y 

a s d i f f e r e n t p r o c e d u r e s a r e f o l l o w e d . 

(1) T h e s i m p l e s t c a s e i s t h e o n e i n w h i c h s a m p l e s a n d s t a n d a r d s 

h a v e t h e s a m e c o m p o s i t i o n , a n d t h e c o i n c i d e n c e r a t e С is 

p r o p o r t i o n a l t o m, i . e . I i s i n d e p e n d e n t o f b o t h m a s s a n d 

c o m p o s i t i o n o f t h e s a m p l e . T h i s m a y , e . g . , b e t h e c a s e 

f o r f u e l r o d s f a b r i c a t e d f r o m o n e b a t c h o f m a t e r i a l . E v i 

d e n t l y n o n u c l e a r d a t a a r e n e e d e d a t a l l . 

(2) I n g e n e r a l , h o w e v e r , t h e c o m p o s i t i o n o f t h e s t a n d a r d s d i f f e r s 

f r o m t h a t o f t h e u n k n o w n s a m p l e s , a n d t h e v a l u e o f I m u s t b e 

a s s u m e d t o b e a f u n c t i o n o f b o t h q u a n t i t y a n d c o m p o s i t i o n 

o f t h e s p o n t a n e o u s l y f i s s i o n i n g f r a c t i o n . A s o l u t i o n o f 

t h e p r o b l e m (at l e a s t t h e o r e t i c a l l y ) i s a s u f f i c i e n t l y l a r g e 

s e t o f s t a n d a r d s t h a t a l l o w s t o d e t e r m i n e t h e t e r m s yikj_I 

o r c o m b i n a t i o n s t h e r e o f w h i c h e n t e r i n t o e q . (3). N o n u 

c l e a r d a t a a r e r e q u i r e d ; i f a v a i l a b l e , h o w e v e r , t h e y p r o v i d e 

a v a l u a b l e c o n s i s t e n c y c h e c k o f t h e e x p e r i m e n t a l r e s u l t s . 

(3) I n a l l p r a c t i c a l c a s e s f e w s t a n d a r d s a r e a v a i l a b l e , a n d n u 

c l e a r d a t a a r e n e e d e d f o r i n t e r p o l a t i o n a n d e x t r a p o l a t i o n . 

G e n e r a l l y s p e a k i n g t h e d a t a m u s t b e t h e m o r e a c c u r a t e t h e 

s m a l l e r t h e n u m b e r o f s t a n d a r d s a n d t h e m o r e t h e i r m a s s a n d 

c o m p o s i t i o n d i f f e r f r o m t h o s e o f t h e s a m p l e s . 

A s s o m a n y p a r a m e t e r s c a n v a r y , l e t u s c o n s i d e r t h e e x a m p l e 

o f o n e " g o o d s t a n d a r d " , i . e . m a k e t h e r e s t r i c t i o n t h a t i t is 

s o s i m i l a r t o t h e u n k n o w n s a m p l e i n b o t h c o m p o s i t i o n a n d 

m a s s t h a t I d o e s n o t d i f f e r . T h e n t h e m a s s m o f t h e s p o n 

t a n e o u s l y f i s s i o n i n g p l u t o n i u m i n t h e u n k n o w n s a m p l e is 

r e l a t e d t o t h e m a s s m s i n t h e s t a n d a r d a n d t h e c o r r e s p o n d i n g 

c o u n t r a t e s С a n d C g v i a t h e r e l a t i o n 

m = m g C / C s {1 + у( k e - k o ) / ( u e k s + U o k o ) } 

a n d i t s r e l a t i v e e r r o r i s g i v e n b y 

T ■ a - A w , , I2 » “ > 

w h e r e у = ys ( s t a n d a r d ) - U e ( s a m p l e ) i s a m e a s u r e o f t h e d i f 

f e r e n c e i n c o m p o s i t i o n o f t h e s a m p l e a n d t h e s t a n d a r d . T h e 

y. r e f e r t o t h e u n k n o w n s a m p l e . U n c e r t a i n t i e s i n t h e k ^ h a v e 

o b v i o u s l y n o e f f e c t w h e n y = o , i . e . s t a n d a r d a n d s a m p l e h a v e 

t h e s a m e c o m p o s i t i o n . U s i n g n u c l e a r d a t a a s l i s t e d i n 

T a b l e V I , a s s u m i n g a c o m p o s i t i o n o f 1 % 2 3 8 P u , 7 5 % 2 3 9P u

IA E A -S M -1 70/7 8 209 

TA B L E VI. RELEVANT DATA FOR ASSAY OF PLUTONIUM BY 

COINCIDENCE COUNTING OF NEUTRONS FRO M SPONTANEOUS 

FISSION 

Isotope V (V -1) / 

V 

P P P 

P T l/2' y ears 

238 Pu 0.8 (after /~41 7) 2.21 ± 0.07/"~42 7 5.0 ± 0 . 6 х 10 1 0 /~4 з7 

240 Pu 0.807 ± 0.008/- 44_7 2.150 ± 0.008/- 42 7 1.32 ± 0.05x10* V"4^ 7 

242 Pu 0.8 (after /~41 _/) 2.141 ± 0.009/_ 42_? 7.00 ± 0.10xl01C^ _52_7 

a n d 2 4 % 21f °Pu, a n d t a k i n g y = 0 . 5 U e ( i . e . a s t a n d a r d w i t h 

t w i c e a s m u c h 2 3 8 P u ) , e q . (4) t r a n s f o r m s i n t o 

— = { ( 0 . 0 3 5 ^ ) 2 + ( 0 . 0 5 7 ^ - ) 2 + ( 0 . 0 5 7 

1П У K'8 * 0 

T h i s m e a n s t h a t a n e r r o r o f 1 % i n t h e d e t e r m i n a t i o n o f t h e 

23 8 P u p e r c e n t a g e ( w h i c h i s r e a l i s t i c ) c o n t r i b u t e s n e g l i 

g i b l y ( 0 . 0 4 %) t o t h e t o t a l e r r o r A m / m , w h e r e a s 1 0 % e r r o r 

i n e a c h o f t h e Дк/к ( w h i c h i s a n a r b i t r a r y b u t n o t t o o f a r 

f e t c h e d a s s u m p t i o n ) w o u l d r e s u l t i n a m a s s e r r o r A m / m o f 

0.8 %. 

(4) I n s o m e c a s e s i t c a n e v e n b e a d v a n t a g e o u s t o u s e w e l l - c a l i 

b r a t e d s t a n d a r d s o u r c e s o f a d i f f e r e n t i s o t o p e , e . g . 2 5 2 C f . 

T h e n t h e c o n s t a n t s k ^ e n t e r d i r e c t l y i n t o t h e c a l c u l a t i o n s . 

T h e i r a c c u r a c y i s f a r f r o m s u f f i c i e n t f o r t h i s p u r p o s e . 

I t m a y b e c o n c l u d e d t h a t t h e n u c l e a r d a t a n e e d e d f o r s o m e 

v a r i a n t s o f c o i n c i d e n c e t e c h n i q u e s a r e n o t s u f f i c i e n t l y a c c u r a t e . 

I t s h o u l d b e k e p t i n m i n d , h o w e v e r , t h a t p r o p e r p r e p a r a t i o n o f 

s t a n d a r d s u s u a l l y s o l v e s t h e p r o b l e m t o a n a c c u r a c y w h e r e ô t h e r 

e f f e c t s i n c l u d i n g p l a i n s t a t i s t i c s l i m i t t h e t o t a l a c c u r a c y t h a t 

c a n b e a c h i e v e d . 

9. P A S S I V E G A M M A A S S A Y 

F o r t h e p a s s i v e a s s a y o f u r a n i u m b y g a m m a s p e c t r o s c o p y n o 

i n c r e a s e i n a c c u r a c y c a n b e e x p e c t e d f r o m i m p r o v e d n u c l e a r d a t a 

b e c a u s e s e l f - a b s o r p t i o n o f t h e 1 8 5 k e V y r a y o f 2 3 5U i s t h e 

l i m i t i n g f a c t o r a n d t h e u s e o f s t a n d a r d s a m p l e s i s m a n d a t o r y . 

W h e r e c o r r e c t i o n s h a v e t o b e a p p l i e d , t h e n e c e s s a r y d a t a 

( m a i n l y y - r a y i n t e r a c t i o n c r o s s s e c t i o n s ) a r e u s u a l l y a c c u r a t e 

t o 3 % o r b e t t e r 46_J . T h e s a m e a p p l i e s t o t h e p a s s i v e 

Y m e a s u r e m e n t o f p l u t o n i u m . T h e s i t u a t i o n i s s o m e w h a t d i f f e r e n t 

i f p l u t o n i u m i s o t o p e r a t i o s a r e t o b e d e t e r m i n e d . B e c a u s e 

d i f f e r e n t i s o t o p e s e m i t y r a y s w i t h v e r y s i m i l a r e n e r g i e s , s o m e 

i s o t o p e r a t i o s c a n b e d e t e r m i n e d q u i c k l y a n d n o n d e s t r u c t i v e l y , 

a l t h o u g h n o t q u i t e a s p r e c i s e l y a s b y m a s s o r a s p e c t r o m e t r y . 

I n o r d e r t o d o s o r e l a t i v e y i n t e n s i t i e s a r e n e e d e d . M e a s u r e 

m e n t s f r o m d i f f e r e n t a u t h o r s d o , h o w e v e r , n o t a g r e e v e r y w e l l .

TABLE VII. COMPARISON OF INTENSITIES OF PROMINENT y RAYS FROM VARIOUS 

PLUTONIUM ISOTOPES AND 241Am AS MEASURED B Y TWO AUTHORS 

Isotope Energy3 

keV 

Absolute 

L 47_/ 

Intensity*3 

L ieJ 

% Error 

/ 48_/c 

Isotope 

r, a 

Energy 

keV 

Absolute 

L M j 

Intensity13 

L 48_/ 

%Error 

/ 48_/ 0 

238Pu 43.5 3.80-4 3.92-4 1 

240 

Pu 160.3 1.04-5 4.20-6 1 

99.8 6.00-5 7.40-5 1 (cont'd) 642.5 4.10-7 1.45-7 3 

152.6 1.23-5 1.01-5 1 688.0 8.10-8 3.70-8 4 

766.4 

786.0 

2.80-7 

7.20-8 

2.40-7 

3.53-8 

1 

1 

241 

Pu 77.0 

103.5 

1.00-6 

1.01-6 

2.41-7 

1.04-6 

3 

1 

239PU 51.6 1.35-4 2.08-4 1 148.6 2.07-6 , 1.90-6 1 

129.3 5.60-5 6.20-5 1 160.0 7.45-8 6.45-8 2 

203.6 

375.0 

413.7 

4.80-6 

1.50-5 

1.50-5 

5.60-6 

1.58-5 

1.51-5 

1 

1 

241a Am 59.5 

125.3 

208.0 

3.53-1 

2.65-5 

7.06-6 

3.59-1 

3.95-5 

7.60-6 

1 

3 

2 

240PU 45.3 4.50-4 4.50-4 1 335.4 4.83-6 4.70-6 2 

104.2 1.00-4 7.00-5 1 722.0 1.90-6 1.85-6 1 

aEnergies taken from Ref. 47_/; as absolute values are relatively unimportant for the pur- 

pose, no comparison of energies was attempted. 

Intensities in photons per_disintegration. The notation 3.80-4 means 3.80x10 

CFor the figures of Ref. /_ 47_/ intensity errors are not quoted explicitly. An upper limit of 

10 % is estimated even for weak lines at low energies where self-absorption is maximum.

IA E A -S M -1 70/7 8 211 

T a b l e V I I s h o w s a s e x a m p l e s i n t e n s i t i e s o f t h e m o s t p r o m i n e n t - 

Y l i n e s w h i c h o c c a s i o n a l l y d i f f e r b y a f a c t o r o f 2 a l t h o u g h t h e 

e r r o r s q u o t e d f o r e a c h o f t h e m e a s u r e m e n t s a r e b e l o w 1 0 %. 

A n i m p r o v e m e n t o f t h e s e d a t a i s d e s i r a b l e . 

10. I S O T O P E C O R R E L A T I O N S 

I s o t o p e a n a l y s i s o f s p e n t f u e l i s a k e y p o i n t i n t h e f u e l 

c y c l e b e c a u s e t h e b u r n u p a n d t h e c o n t e n t o f f i s s i l e m a t e r i a l 

c a n b e d e t e r m i n e d m o r e p r e c i s e l y b y e x p e r i m e n t a l t h a n b y c o m 

p u t a t i o n a l m e t h o d s . H o w e v e r , h i g h e x p e n d i t u r e s n e c e s s a r y f o r 

i s o t o p e d i l u t i o n a n a l y s i s a s p r e s e n t l y i n u s e s t i m u l a t e d 

t h e s e a r c h f o r l e s s e x p e n s i v e m e t h o d s w h i c h m a y n o t r e p l a c e , 

b u t c a n b e u s e d f o r v e r i f i c a t i o n o f t h e r e s u l t s o f i s o t o p e 

d i l u t i o n a n a l y s i s . I s o t o p e c o r r e l a t i o n s f r e q u e n t l y o b s e r v e d i n 

p o s t - i r r a d i a t i o n e x a m i n a t i o n s o f r e a c t o r f u e l o f f e r s u c h a 

p o s s i b i l i t y . 

I s o t o p e c o r r e l a t i o n s w e r e f o u n d b e t w e e n ra tio s o f i s o 

t o p e s a n d t h e concentration o f i s o t o p e s i n t h e f u e l . T h e p r e s e n t 

k n o w l e d g e i s o b t a i n e d f r o m e x p e r i m e n t a l r e s u l t s o f a n a l y s é s 

d u r i n g f u e l r e £ r o c e s s i n g o r f r o m p o s t - i r r a d i a t i o n a n a l y s é s o f 

f u e l p e l l e t s ¡_ 1 4 , 4 9 _ 7 . T h e a d v a n t a g e s o f i s o t o p e c o r r e l a t i o n s 

a r e t h e s i m p l i c i t y a n d h i g h a c c u r a c y o f i s o t o p e r a t i o m e a s u r e m e n t s 

a s c o m p a r e d t o t h e c u m b e r s o m e a n d l e s s p r e c i s e d e t e r m i n a t i o n o f 

i s o t o p i c c o n c e n t r a t i o n s . I s o t o p e c o r r e l a t i o n s c a n b e g r o u p e d i n 

t o t h o s e d e p e n d i n g u p o n h e a v y i s o t o p e r a t i o s a n d t h o s e d e p e n 

d i n g o n t h e r a t i o s o f f i s s i o n p r o d u c t s . 

H e a v y i s o t o p e s a r e m e a s u r e d r o u t i n e l y i n r e p r o c e s s i n g 

i n p u t a n a l y s i s o r p o s t - i r r a d i a t i o n e x a m i n a t i o n s . T h e r e f o r e n o 

a d d i t i o n a l a n a l y t i c a l e f f o r t i s r e q u i r e d f o r t h i s m e t h o d . 

A f e w e x a m p l e s a r e g i v e n . T h e 2 3 5U d e p l e t i o n D 5 d e f i n e d a s t h e 

c h a n g e o f * 3 5U c o n c e n t r a t i o n r e l a t i v e t o i t s i n i t i a l v a l u e c a n 

b e c o r r e l a t e d t o t h e 21,0P u / 2 3 9P u r a t i o (Fig. 1 a ) . T h i s c o r r e 

l a t i o n s e e m s t o b e i n d e p e n d e n t o f t h e i n d i v i d u a l r e a c t o r a n d is 

n o t s e n s i t i v e t o t h e i n i t i a l 2 3 5 U e n r i c h m e n t . O t h e r c o r r e l a t i o n s , 

h o w e v e r , d o d e p e n d u p o n t h e i n i t i a l e n r i c h m e n t . A n e x a m p l e i s 

s h o w n i n F i g . 1 b. 

T h e s e t w o e x a m p l e s i l l u s t r a t e t h e b e n e f i t o f c o r r e l a t i o n 

m e t h o d s a s w e l l a s t h e i r l i m i t s w h i c h æ s u l t f r o m t h e s e n s i 

t i v i t y t o t h e i n i t i a l f u e l c o m p o s i t i o n . T h i s p r o b l e m w i l l b e 

e n h a n c e d i n t h e c a s e o f p l u t o n i u m r e c y c l i n g . F i s s i o n p r o d u c t s 

o f f e r a b e t t e r c h o i c e i n t h i s r e s p e c t . E . g . t h e c o r r e l a t i o n 

b e t w e e n b u r n u p a n d 1 3 2 X e / 1 3 1 X e r a t i o i s i n d e p e n d e n t o f i n i t i a l 

e n r i c h m e n t a n d o f t h e i n d i v i d u a l r e a c t o r (Fig. 1 c ) . T h i s is 

a l s o t h e c a s e f o r t h e c o r r e l a t i o n o f t h e 21*°Pu c o n c e n t r a t i o n w i t h 

t h e 1 ц sN d / 1 14 eN d r a t i o (Fig. 1 d) . T h e r o l e o f n u c l e a r d a t a i n t h i s 

f i e l d i s a s f o l l o w s . 

I n o r d e r t o u n d e r s t a n d t h e r e a c t o r p h y s i c s b e h i n d t h e s e c o r 

r e l a t i o n s b u r n u p c a l c u l a t i o n s a r e r e q u i r e d . P r e d i c t i o n s w i t h 

e x i s t i n g c o d e s h a v e s o f a r n o t g i v e n g o o d a g r e e m e n t w i t h e x 

p e r i m e n t . I t i s n o t c l e a r , h o w e v e r , t o w h a t e x t e n t u n c e r t a i n t i e s 

o f n u c l e a r d a t a c o n t r i b u t e t o t h i s d i s c r e p a n c y . T h e r e f o r e t h e 

a d e q u a c y o f d e t a i l s o f t h e c o m p u t a t i o n s , s u c h a s t h e e n e r g y

2 12 W E IT K A M P e t al. 

2-00E-01 2-80E-01 3-60E-01 ¿-¿OE-01 

2t0Pu/ 239Pu -------- - 

2-80E-00 

2-60E-00 

2Ч0Е-00 

2-2ÛE-00 

2-OOE-OO 

2-80E-00 \ 

V 

v □ 

1-60E-00 

■ 

Ы0Е-00 

■ 

1-20E-00 

\\\\ 

\ V \ \ \ \ 

\ V\ \ 

1-00E-00 

>; % \ 

У \ \ 

1-00E-01 x \ \ (b) 

2-20E-03 

2-00E-03 

1-80E-03 

1-60E-03 

i к о е -оз 

1-20E-03 

1-00E-03 

8-Ü0E-04 

6-00E-0A 

4-00E-03 Ц-20Е-02 \ 2-00E*02| 2-80E-02) 3-60E-02 

8-00E-03 1-6ÛE'02 2-40E-02 3-20E-02 

4-00E-CW. (d) 

8-00E-01 8-40E-01 8-80E-01 9-20E-01 9-60E-01 

8-20E-01 8-60E-01 9-OOE-Ol 9Ч0Е-01 

U6Nd/ usNd ------ ► 

FIG. 1. C o rre la tio n betw een (a) 235U de p letio n D 5 and 240P u / 239Pu ratio; (b) b u in -u p F j (fissions per 

100 h e a v y n u c le i in it ia lly present) and 235U / 238U ratio; (c) F-j.and i32X e / 131X e ratio; (d) 240Pu content 

and I46N d / 145N d ratio. D iffe re n t sym bols refer to d iffe re n t lig h t-w a te r reactors w ith six d iffe re n t in it ia l 

e nrichm ents. 

g r o u p s t r u c t u r e , s h o u l d b e c h e c k e d m o r e c a r e f u l l y , a n d t h e d e 

p e n d e n c e o f t h e r e s u l t s u p o n n u c l e a r d a t a s h o u l d b e i n v e s t i g a t e d . 

O n l y t h e n c a n t h e r e q u i r e m e n t f o r i m p r o v e d o r a d d i t i o n a l n u c l e a r 

d a t a b e a s s e s s e d . 

11. C O N C L U S I O N 

A l t h o u g h m o s t m e t h o d s o f n u c l e a r m a t e r i a l a s s a y f o r s a f e 

g u a r d s a r e b a s e d u p o n s o m e f o r m o f n u c l e a r d a t a , t h e r e a r e f e w 

e x a m p l e s w h e r e a b e t t e r o r m o r e p r e c i s e v a l u e o f a g i v e n q u a n 

t i t y w o u l d r e s u l t i n a n i m m e d i a t e a n d d r a s t i c i m p r o v e m e n t o f 

t h e p e r f o r m a n c e o f a m e a s u r e m e n t t e c h n i q u e f o r t h e f o l l o w i n g 

r e a s o n s :

IAEA-SM “ 17 0 /7 8 213 

(1) E v e n t h e m o s t a c c u r a t e n u c l e a r d a t a w i l l n o t m e e t t h e 

a c c u r a c y o f c l a s s i c a l ( i . e . , c h e m i c a l ) a n a l y t i c a l 

m e t h o d s s o c a l i b r a t i o n i s a n d w i l l p r i m a r i l y b e d o n e b y 

u s e o f £tandarás. 

(2) N u c l e a r S a f e g u a r d s b e i n g a r e l a t i v e l y y o u n g f i e l d f e w 

m e t h o d s h a v e b e c o m e r o u t i n e , a n d s e c o n d - o r d e r e f f e c t s t h a t 

c a n b e d e a l t w i t h b y i m p r o v e d n u c l e a r d a t a c o m p e t e w i t h m u c h 

l a r g e r uncertain ties from other e ffe c t s a s , f o r e x a m p l e , i n s u f 

f i c i e n t k n o w l e d g e o f m a t r i x m a t e r i a l i n t h e s a m p l e . 

(3) U n l i k e n u c l e a r d a t a f o r r e a c t o r s , n u c l e a r d a t a f o r s a f e 

g u a r d s a r e n o t d i r e c t l y a m e n a b l e t o c o s t - b e n e f i t c a l c u 

l a t i o n s b e c a u s e t h e v i r t u e o f a d e c r e a s e i n t h e a m o u n t o f 

m a t e r i a l u n a c c o u n t e d f o r , o r M U F , i s hard to quantify. 

(4) M o s t o f t h e r e s e a r c h w o r k d o n e s o f a r h a s b e e n c o n c e n t r a t e d 

o n t h e d e v e l o p m e n t o f instruments, n o t o f s y s te m s t h a t s p e 

c i f y t h e u s a g e o f t h o s e i n s t r u m e n t s f o r p a r t i c u l a r a p p l i c a 

t i o n s a n d h e l p d e t e r m i n e p r o b l e m a r e a s i n w h i c h n u c l e a r 

d a t a a r e m o s t u r g e n t l y n e e d e d . 

T h e r e f o r e s t u d i e s o f t h i s k i n d a r e a p r e r e q u i s i t e f o r t h e 

e f f i c i e n t i m p r o v e m e n t o f e x i s t i n g n u c l e a r d a t a f o r s a f e g u a r d s , 

a n d m o r e t h o r o u g h i n v e s t i g a t i o n s o f t h e q u a n t i t a t i v e r o l e o f 

n u c l e a r d a t a i n e v e r y i n d i v i d u a l m e t h o d d e s e r v e a l l p o s s i b l e s u p p o r t . 


¿~ 1 _ J B Y E R , T . A . , I N D C ( N D S ) - 4 4 / G ( 1 9 7 2 ) . 

£ ~ 2 j M E T Z G E R , F . R . , i n O . R . F r i s c h e d . , P r o g r e s s i n N u c l e a r 

P h y s i c s 7 (1959) 54. 

/ ~ 3 _ 7 W E I T K A M P , C . , K F K 1 7 4 5 ( 1 9 7 3 ) . 

¿ - 4 _ 7 H E L M E R , R . G . , G R E E N W O O D , R . C . , G E H R K E , R . J . , N u c l . 

I n s t r . a n d M e t h . 9 6 (1971) 173. 

/ “5 _ 7 M E T Z G E R , F . R . , P h y s . R e v . L e t t e r s 18 (1967) 4 3 4 . 

/ - 6 _ 7 R I C K E Y , F . A . , J U R N E Y , E . T . , B R I T T , H . C . , P h y s . R e v . С 5 

(1972) 2 0 7 2 . 

/ ~ 7 _ 7 M I C H A E L I S , W . , A t o m k e r n e n e r g i e 14 (1969) 3 4 7 . 

¿ b _ 7 C H R I E N , R . E . , e t a l . , B N L 1 5 6 9 8 ( 1 9 7 0 ) . 

/ “9 _ 7 K A N E , W . R . , P h y s . R e v . L e t t e r s 2 5 (1970) 953. 

l_ 1 0 _ 7 M A T U S S E K , P . , e t a l . , Safeguards Techniques , V o l . II, I A E A , 

V i e n n a 1 9 7 0 , p. 113. 

1 1 _ 7 M A T U S S E K , P . , e t a l . , Contributions to the Conference on 

Nuclear Structure Study with Neutrons, B u d a p e s t , J u l y 31 - 

A u g u s t 5, 1 9 7 2 , p. 84. 

j_ 12 J G R O S H E V , L . V . , e t a l . , N u c l e a r D a t a A 5 (1969) 2 4 3 .


L i3_7 

Z _ 1 4 _ 7 

¿ " « _ 7 

L i6 _ 7 

Z ~ 17_7 

/ " 18_7 

Z~ 1 9 _ 7 

L 2 o_7 

Z " 2 i _ 7 

Z " 2 2 _ 7 

Z " 2 3 _ 7 

Z“24_7 

L 25_7 

Z" 2 6 _ 7 

Z~ 2 7 _ 7 

Z ~ 2 8 _ 7 

Z~2 9_7 

L 30_7 

Z“31_7 

Z ~32_7 

Z ~ 3 3 _ 7 

Z“34_7 

Z “35_7 

B O R K , G . , e d . , K F K 1 4 2 9 ( 1 9 7 1 ) . 

B O R K , G . , e d . , K F K 1 6 1 8 ( 1 9 7 2 ) . 

B A R T H O L O M E W , G . A . , e t a l . , N u c l e a r D a t a A 3 (1969) 3 6 7 . 

H O F F M A N N , D . C . , e t a l . , J. I n o r g . N u c l . C h e m . 5 (1957) 

6 . 

S M I T H , W . H . , R O G E R S , D . R . , S I L V E R , G . L . , M o u n d L a b o r a 

t o r i e s R e p o r t M L M - 1 6 9 1 ( 1 9 6 9 ) . 

W E I T K A M P , C . , e t a l .,K F K 1 2 9 9 ( 1 9 7 1 ) . 

W A P S T R A , A . H . , G O V E , N . B . , N u c l e a r D a t a A 9 (1971) 

2 6 5 . 

G R E N N B E R G , B . , R Y T Z , A . , M e t r o l o g í a 7 (1971) 65. 

B A R A N O V , S . A . , e t a l . , Y a d e r n . F i z . 7 (1968) 7 2 7 ; 

S o v j e t J o u r n a l o f N u c l e a r P h y s i c s 7 (1968) 4 4 2 . 

D O K U C H A E V , Y a . P . , A t o m n a j a E n e r g i j a 6 (1959) 74; 

J. N u c l e a r E n e r g y 11 A (1960) 195. 

M A R K I N , T . L . , J. I n o r g . N u c l . C h e m . 9 (1959) 3 2 0 . 

O E T T I N G , F . L . , Thermodynamics o f Nuclear Materials , I A E A , 

V i e n n a 1 9 7 0 , p. 55. 

L E A N G , C . F . , C o m p t e s R e n d u s A c a d . S e i . 2 5 5 ( 1 9 6 2 ) 3 1 5 5 . 

C A B E L L , M . J . , Chemical Nuclear Data, Measurements and Application 

s, P r o c e e d i n g s o f t h e I n t e r n a t i o n a l C o n f e r e n c e , 

20-22 S e p t e m b e r 1 9 7 1 , C a n t e r b u r y . 

C A B E L L , M . J . , W I L K I N S , M . , J. I n o r g . N u c l . C h e m . 33 

(1971) 9 0 3 . 

O E T T I N G , F . L . , P h y s . R e v . 1 6 8 (1968) 1 3 9 8 . 

S T O N E , R . E . , H U L E T , E . K . , J. I n o r g . N u c l . C h e m . 3 0 

(1968) 2 0 0 3 . 

O E T T I N G , F . L . , G U N N , S . R . , J. I n o r g . N u c l . C h e m . 29 

(1967) 2 6 5 9 . 

A U G U S T S O N , R . H . , e t a l . , Safeguards Techniques, V o l . II, 

I A E A , V i e n n a 1 9 7 0 , p. 53. 

H A W A , A . H . , T h e s i s , K a r l s r u h e , i n p r e p a r a t i o n . 

J A C Q U E S S O N , J . , J. P h y s . 24, S u p p l . t o N o . 6 (1963) 

1 1 2 A. 

K E E P I N , G . R . , e d . , L A - 3 9 7 4 - M S (1968) 14. 

O M O H U N D R O , R . J . , N R L - M e m o r a n d u m R e p o r t 2 0 0 5 ( 1 9 6 9 ) .

IA E A -S M -1 70/78 

l_ 36 / G O Z A N I , T . , C O S T E L L O , D . G ., T r a n s a c t i o n s o f t h e A m e r i e a n 

— N u c l e a r S o c i e t y 13 (1970) 7 4 6 . 

¿ ~ 3 7 _ 7 F O L E Y , J . E . , T H O R P E , M . M . , L A - 4 7 0 5 - M S (1971) 9. 

¡_ 3 8 _ 7 B I R K H O F F , G . , e t a l . , Safeguards Techniques, V o l . I I , 

I A E A , V i e n n a , 1 9 7 0 , p. 4 7 7 . 

/“3 9 _ 7 S T R A I N , C . V . , N R L - M e m o r a n d u m R e p o r t 2 1 2 7 ( 1 9 7 0 ) . 

/ ~ 4 0 _ 7 B Ö H N E L , K . , T r a n s a c t i o n s o f t h e A m e r i c a n N u c l e a r 

S o c i e t y 1 5 (1972) 6 7 1 . 

j_ 41J K E E P I N , G . R Physics o f Nuclear K in etics, A d d i s o n - 

— W e s l e y , R e a d i n g , 1 9 6 5 , p. 60. 

/ “4 2 _ 7 M A Ñ E R O , F . , K O N S H I N , V . A . , I N D C ( N D S ) - 3 4 / G ( 1 9 7 2 ) . 

¿~ 4 3 _ 7 E L L I S , Y . A . , N u c l e a r D a t a В 4 (1970) 6 3 5 . 

/ ~ 4 4 _ 7 D I V E N , B.C., e t a l . , P h y s . R e v . 1 0 1 (1956) 1 0 1 2 . 

/ ~ 4 5 _ 7 S C H M O R A K , M . R . , N u c l e a r D a t a B 4 (1970) 6 6 1 . 

¿ ~ 4 6 _ 7 S T O R M , E . , I S R A E L , H . I . , N u c l e a r D a t a A 7 (1970) 5 6 5 . 

/ “4 7 _ 7 C L I N E , J . E . , e t a l ., A N C R - 1 0 6 9 ( 1 9 7 2 ) . 

/ “4 8 _ 7 G U N N I N K , R . , M O R R O W , R . J . , U C R L - 5 1 0 8 7 ( 1 9 7 1 ) . 

£ ~ 4 9 _ 7 K O C H , L. , e t al. , A nalytical Methods in the Nuclear Fuel 

~ Cycle, I A E A , V i e n n a 1 9 7 2 , p. 523. 

!_ 5 0 _ / O E T T I N G , F . L . , Plutonium 1970 and oth er A ctin id es, P r o c e e - 

— d i n g s o f t h e 4 t h I n t e r n a t i o n a l C o n f e r e n c e , S a n t a F e , 

N e w M e x i c o , O c t o b e r 5 - 9 , 1 9 7 0 , P a r t I, p. 154; 

N u c l e a r M e t a l l u r g y 17 (1970) 154. 

/ ~ 5 1 _ 7 B E M I S , C . E . , J r . , H A L P E R I N , J . , E B Y , R., 0 R N L - 4 3 0 6 

(1968) 31; J. I n o r g . N u c l . C h e m . 31 (1969) 599. 

52J E L L I S , Y . A . , N u c l e a r D a t a В 4 (1970) 6 8 6 . 


B. GRINBERG: In the ora l presentation you showed two tables, the 

first drawing attention to the d ifferen ces in the values which have been 

determ ined for the h a lf-liv e s of am ericiu m -241 and plutonium and the 

second giving the recom m ended values ("b est valu es") for these h a lf-liv e s. 

I would like to ask the follow in g questions in this connection: 

— By what method was the list of recom m ended values drawn up? 

— D o you think that a thorough evaluation o f these h a lf-liv es should 

be undertaken, coverin g in particular the m atter of a ccu ra cie s? 

— Do you fe e l that in som e ca ses new, high-quality determ inations 

would be d esira ble? 

215

216 W E IT K A M P e t a l. 

C. W EITKAM P: The p roced u res used in com pilin g the tables of r e 

com m ended values varied accord in g to the m ethod used fo r obtaining the 

data, the num ber and nature of co rre ctio n s introduced, and the details 

given in the original papers. In the m ost ca ses the h a lf-liv es and the 

sp e cific decay heats w ere rep laced by the m ost recen t values; for 239Pu 

and 240Pu a sim ultaneous analysis was ca rried out, but sin ce in the case 

of 240Pu the e r r o r s w ere greater than those given in two e a rlie r publications, 

the m ean of the latter was selected . 

As regard s im provem ent of the situation as a whole, I would,in fact, 

recom m en d that som e new experim ental determ inations be undertaken and 

that a thorough analysis of the e r r o r s be made beforehand, s o that all the 

p roblem s can be taken into account when the experim ents are designed.

IA E A -SM -П О /5 4 

THE ROLE OF NUCLEAR DATA IN 

THE PRACTICAL APPLICATION OF 

NON-DESTRUCTIVE NUCLEAR ASSAY METHODS* 

M .M . THORPE 

University o f California, 

Los Alamos Scientific Laboratory, 

Los Alam os, N. Mex. , 

United States o f America 

Abstract 

T H E R O LE O F N U C L E A R D A T A IN T H E P R A C T I C A L A P P L IC A T IO N O F N O N - D E S T R U C T IV E N U C L E A R 

A S S A Y M E T H O D S . 

Uses o f n u cle a r data in the d e ve lo p m e n t o f p r a c t ic a l n u cle a r assay techn iqu es f a ll n a tu ra lly in to 

three categories. First, there are param eters w h ic h ca n enter d ire c tly in to the c a lib ra tio n o f equip m ent, 

such as d e ca y rates, g a m m a in te n sitie s and atten uation co e ffic ie n ts , neutron y ield s, etc. T h e second 

categ o ry in v o lv e s the use o f n u cle a r data in the p re d ic tiv e sense as in p u t to neutron and g a m m a -ra y 

transport codes w h ic h p rovid e c a lc u la t io n a l support and g u id an ce to the safeguards research and d evelopm ent 

program . T h is support is necessary for the d e ta ile d understanding o f techniques under in v estig a tio n as 

w e ll as for design o p tim iz a tio n o f systems a lre a d y proven to be w orthy o f d evelopm ent to the prototype 

stage. T h e th ird categ o ry u t iliz e s n u cle a r data as a reservoir o f b a sic in fo rm a tio n to a id in the search 

for new m ethods and signatures. 

T o illu s tra te these three categories o f use o f n u cle a r data, the d e v e lo p m e n t o f several systems 

from in it ia l research through prototyp e constru ction, c a lib ra tio n and fin a l fie ld testing is o u tlin ed . 

T y p ic a l o f the systems described are: d e la y ed and prom pt neutron m ethods a p p lie d to scrap and s m a ll 

sa m p le assay; the a p p lic a tio n o f ra d io a c tiv e sources to the m easurem ent o f the fis s ile co n te n t o f reactor 

fu e l pins; c o in c id e n c e co u n tin g o f fission events, e ith e r spontaneous or induced; gam m a m ethods a p p lie d 

to m easurem ent o f e n rich m en t, m in or isotope co m p o sitio n , and fis s ile content o f feed, product, scrap 

and w aste. A n e x p e rim e n ta l program to e v a lu a te the use o f jj-m eson captu re X -ra y s is described as an 

e x a m p le o f the ro le o f ba sic data in e x p lo rin g p ro m isin g e le m e n ta l and is o to p ic signatures. 

Future ch a lle n g e s for no n -d e stru ctive assay are: to m eet the assay req uirem en ts o f new c h e m ic a l 

and p h y s ic a l form s o f nu cle a r fuels, to red uce the costs w h ile m a in ta in in g or in cre a sin g the a ccu ra cy 

and p re cisio n o f the m ethods, and to establish the ra p id ly advancin g no n -d e stru ctive assay m ethods as an 

in depen dent a lte rn a tiv e to tra d itio n a l c h e m ic a l analysis. T y p ic a l ca teg o rie s and a ccu ra cies o f nu cle a r 

data needed to m eet these m ajor ch a lle n g e s are described. 

INTRODUCTION 

Practical nuclear nondestructive assay methods for fissionable material 

gaining acceptance today are based mainly on two fundamental signatures. 

First, the naturally occurring radioactivity characteristic of the nuclides 

of interest and second, the ability of these same nuclides to be fissioned 

either by neutrons or gamma rays. With some important exceptions, the basic 

nuclear data relating to these properties has been available for a number of 

years. Why then are nuclear data important? The answer lies in the diversity 

of purpose of the assay methods. The hundred-thousand-dollar machine 

designed to provide precise assay of several million dollars worth of fuel 

pins is hardly comparable to the device used for the occasional measurement 

of a dozen or so waste barrels. Because of this diversity of purpose an 

array of instrumentation is being developed, each m aking use of the basic 

signatures in a different way to satisfy a different set of conditions. 

* W ork perform ed under the auspices o f the U . S. A t o m ic Energy C om m ission 

217

218 THORPE 

Uses of nuclear data in the development of practical nuclear assay 

techniques fall naturally into three categories. First, there are parameters 

which can enter directly into the calibration of equipment, such as 

decay rates, gamma intensities and attenuation coefficients, neutron yields, 

etc. The second category involves the use of nuclear data in the predictive 

sense as input to neutron and gamma-ray transport codes which provide calcu- 

lational support and guidance to the safeguards research and development 

program. This support is necessary for the detailed understanding of techniques 

under investigation as well as for design optimization of systems already 

proven to be worthy of development to the prototype stage. The third 

category utilizes nuclear data as a reservoir of basic information to aid in 

the search for new methods and signatures. 

FUEL PIN ASSAY 

A number of fuel pin assay systems either complete or under development 

serve as an illustration of some of these uses of nuclear data. These systems 

are for the measurement of: 

1. Uranium-235 content of LWR fuel. 

2. Uranium-235 content of LWR fuel and the detection of out of 

specification fuel pellets. 

3. Plutonium content and isotopic composition of fast breeder 

reactor (FBR) fuel. 

4. Plutonium recycle LWR fuel. 

5. Fissile content of irradiated fuel. 

6. Uranium-235 content of LWR fuel which also contains burnable 

poison. 

Three properties of the system for measuring LWR pins are most 

important : 

1. High throughput rate to take care of a modern plant capacity of 

several hundred pins per shift. 

2. Sensitivity to all of the fissile material within the pins. 

3. Reliability. 

These three criteria lead to the choice of thermal neutron interrogation; 

the thermal flux supplied by a moderated 252Cf source, and the detection of 

prompt fission neutrons from the thermal fission of 23 5U furnishing the primary 

signature and differentiation from 238U, the major constituent of LWR 

f u e l . 

The moderator for the neutron source must provide sufficient thermal 

flux at the fuel channel while providing maximum discrimination between 2 3 5U 

and 23 8U as well as minimizing the source strength and biological shielding 

required. The configuration of source, moderator materials and detectors 

was optimized by modeling the system on the computer using only enough actual 

experimentation to assure confidence in the computer calculations [1]. The 

method of optimizing a design by computer calculations illustrates one of the 

more important uses of nuclear data as input to computer codes which provide 

the calculational tool necessary to design practical nondestructive assay 

ins trumentat i o n .

IAEA-SM-170/54 

The assay of a fuel pin requires a mathematical calibration function 

which describes as accurately as possible the response for various enrichments 

and yet is simple enough to permit on-line data reduction. Analysis [2] 

indicates that the response of a fuel rod having an enrichment less than 4% 

23 5U is adequately described by a function of the form 

R = A(1 - e“BU) 

R is the measured response, U is the 23 5U content of the fuel rod, and A 

and В are parameters determined from measurements of standard fuel pins. 

In addition to the 235U content, the response of an actual fuel pin 

depends on a number of factors: cladding thickness and composition, fuel 

section length, density, diameter, impurity content, etc. It is important 

to investigate the sensitivity of the assay system to changes in these various 

parameters. Here again, the computer and nuclear data are used to obtain 

the information. These calculations and other considerations provide 

the basis for a systematic error analysis [3]. The precision of a single 

fuel rod assay is dominated by propagated counting statistics amounting to 

~1.1 to 1.5% (1er) over the mass range of 30 to 120 g of 2 3 5U per rod. After 

100 fuel rod assays, the statistical uncertainty in the total mass decreases 

to less than 0.15%. At this point the error becomes dominated by factors 

other than counting statistics (e.g., the error in the calibration curve). 

In-plant experience has proven the practicality of measuring the entire 

2 3 5U throughput of a modern p l a n t . The system can be operated by plant personnel 

with little technical training at a rate of 400- to 600-rod assays 

per eight-hour shift. This rate includes the time taken for pin identification, 

handling, and the assay of several standard rods to provide a calibration 

check. A m ore detailed description of the construction and operation 

of the units may be obtained from a paper by R. A. Forster, et al. [4]. 

A series of Monte Carlo calculations and measurements [5] led to the 

following modifications of the thermal neutron 252Cf fuel rod system to include 

measurements of pellet-to-pellet variations: 1) lengthening the m o d 

erator assembly in the direction of fuel rod travel, which results in a 

longer region of high thermal flux; 2) positioning the fuel rod channel 

closer to the 252Cf source to take advantage of the higher intensity flux 

near the source while still preserving a high fissile/fertile fission ratio 

(-IO1*) to ensure- accurate measurement of fissile content in the presence of 

much larger amounts of fertile material; 3) replacing the D 2O in the m oderator 

assembly w ith deuterated water-extended-polyester resin and carbon to 

decrease cost while simplifying the fabrication and shipping; 4) changing 

the fuel channel position requires that the ‘He detectors be shortened and 

displaced to one end of the carbon moderator to give a sufficiently large 

signal/2S2Cf background ratio in the цНе detectors; and 5) the addition of 

a small (2 by 2 by 3/4 in.) Nal detector near the exit port of each fuel-rod 

channel to give pellet-to-pellet fissile content by counting fission-induced 

gamma rays. Figure 1 is a schematic diagram of the Pin and Pellet Assay 

System (PAPAS). Figure 2 illustrates the system capability for the detection 

of off-specification pellets. 

A complete assay and quality control station for FBR fuel rods has been 

delivered to Westinghouse-Hanford Engineering Development Laboratory (HEDL). 

These rods contain m ixed oxide fuel with a 2 P u / 238U ratio of ~l/4, and a 

total 239Pu mass of ~30 g. The instrumentation has been calibrated and is 

now in routine operation. The station consists of two units. One unit [6] 

contains a 252Cf (619 yg) source tailored to provide fast neutron irradiation 

of the pins. The delayed gamma rays from fission (Ey > 1.2 MeV) are detected 

as a measure of the total fissile content. The gamma rays from 21,1Am, 239Pu 

219

220 THORPE 

FIG. 1, T h e rm a l-n e u tro n 252C f fu e l- ro d assay system w it h m o d ific a tio n s for p e lle t - t o - p e lle t scan. T h e 

4H e neutron detectors in the carbon core co u n t the prom pt fission neutrons fo r to ta l fissile d e te rm in a tio n , 

and the N a l detectors near the fu e l-ro d e x it ch a n n e l count the d elayed ga m m a rays for p e lle t - t o - p e lle t 

dete rm in a tio n . 

FIG. 2. A ty p ic a l d e la y ed g a m m a -ra y scan o f a 6 6 -in . -lo n g 3. 3°Jo PW R fu e l rod w ith p e llets o f low er 

e nrichm ents interspersed as shown above. T h e lo w e r curve is a sm oothed version o f the raw data in the 

upper curve (the error bars represent 2о u n certainties). Each poin t represents the to ta l counts a ccu m u la te d 

in 0 .4 s for a rod feed rate o f 8 ft/m in .

IA E A -S M -1 7 0 /5 4 221 

FIG. 3. Photograph o f m oderator and sh ield assem bly for a fast neutron 252C f assay system . T h e 25zC f 

source is p o sitio n e d in the ce n tre o f the tungsten and th e sam p le is p la c e d in the n ic k e l re fle c to r for the 

neutron irra d ia tion . 

are counted and used to provide pellet-to-pellet Information. The second 

unit measures the 2l*0Pu content by coincidence counting the neutrons emitted 

from the spontaneous fission of 2 °Pu [7]. 

Because of the high fissile loading of FBR fuel pins, thermal neutron 

irradiation w ould have yielded an unacceptably nonlinear response curve. 

Calculations led to the choice of the cylindrical moderator assembly shown 

in Fig. 3. The assembly has a core of tungsten (2.5 cm radius) surrounded 

by a 7.5-cm-thick shell of beryllium followed by 5 cm of lead and nickel. 

The nickel reflector increased the fission rate ~70% over the lead reflector 

alone. This moderator design resulted in a 239P u / 238U fission ratio 

of ~400/l for irradiation neutrons above the cadmium cut-off energy (~0.4 

eV).

222 THORPE 

5x5 No I DETECTOR 

I-----------------------------------------------------------58.00- 

FIG. 4. S c h e m a tic d ia g ra m o f the z a C f fast-n eutron assay system for FBR-type fu e l rods. T h e d elayed 

g a m m a rays in d u ce d by the fast-neutron irra d ia tio n are subsequently counted w ith the tw o N a l detectors that 

also m easure the passive ga m m a rays to determ in e p e lle t - t o - p e lle t u n ifo rm ity . 

FIG. 5. Fast neutron 252C f assay system for F F T F fu e l rods. System in clu d es 619 pg 252C f source and 

s h ie ld , tw o 5 b y 5 -in . N a l detectors to count the d e la y e d ga m m a rays, autom ated fu e l-ro d h a n d lin g , and 

data red u ctio n system.

IA E A -S M -17 0 /5 4 223 

FIG. 6. F F T F fu e l p in w it h various co m b in a tio n s o f p lu to n iu m e n rich m en ts for p e lle t - t o - p e lle t scanning. 

T o p cu rve corresponds to 60 K e V e nergy w in dow and b ottom curve corresponds to 100 to 500 k e V w in dow . 

FIG. 7. Passive n e u tro n -c o in c id e n c e counter fo r m easuring 240Pu content in FB R -type fu e l pins. T h e 

system in clu d e s 3H e th erm a l-n e u tro n de te cto r, autom ated fu e l p in lo a d e r and translator, and e le ctro n ics 

a nd data co n tro l rack.

224 THORPE 

FIG. 8. Photoneutron assay system using e ith er 124Sb or 8sY in the b e ry lliu m core surrounded b y n ic k e l and 

tita n iu m neutron reflecto rs and le a d g a m m a -ra y s h ie ld in g 

Figure 4 is a schematic diagram of the unit showing the Nal detectors 

each having a different degree of collimation, moderator, and shield assembly. 

Americium-241 doped, Nal seeds embedded in each crystal provide a 

source of constant amplitude pulses (roughly equivalent to a 3 M e V gamma ray) 

which are used in conjunction with an electronic stabilizing unit to reduce 

the effects of long-term photomultiplier and electronic drifts. Figure 5 is 

a photograph of the entire unit showing the moderator-shield assembly, the 

pin handling equipment, the programmable calculator and associated electronics. 

The automated translator picks up the rod to be assayed and moves it 

through the Nal crystals and the 252Cf assembly at a rate of 2.5 in./sec in 

order to take a background count of the unirradiated rod. The direction of 

travel is then reversed and the rod is withdrawn at 0.36 in./sec during

LAEA-SM-17 0/5 4 225 

w hich time the delayed fission gannna-ray data are acquired and the pellet- 

to-pellet scans are made. The rod is then unloaded in the tray directly 

b elow the loading magazine and the cycle is repeated for the next rod. The 

translator speeds are set to give a 5-min cycle per rod. 

Error analysis and measurements indicates that the standard deviation 

of the measured fissile content of a rod is -0.2 g. Figure 6 illustrates 

the sensitivity to pellet-to-pellet changes as observed with a test pin containing 

various pellet and enrichment combinations. It can b e seen that 

small changes in enrichment (1.7% to 3.12! relative) can be detected. The 

2l,0Pu assay system, shown in Fig. 7, contains 32 3H e tubes (1 in. diam by 

20 in. long, 4 atm gas pressure). The detector efficiency is ~36% and the 

neutron lifetime was measured to b e 28 ysec. Assay precision is a little 

greater than It (la) for a counting time of 100 sec. 

Assay units using Sb-Be or ®eY-Be as fast, subthreshold neutron sources 

are under investigation. A relatively hard nonthermal interrogation flux 

offers the potential advantage of insensitivity to the presence of fission 

product or burnable poisons as well as providing good penetrability and linearity 

of response. Figure 8 is a photograph of an experimental photoneutron 

system [8]. There is a central cadmium lined assay channel in beryllium with 

adjacent holes for the gamma sources followed by rings of titanium and nickel 

Three inches of lead shield the '‘H e detectors from the source gamma rays. 

The ''He detectors are embedded in a thick (2 cm) nickel ring w hich serves as 

a fast neutron reflector. The nickel reflector added about 40Z to the signal 

rate. The energy of the neutrons from the photoneutron sources is such that 

the l>H e detectors can be biased to eliminate m ost of the neutron signal from 

the source. This in turn permits the addition of sufficient lead to shield 

the detectors from the intense gamma radiation of either the source or the 

sample. The photoneutron unit just described is being used to acquire data 

on optimum detector gas pressure, signal rates and signal-to-background ratios, 

response linearity, etc. The unit is also being used to determine its 

suitability for other applications such as small-sample assay [9]. 

L W R fuel containing recycled plutonium will become important in the 

near future. The special assay problems associated with this type of fuel 

are being studied. 

NEUTRON METHODS APPLIED TO SCRAP AND SMALL SAMPLE ASSAY 

One of the most significant problems associated with the assay of scrap 

and waste is the lack of control over the extraneous material that might be 

present within the sample. Assay by means of fast neutron irradiation and 

detection of delayed or prompt fission neutrons has been found to be relatively 

insensitive to all matrix materials except hydrogen and other low Z 

elements which are good neutron m o d e r a t o r s . Fission chambers (or other detectors 

sensitive to low energy neutrons) closely coupled to the sample provide 

a means of detecting or correcting for the effects of neutron moderation. 

Gamma-ray assay methods are m ost suitable for light, hydrogenous 

matrix materials. Together, the two techniques, gamma-ray and neutron assay 

methods, provide broad capability for m a n y of the assay problems associated 

with scrap and waste. 

The development of the technique of neutron interrogation with delayed 

neutron detection is an example of the key role that nuclear data can play. 

When this method was first being considered it was necessary to undertake an 

experimental program to measure the delayed neutron yield from fission as a

226 THORPE 

FIG. 9. V ie w o f s m a ll-s a m p le assay station w ith B4 С sh ie ld rem oved. 

function o f incident neutron energy. I n it ia l emphasis was placed on measurements 

at 14 MeV [10] since 14 MeV neutron generators are a re la tiv e ly inexpensive, 

copious source o f neutrons. This program was follow ed by another 

set o f measurements using a Van de Graaff as a variable energy neutron 

source [11]. 

These experiments were designed to confirm and extend the available delayed 

neutron y ield data. The resu lts show that the delayed neutron yield 

is not sig n ifica n tly dependent on the energy o f neutrons causing fis s io n fo r


energies b elow 5 MeV. Above 5 M e V there is a drop in yield corresponding to 

the onset of second chance fission. The data obtained so far are in general 

sufficient to satisfy most immediate practical needs. Nonetheless there is 

interest in the delayed neutron yield in the energy region 6 to 14 M e V and in 

data for the higher plutonium isotopes. These basic data are used for computer 

calculations to explore and define possible technique refinements. 

An example of the application of subthreshold neutron interrogation and 

delayed neutron detection is the fissile assay of small samples [12] taken 

from various portions of a plant inventory for process control or inventory 

verification. Several thousand such samples are chemically analyzed yearly. 

To be generally useful, a small sample assay technique must be able to furnish 

few percent or less accuracy for a wide variety of chemical forms and 

concentrations of fissile material. Figure 9 is a photograph of a small 

sample assay apparatus w hich utilizes a Van de Graaff accelerator as a pulsed 

source of few hundred kilovolt neutrons. The delayed neutrons are detected 

between accelerator pulses by a large, flat efficiency detector. Closely 

coupled fission chambers monitor the fission rate in the samples. A background 

equivalent of 15 m g 235B has been achieved. 

Assay precision depends on sample fission rate and detector efficiency. 

It is advantageous to closely couple the detector and to provide neutron reflectors 

to increase the flux at the sample. The presence of extraneous 

materials in the vicinity of the sample degrades the incident neutron energy 

and causes undesirable sample self-absorption and matrix effects. An acceptable 

compromise, found experimentally, is to use iron reflectors adjacent to 

the target and sample in conjunction with a 3/4-in.-thick boron carbide 

sleeve surrounding the sample to eliminate the majority of neutrons below 

100 eV. Favorable experience gained to date from several hundred assays has 

provided the incentive to undertake the following major improvements in the 

system: automatic sample handling, automated data processing, and a more 

efficient detector-reflector geometry. Ongoing research effort involves 

finding methods of increasing precision, reducing the number of standards 

required, and defining and eliminating sources of bias. 

GAMMA METHODS 

Gamma-ray spectroscopy, particularly with lithium drifted germanium 

(GeLi) detectors, is a general purpose method with a wide range of applications. 

In this instance, nuclear data is not so important in the design of 

the hardware, but is essential for its application. Usually only a few lines 

from the complex decay spectra of the nuclides of interest are used for assay. 

Nonetheless extensive knowledge of gamma spectra is required to provide the 

assurance that the lines used are specific and that the presence of unusual 

or unsuspected activity will not yield an erroneous assay. Attenuation corrections 

for the matrix m aterials involved are the major sources of uncertainty 

in the assay. Attenuation corrections are usually obtained through: 

preparation of standards which are representative of the material being 

measured; measurement of the transmission of a source [13]; comparison of 

the relative intensities of two or more characteristic gamma rays [14]. 

In addition to quantitative assay gamma-ray detection has been applied 

to the measurement of enrichment, concentration, and isotopic composition. 

Relatively simple instrumentation, particularly w h e n used by knowledgeable 

personnel, can be quite effective. Figure 10 shows one of the devices which 

was used to estimate the holdup in a shutdown diffusion plant cascade. The 

instruments were also used in the operating cascade to monitor UFg retention 

in NaF traps, measure enrichment and to detect plating or holdup in the m a i n 

gas pipes [15].

228 THORPE 

FIG. 10. C o o le d , p o rta b le N a l g a m m a spectrom eter for assay o f 235U in sid e an o p eratin g gaseous-d iffiisio n 

p la n t. 

COINCIDENCE COUNTING OF FISSION EVENTS 

Coincidence detection o f the many neutrons and gamma rays from fis s io n 

provides a convenient method fo r separating the occurrence o f fis s io n from 

the source producing the fis s io n or from extraneous radiation which might be 

present [ e .g ., neutrons from (a,n) rea ction s]. Neutron coincidence counting 

o f 21f0Pu spontaneous fis s io n provides a simple method o f plutonium assay when 

the isoto p ic composition is known. The spontaneous fis s io n rate o f 238U can 

also be used fo r assay purposes. Both rates are low and high e ffic ie n c y 4ir 

neutron counters are required fo r rapid quantitative assay. 

Organic scintillation detectors permit the detection of time correlated 

events, neutrons or gamma rays, using coincidence gate widths of only a few 

tens of nanoseconds. Since the ratio of accidental coincidence rate to true


coincidence rate is directly proportional to the coincidence gate width, the 

short gate width allows the detection of fission in the presence of relatively 

large backgrounds of uncorrelated neutrons and gamma rays. Conversely, an 

uncorrelated or random source can be introduced to cause fission in the sample. 

The detected fission rate then is a measure of the fissionable content. 

Neutron source energies can be changed to increase sensitivity, and to provide 

both fissile and fertile assay. Figure 11 is a photograph of a system 

called the "Random Driver" which uses an Am-Li neutron source to cause fission 

in the sample. This system proved an effective instrument for the 

assay of uranium [16,17]. 

BASIC SIGNATURES 

Although natural radioactivity and fission have furnished the basic 

signatures w hich have proven to be the most utilitarian, there are other 

characteristics w hich can be used to identify particular elements or isotopes. 

A few examples are: neutron capture gamma rays; delayed-neutron 

and gamma-ray spectra, gamma-ray and x-ray fluorescence; selective neutron 

and gamma-ray absorption. The gathering of information, particularly basic 

data, pertaining to any physical phenomenon which might be applicable to 

materials analysis should be encouraged. This reservoir of basic information 

can then be used as a basis to continually review the techniques for 

possible application to the changing and differing needs for quantitative 

FIG. 11. T h e random so u rce-in te rro g a tio n system used to de te rm in e the Z35U co n te n t in co n ta in ers o f 

up to 5 - g a l c a p a c ity .

230 THORPE 

assay. These needs range from the detection of trace quantities in effluents 

to detailed analysis of spent reactor cores. New facilities and improvements 

in detector characteristics, for example, may render completely 

practical a technique previously thought not worthy of further development. 

An example of the Information gathering process is a program that is 

designed to investigate the application of p-meson capture x-rays to elemental 

and isotopic analysis. The objective of this program is to obtain high 

quality spectra for each fissionable isotope and to obtain information on 

h ow the chemical form of the material might affect possible assay applications. 

Using the facilities at the Space Radiation Effects Laboratory (NASA) 

data have been taken on m etal targets of 208Pb, 232Th, 235U, 23eU, and 239Pu. 

Some data were also obtained for depleted uranium compounds, mainly oxides. 

The experiments are expected to continue early next year when m ore intense 

beams become available at the Los Alamos Meson Physics Facility. 

CONCLUSIONS 

The number of systems for assay that exist, complete with operations 

manual, error analysis, and operational history of reliability and effectiveness, 

is testimony to the growing maturity of nondestructive assay. A m ore 

difficult phase is beginning w h i c h emphasizes accuracy without undue increase 

in cost and complexity, the development of standard procedures, and 

the establishment of nondestructive assay m ethods as independent alternatives 

to traditional chemical analysis. 

Calorimetry is an example of a technique for which refined nuclear data 

would have a direct effect on meeting the challenges listed above. The radioactive 

decay data and methods of determining isotopic composition are not sufficiently 

accurate to establish the relationship of heat output and quantity 

of material to an accuracy comparable to the precision available [18]. 

The value of readily available data which form the basis for design 

calculations and the foundations from which to explore n e w concepts can 

hardly be overemphasized. Routine calibration of equipment is accomplished 

by means of standards. Improvements of the data and calculational techniques 

will permit more precise evaluation of system performance w hich will reduce 

the number of these costly standards required. 

REFERENCES 

[1] FORSTER, R. A. and MENLOVE, H. 0., LA-4605-MS (1970) 8. 

[2] FORSTER, R. A., LA-4994-PR (1972) 9. 

[3] FORSTER, R. A., SMITH, D. B., MENLOVE, H. 0., Error Analysis of a 

252Cf Fuel Sod Assay System (LA report to be published in 1973). 

[4] FORSTER, R. A., SMITH, D. B., and MENLOVE, H. 0., "252Cf fuel rod 

assay system: in-plant performance," Froc. Thirteenth Annual Meeting 

of the Institute of Nuclear Materials Management, Boston, Massachusetts 

(1972). 

[5] FORSTER, R. A. and MENLOVE, H. 0., LA-4883-PR (1971) 6. 

[6] MENLOVE, H. 0., FORSTER, R. A., PARKER, J. L., and SMITH, D. B., 

2S2Cf Assay System for FBR Fuel Pins: Description and Operating 

Procedures Manual, LA-5071-M (1972). 

[7] MENLOVE, H. 0., FORSTER, R. A., and SMITH, D. B., LA-5091-PR (1972) 7.


[8] MENLOVE, H. 0. and FORSTER, R. A., LA-4994-PR (1972) 6. 

[9] MENLOVE, H. 0. and MATTHEWS, D., LA-5091-PR (1972) 16. 

[10] MASTERS, C. F., THORPE, M. M., SMITH, D. B., The measurement of 

absolute delayed neutron yields from 3.1 and 14.9 M e V fission, Nucl. 

Sei. Engng 36 (1969) 202. 

[11] KRICK, M. S. and EVANS, A. E., The measurement of total delayed neutron 

yields as a function of the energy of the neutron inducing fission, 

Nucl. Sei. Engng 47 (1972) 311. 

[12] EVANS, A. E., THORPE, M. M., and MALANIFY, J. J., Fissile assay of 

small samples by subthreshold neutron interrogation, Trans. Am. Nucl. 

Soc. 15 2 (1972) 673. 

[13] PARKER, J. L., REILLY, T. D., WALTON, R. B., SMITH, D. B., and EAST, 

L. V., LA-4705-MS (1971) 12. 

[14] CLINE, J. E., A Relatively Simple and Precise Technique for the Assay 

of Plutonium Waste, ANCR-1055 (1972). 

[15] LA-4994-PR (1972) 15. 

[16] FOLEY, J. E., Random Source Interrogation System (Random Driver) at 

the Oak Ridge Y-12 Plant - Preliminary Results, LA-5078-MS (1972). 

[17] FOLEY, J. E., LA-5091-PR (1972) 14. 

[18] O'HARA, F. A., NUTTER, J. D., RODENBURG, W. W., DINSMORE, M. L., 

Calorimetry for Safeguards Purposes, MLM-1798 (1972).

I A E A - S M -1 7 0 /1 2 

INFLUENCE OF UNCERTAINTIES 

IN FISSION-PRODUCT NUCLEAR DATA 

ON THE INTERPRETATION OF 

GAMMA-SPECTROMETRIC MEASUREMENTS 

ON BURNT FUEL ELEMENTS 

O .J. EDER, M.LAMMER* 

Österreichische Studiengesellschaft 

für Atomenergie, Seibersdorf, 

Austria 

Abstract 

IN F L U E N C E O F U N C E R T A IN T IE S IN FIS S IO N -P R O D U C T N U C L E A R D A T A ON T H E IN T E R P R E T A T IO N O F 

G A M M A - S P E C T R O M E T R I C M E A S U R E M E N T S O N B U R N T FU E L E L E M E N T S . 

T h e c o m b in a tio n o f co m p u ter c a lc u la tio n s and gam m a sp e ctro m e tric m easurem ents offers new 

p o ssib ilitie s for in vestig a tion s on burnt fu e l elem en ts. T h e a ccu ra cy o f such a m ethod is m a in ly lim ite d by 

the a ccu ra cy o f n u cle a r data used and u n certa in tie s in the e v a lu a tio n o f measured ga m m a spectra arising 

from e x p e rim e n ta l co n d ition s. 

A m ethod is described that com b in es "fo rw ard " c a lc u la tio n s and measured a c tiv ity ratios o f fission 

products and e xam p les o f a p p lic a tio n are g iv e n . 

T h e a v a ila b ilit y o f c o m p ila tio n s o f nu cle a r data re le v a n t for burnt fu e l e le m e n t a nalysis is surveyed 

and im provem ents are proposed. A set o f fu e l isotope and fission product nu cle a r data is presented w h ich 

resulted fro m our ow n c o m p ila tio n efforts. 

F in a lly , u n certa in tie s are review e d th at arise from detector c a lib ra tio n , e x p e rim e n ta l co n d ition s, nu clear 

data o f fissio n products and s im p lific a tio n s in c a lc u la tio n s . T h e in flu e n c e o f u n certa in tie s in nu cle a r data on 

results o f c a lc u la tio n s and m easurem ents is dem onstrated by som e exam ples. 


The combination of gammaspectrometric measurements and. theoretical 

calculations provides a powerful tool to gain information about burnup 

and the history of fuel elements. The possibilities and limitations of 

this combined method from both the experimental and theoretical point of 

view have been investigated for about ten ye a r b y now [1-7]. 

Experimentally the development of high resolution semi-conductor 

detectors, the Compton coincidence spectrometer [2,3] and the summing 

Compton coincidence spectrometer [5] provided the basis to measure gamma- 

spectrometrically the activities of a number of isotopes in burnt fuel 

elements with sufficient accuracy (e.g. ^ 7 c s , 95zr, 95}Jb 103r u 

106Ru + 10§Rh) 131!f Ü 2 Te + Í 3 ^ / l 4 6 Ba + l|óLa> ll4Ce + Í44Pr) 2 3 3 p a ( 

239Np etc.) Model calculations using the well-known build-up and decay 

formulae and simplified assumptions of the neutron flux distribution together 

with an iteration matching procedure are the basis for non-destructive 

fuel element investigations. 

* Present address: N u c le a r D a ta S ection, IA E A , V ien n a 

233

234 EDER and LAM M ER 

In a "forward." calcu lation fis s io n product a c tiv itie s are calculated from 

known irradiation con ditions, whereas in a "backward" calcu lation irradiation 

history and/or fu el composition are derived from measured a c tiv itie s . The 

parameters which enter such inventory calcu lation s are 

- reactor operation conditions (space, energy and time distribu tion o f the 

neutron flu x , integrated neutron flu x, fu el element cy clin g , coolin g 

time) 

- fu el element ( i n i t ia l composition, resonance se lf-sh ie ld in g e t c .) 

- nuclear data (fis s io n y ie ld s , h a lf liv e s , neutron capture and fis s io n 

cross sections, gamma ray energies and absolute in te n sitie s) 

- experimental conditions (d etector e ffic ie n c y , geometry, gamma ray attenuation, 

quality and processing o f gamma spectra e t c .) . 

The information that can be obtained from gamma spectrometric measurements 

are (fo r a detailed discussion see [ 7 ] ) : 

- Burn-up: from 137Cs, 134Cs (ra tio 137Cs/134Cs), 144Ce - 144Pr, 106Ru - 

J-UbRh and 95zr - 95кь. 

- Cooling time: from ra tio s 14°Ba/95Zr, I4°Ba/141Ce, 141Ce/95Zr, 95Z r/95Nb ' 

and other combinations. 

- Integrated neutron flu x : from ra tio '*'34Cs/1^ c s> 

106 106„, x / 144,, 144„ \ / / 106„ 106_ ^ 

- Plutonium fis s io n s : from Ru - Rh, ra tio ( Ce- P r )/( Ru- Rh). 

233 2З2 

- Breeding rates at shutdown: from Pa ( Th as breeding m aterial) and 

“^ N p ( 23ÖU as breeding m aterial). 

M odifications and further combinations o f fis s io n products are presently 

investigated and some w ill be discussed in the next chapter, preceded by 

a b r ie f description o f the computer programs used fo r our calcu lation s. After 

a b r ie f review o f the a v a ila b ility o f nuclear data and presentation o f our 

own data set we show the influence o f nuclear data uncertainties on resu lts 

from calcu lation s and measurements. 

2. SOME DETAILS OP THE PRESENT INVESTIGATIONS 

2 .1. P rin ciple Considerations 

C haracteristic dependencies o f fis s io n product concentrations on 

irradiation conditions and f i s s il e material have been observed by several 

in vestigators (e .g . [6 ,8 ,9 ]). The use o f a ctiv ity ra tios as an interpretation 

method was, as we b elieve, fo r the fir s t time proposed in [7 ] 

together with some examples. The ra tio s shown in [7 ] as w ell as other 

combinations o f fis s io n products are presently investigated in more d e ta il. 

Only interpretations in terms o f a ctiv ity ra tios (instead o f absolute a ctiv it 

ie s ) allow to establish general rules which are independent o f the amount 

o f f i s s ile m aterial. Also the use o f such ra tios has many advantages regarding 

accuracy and correction s that have to be applied (fo r a detailed 

d iscu ssion,see chapter 5)*


The selection o f fis s io n products used fo r interpretation is guided 

by several considerations: 

- Nuclear data and neutron flu x models used in calcu lation s as w ell as the 

a ctiv ity measurements themselves are associated with some uncertainties. 

- Depending on th eir h a lf liv e s and the irra d iation time most o f the fis s io n 

products w ill only y ie ld information about the la ter part o f the irradiation 

h istory. 

- Therefore a ctiv ity ra tio s have to depend sig n ifica n tly on irradiation 

parameters o f fuel elements in order to enable the derivation o f these 

parameters from the r a tio . 

- From a p ra ctica l point o f view the fis s io n products used fo r interpretation 

have to be suitable fo r gamma spectrom etric measurements. 

Bearing these fa cts in mind fis s io n products were selected considering 

th eir nuclear data, modes o f production in fis s io n and the possible information 

they can y ie ld . According to th is selection a ctiv ity ra tios o f fis s io n 

produots were calculated fo r a wide range o f irradiation conditions and 

d iffere n t f i s s ile isotopes with the aid o f computer programs and checked 

against experimental resu lts. 

2.2. Description o f computer programs 

We used two computer programs with d ifferen t features for our forward 

ca lcu la tion s presented in [7 ]. The resu lts obtained were generally in good 

agreement. 

2 .2 .1 . The computer program IRBEL 

This program calcu lates day by day inventories by approximating the 

d iffe r e n tia l equation 

dNx ( t ) = [a 2N2 ( t ) - ax ^ ( t ) ] dt 

by the d ifferen ce equation 

AN1 < V - i>2N2 ( V l > - aA ( V l ^ A t i 

Here the symbols used mean: 

. number o f atoms o f isotope 1 

. number o f atoms o f precursor 2 o f any kind 

. constant giving the rate o f decrease in (decay constant, 

neutron cross section ) 

. constant giving the rate o f production o f N-^ from precursor 

Ng (decay, neutron capture, fis s io n ). 

. i-th time interval from start o f irradiation ( = 1 day) 

■tj 

a2 Ng stands fo r a ll modes o f production o f fis s io n product N^. 

This approximation is s u ffic ie n tly accurate fo r fis s io n products with 

h a lf liv e s o f several days. Some m odifications ex ist to take account o f 

important shorter lived fis s io n products (e .g . -^ X e ). In one version the


decay during each day is calculated exponentially. Other versions use 

numerical approximation methods or shorter time intervals within one day 

fo r such short lived fis s io n products. 

The program has the option either to enter the neutron flu x as input 

parameter, or the to ta l core power together with the core fra ction o f the 

investigated fu el element. In the la tte r case the neutron flux is calculated 

from the energy release per fis s io n o f the f i s s ile material present in the 

fu el element. The neutron flux is represented by 

- a maxwellian component, sp ecified Ъу the neutron temperature T, 

- an epithermal component, varying with l/E 

“ a fis s io n spectrum conqponent, 

both o f the la tte r sp ecified by th eir ra tios to the maxwellian flu x . Date 

and time o f start and end o f each power period complete the description 

o f the irra d ia tion h istory. 

This numerical method is esp ecially well suited fo r calcu lation s o f 

inventories a fter varying irradia tion conditions as th is causes no increase 

in computer time and the equations involved are rather simple. The program 

IRREL is presently su ccessfu lly used fo r routine calcu lation s o f isotope 

inventories in fu el elements from known irradiation conditions and described 

in more d eta il in [1 0 ]. 

2 .2 .2 The computer program CHAIN 

This computer program solves a n alytically the d iffe re n tia l equations 

that describe the complicated decay and activation processes. D iffic u ltie s 

due to the lim ited number o f d ig its available have been su ccessfu lly overcome 

by expansion o f a complete set o f exponential functions in one power 

series. An algorithm could be found which is esp ecia lly suitable for 

machine coding. A convergence test o f the exponents decides whether the 

power series or an ordinary exponentiation is to be used. 

During the stage o f testin g the program it proved most convenient to 

store separately each individual decay and activation chain leading to a 

certain fis s io n product. Similar chains are used fo r heavy elements from 

232xh to 241pu. Proceeding chain by chain, the contributions to the 

inventory o f the isotope at the end o f each chain are calculated for a 

given input time in terval. 

Here only the neutron flu x can enter the calcu lation s together with 

a time interval o f constant flu x . The input format o f the neutron flu x is 

optional: 

a) As in IRREL the absolute value o f the thermal flu x can be given together 

with the ra tio s o f epithermal and fa st component. This is more suitable 

i f the information comes from core calcu la tion s. 

b ) The absolute value o f the tota l flu x can be given including maxwellian 

and epithermal component. The to ta l flu x is sp ecified by neutron temperature 

and an epithermal index. The fa st flu x is given as ra tio to the 

to ta l flu x . This version is more suitable i f the flu x value is obtained 

from flu x monitors and threshold detectors. [1 1 ]. 

In each case the type o f flux representation and epithermal fa ctor 

has to be sp e cifie d . A ll modes o f input neutron flu x are transferred into 

Westcott formalism [11] fo r the calcu la tion o f reaction rates. D ifferent

IAEA-SM-17 0 / 12 237 

m u ltiplication factors are derived according to whether p ile neutron cross 

section s, maxwellian average cross sections together with reduced resonance 

integrals or 2200 m/s cross sections together with g and s factors are used. 

Various options make th is computer program very fle x ib le : 

- continuation with the calculated inventory, new start or termination, 

- selection o f d ifferen t irra d ia tion parameters or fis s io n products to 

be calculated, 

- continuation with coolin g time, 

- intermediate or fin a l printout o f inventory, 

- storage o f inventory on d isc, which can be reca lled repeatedly for 

further calcu lation s. 

In th is manner a real irradiation h istory o f varying neutron flux 

subdivided by coolin g periods can be simulated, as the program always 

returns to th is point. A m odification is in preparation that allows us 

to calcu late and p lot gamma spectra o f irradiated fu el elements to fa c ilit a 

te id e n tifica tio n o f gamma lin es in measured spectra. This m odification 

makes use o f the advantage that calculated inventory and fis s io n product 

gamma ray catalogue are both stored on d isc. These features and the ana^- 

ly t ic a l solu tion o f d iffe re n tia l equations make the program CHAIN esp ecially 

suitable fo r th eoretica l studies o f d ifferen t fission products under various 

con ditions. On the other hand i t is rather time consuming and less suitable 

i f used for simulation o f a complex irradiation h istory. Therefore i t is 

mainly used for th eoretical forward calcu lation s and fo r small test samples 

to check the quality o f the prediction s. 

2.3. Examples o f application 

2 .3 .1 . Irradiation o f samples 

In order to check the predictions several samples o f d ifferen t fuel 

compositions were irradiated in d ifferen t core p osition s for varying time 

in tervals with and without flu x m onitors.. When the resu lts o f these 

measurements are compared with calcu lation s the agreement is naturally 

better than in routine examinations o f fu el elements. A more precise 

value for the neutron flu x can be obtained and the measurement i t s e l f can 

be performed with great care and high s ta t is tic a l accuracy as i t involves 

only small samples and is not s t r ic tly lim ited in time. An agreement o f 

better than lfo to 5$ was obtained, depending in the fis s io n products investigated. 

The coolin g time could be derived su ccessfu lly in one case where 

acciden tally the time o f discharge o f the sample from reactor was unknown. 

Due to the operation cycle o f the reactor i t had to be a Saturday and 

the exact date could be fixed after a h a lf year coolin g time by comparison 

o f measured and calculated a ctiv ity r a tio s. 

2 .3 .2 . Adjustment o f irradia tion parameters from known operation 

history 

Generally irradiation conditions or at least to ta l core power and 

time intervals as w ell as fu el composition are known. However, the 

neutron flu x and contribution o f epithermal neutrons within an individual 

fu el element w ill generally deviate from that obtained from physical 

core ca lcu lation s and op erator's data, esp ecially at higher burn-up le v e ls. 

In th is case the comparison o f measured and calculated a ctiv ity ra tios can be 

applied su ccessfu lly to adjust these parameters in ал itera tiv e procedure.


The ra tio o f fin a l flu x to reactor power can he derived from a set o f 

fis s io n products with shorter h a lf liv e s . I f the change o f th is ra tio with 

time due to burnup and fuel cyclin g has a noticeable e ffe c t on the resu lt, 

i t can be estimated by including a set o f fis s io n products which "remember" 

e a rlie r parts o f or. the complete irradiation h istory , a ll o f them being not 

sen sitive on the neutron spectrum. Epithermal index and neutron temperature 

can be adjusted using the *34cs/ 137os a ctiv ity ra tio . All these independent 

inform ations have tob e considered simultaneously. Starting with fir s t 

estim ates, the irradia tion parameters can be improved in an itera tive 

procedure. 

The matching o f a ll calculated a c tiv itie s with the measured ones is , 

however, rather cumbersome i f not done automatically by computer. I f less 

p recision is required and a constant neutron flu x to core power ra tio can 

be assumed throughout the whole irradia tion history within the p recision 

lim its, neutron flu x , epithermal contribution and neutron temperature 

can be obtained merely by matching the ^'34cs and 137qs a c tiv itie s . In th is 

case measured and calcu lated absolute a c tiv itie s have to be compared as 

they in combination with the in it ia l content o f f i s s ile material supply 

additional information. 

2 .3 .3 . Determination o f burn-up 

137 

Burn-up is determined by gamma spectrom etric measurements o f Cs, 

144ce - 144pr, 106Ru _ 10°Rh 95Zr - 95цъ a c tiv itie s su ccessfu lly on 

a routine basis. Limits o f application o f these fis s io n products were 

already discussed in [7 ] and other work. The usefulness o f ^37cs as 

burn-up monitor is , however, doubted because o f it s tendency to migrate. 

The magnitude o f th is e ffe c t depends on the type o f fu e l, i t s temperature 

and the temperature gradient within the fu el. In many p ra ctica l cases 

errors in burn-up determination duetto 137cs migration are not serious. 

I f we assume that the reactor operation history and fuel composition 

are known the integrated neutron flu x is equivalent to the burn-up 

(to ta l number o f fis s io n s ). In th is case the ■'•34cs/ -1'Cs a ctiv ity ra tio offe rs 

1 3 7 

a p o s s ib ility superior to an absolute measurement o f Cs. Apart from 

the advantages o f ra tios regarding correction s and u ncertain ties, i t can 

be expected that 134cs is affected by migration in the same manner as 

•1-37cs. Consequently losses and red istrib u tion o f Cs (lo c a l concentrations) 

should have no serious e ffe c t on th is ra tio . Also errors due to absorption 

corrections assuming a homogeneous radial distribu tion o f Cs in the fuel 

should cancel. 

Not only the axial burn-up p r o file o f a fu el element can be measured 

with higher accuracy from the 134cs/137cs a ctiv ity r a tio . Using the 

matching procedure described in 2 .3.2 the neutron flu x and the con tribution 

o f epithermal neutrons inside a fu el element and it s variation can 

be determined which is not possible by any d irect measurement. Radial 

d istribu tion s can only be determined with confidence for fu el types that 

hinder migration in th is d irection . 

A research co-ordinating meeting on development o f gamma spectrometry in - 

strumentationand techniques for safeguards [12] recommended the experimental 

exp loitation o f the 134cs / ^'Cs ra tio for burn-up determination. 

Investigations in th is d irection are in progress. Results o f a lim ited 

number o f comparisons showed that burn-up determined by th is ra tio agreed 

with destructive U - Pu analysis within about Vfo [1 3 ]. In measurements


o f the axial burn-up p ro file the ■'■^'Cs/^^Cs ra tio showed a good correla 

tion (fa c to r : 0.993 [ 14] ) and proved to be superior to other ra tios 

or measurements o f absolute a c tiv itie s [13)14]. 

2 .3 .4 . Establishment o f fis s io n product inventories, 

In some application fie ld s fe .g .fu d element testin g and development, 

fis s io n product release measurements etc. ) one might be interested in 

fis s io n product concentrations that cannot be measured d ire ctly . Here 

the method described in section 2 .3.2 can be used together with gamma- 

spectrom etric measurements o f fis s io n product a c tiv itie s to adjust the parameters 

used in ca lcu la tion s. In th is manner concentrations o f fis s io n products 

at reactor shut down can be calculated^which cannot be measured because o f th eir 

low a c tiv itie s , short h a lf liv e s or the absence o f suitable gamma lin es. 

This procedure is already in use on a routine basis [Ю ]. 

2.3.5* Application in safeguards 

The main objectiv es o f safeguards measurements on irradiated fuel 

elements are the id e n tifica tio n o f fu el elements and the v e rifica tio n o f 

operators data. In practice th is means a check, i f the measured content 

o f f i s s i l e m aterial, esp ecia lly Plutonium, and fis s io n products 

corresponds to the information about in it ia l fu el composition, irradiation 

h istory and burn-up given by the plant operator [1 2 ]. Here we have the case 

o f known irra diation h istory and fu el composition,and a forward calcu lation 

can be compared with gamma spectrom etric measurements fo r v e r ific a tio n . 

Experiments to check such a v e r ific a tio n technique have been performed 

by IAEA together with Euratom [14] using a ctiv ity ra tio s . Among these 

some ideas presented in [7 ] were adopted. Correlations between burn-up, 

coolin g time and P u -fission s on the one hand and a ctiv ity ra tios on the 

other hand were found to be sa tisfa ctory . D etails and resu lts can be 

found in [1 4 ]. 

Significant in con sistencies exceeding experimental error and uncerta 

in tie s due to nuclear data and sim p lification s in the calcu lation 

(together about 5 - 20^) can easily be detected by th is method. In such 

a case the fu el element can be further investigated by destructive analy 

s is . However, the dependence o f a ctiv ity ra tio s on certain parameters, 

as lis te d in the introduction ( 1 .) and discussed in d eta il in [7 ] , allow us 

to derive some lim ited information about the history and composition o f 

the fu el element with low accuracy. This procedure could be as follow s 

startin g with fir s t rough estimates from curves (e .g . from [7 ] or section 

2 .4 .) : 

Step 1: The coolin g time can be derived roughly from d ifferen t 

fis s io n product ra tio s. I f shorter liv ed fis s io n products can be measured 

(e .g . -*-3 I , Ôjja, 141ce) these should be used as fir s t estimates, as 

they are more lik e ly to be in saturation than fis s io n products with longer 

h a lf liv e s . Shutdown a c tiv itie s can then be calculated fo r a ll measured 

fis s io n products. 

Step 2: The a ctiv ity ra tio y ield s a fir s t estimate o f 

the integral neutron flu x, assuming fissio n s only and a typical 

value fo r the epithermal neutron flu x . With th is parameter fix ed, the 

irradiation time can be derived from the °5Zr/W 7cs a ctiv ity ra tio as 

shown in figure 4 (see also 2 .4 .).


Step 3: The number o f Pu fissio n s can be derived from the Ce/ Ru 

r a tio . The origin a l dependence shown in [7 ] can be modified by p lottin g 

the 144ge/106Ru ra tio against the integral neutron flux.U sing the in it ia l 

235u/ 3 и ra tio (enrichment) as third parameter several curves axe obtained. 

With the assumption that a ll Pu fissio n s resu lt from ^38u breeding 

the in it ia l enrichment o f U can be estimated. 

Step 4 and further steps: An inventory calcu la tion can be performed with the 

fir s t estimates and compared with the measured a c tiv itie s . Discrepancies have 

to be expected as the curves used fo r fir s t estimates are more or less 

independent. A ll parameters can be adjusted, startin g again with Step 1. 

Additional a ctiv ity ra tio s can be included to check the in it ia l assumptions 

o f "th ird " parameters in curves such as epithermal flu x or in it ia l fuel 

composition. So fo r example the ■'■54guyi37(;s a ctiv ity ra tio (P ig. 6, 

see also 2 .4 .3 .) cannot be used as a fir s t estimate, as i t depends strongly 

on the f i s s il e isotope and the epithermal flu x contribution. But in the 

adjustment procedure i t can be used to check the assumptions o f Pu production. 

The value and accuracy o f such ал itera tiv e procedure has to be 

investigated experimentally. 

2.4. Some new resu lts from studies o f a ctiv ity ra tios 

2 .4 .1 . The ■'■‘^C s/ ' ^ C b a ctiv ity ra tio 

The '*'^Cs/'*'^Cs ra tio varies lin e a rily with integrated neutron flu x 

over more than 2 decades. Our fir s t calcu lation s [7 ] showed a strong 

dependence o f th is ra tio on the epithermal neutron flu x contribution and was 

therefore further investigated. Figure 1 shows the variation o f th is ra tio 

with irra d iation time and tota l neutron flux (thermal + epithermal) for 

235U fissio n s. 

The ■'■^Cs/^^Cs a ctiv ity ra tio is almost the same for *Û and *^Pu 

fissio n s and changes by about 25$ when going to 233u fissio n s (F ig .2). 

It can also be seen from figure 2 that the variation with neutron 

temperature is not serious, whereas the strong dependence on the neutron 

spectrum introduces a large uncertainty. 

2 .4 .2 . The ^^Zr/^^Cs a ctiv ity r a tio . 

Due to the comparatively short h a lf l i f e o f ^ Z r (64d)the ^ Z r/^ ^ C s 

a ctiv ity ra tio at reactor shut down should vary sig n ifica n tly with 

irradiation time. This is shown in figure 3 for d ifferen t values o f the 

tota l neutron flux (235u on ly). The dispersion o f the curves esp ecially 

for low values o f the ra tio (F ig .3 ) is due to the high ^35ц depletion 

which is also indicated in figure 3. In th is case 95Zr is no more formed 

in fis s io n in sign ifica n t amounts and decays p ra ctica lly . The depletion 

is equivalent to integrated neutron flu x values which can be obtained 

from 13 4 cs/137Gs. 

2.4 -3 . The ■'■Êu/^^Cs a ctiv ity ra tio 

Due to the low fis s io n y ie ld o f 1Êu, '''"Êu can only be found in 

gamma spectra from highly irradiated fu el elements and after rather 

long coolin g times. Calculated ra tio s are shown in figure 4 and compared 

to the 134cs/-1-37cs a ctiv ity ra tio (on d ifferen t s ca le ). The differen ce 

in the •'■54eu/A37Cs ra tio fo r 235u and 239pu fissio n s is n oticeable. This

IAEA-SM-17 0 / 12 241 

Ю12 Ю’3 10й 

$tol * Tirr (n/fcrrf»s)xyearsl 

FIG . 1. 134C s / 137Cs a c tiv ity ra tio at shutdown versus in tegrated neutron flu x for d iffe re n t v alu es o f neutron flu x 

and irra d ia tio n tim e . 

ra tio has another in terestin g feature: the contributions o f lower mass 

chains to the 154&1 a ctiv ity increase rapidly with integrated neutron 

flu x as shown in the table below: 

Integrated neutron flu x 

[n/om s x years] 

contr ibutions 

153 152 

from masse !S 

151 

149 147 

1013 92$ 4.4$ 3.5$ - - 

5 x 1013 57$ 17$ 23$ 2.6$ - 

1014 31$ 23$ 34$ lOfo 1.4$ 

2 x 1014 10$ 20$ 32$ 32$ 5-5$ 

4 x 1014 0.7$ 7$ 12$ 41$' 39$ 

5 x 1014 0.2$ 3$ 5-5$ 36$ 53$


FIG . 2 

100 10K 

Фшх T,rr ln/(cnŸ*s)xyearsl 

D e p en d e n ce o f 134C s / 137C s a c tiv ity ra tio at shutdown versus in tegrated neutron flu x on d iffe re n t param eters. 

iradiation time Iyears/ 

F I G .3 . D e p en d e n ce o f 95Z r / I37C s a c tiv ity ra tio at shutdow n on irra d ia tio n tim e .


integral neutron flux 

ln/cm!s * yearsI 

F I G .4 . D ep en d ence o f 154E u /137 C s a c tiv ity ra tio at shutdown on in tegrated neutron flu x . 

This e ffe c t has several consequences: 

- The slope o f the '^ 4Eu/'*'37Cs ra tio is steeper than that o f the ^34Cs/^37Cs 

ra tio at lower integrated fluxes. 

- The curve calculated for 239pu fissio n s approaches that for ^35u fissio n s 

at higher integral fluxes as the d ifferen ce in fis s io n y ie ld s is not 

so pronounced at lower mass numbers. 

- The dependence on the fra ction o f epithermal neutrons is lik e ly to vary 

with in tegral neutron flu x. This has not yet been investigated. 

3. COMPILATIONS WHICH INCLUDE NUCLEAR DATA NEEDED IN THIS WORK 

Nuclear data used as input to forward calcu lation s are: h a lf liv e s , 

neutron cross section s, branching ra tio s and fis s io n y ie ld s. 

Data needed for the evaluation o f measured gamma spectra are: gamma 

ray energies and absolute in ten sities o f ca lib ra tion standards (d etector 

e ffic ie n c y ) and fis s io n products, h a lf liv e s and gamma ray attenuation 

c o e ffic ie n ts . 

3.1. F ission y ield s 

Existing evaluations and evaluation methods are discussed in another 

paper at th is Symposium [15]« 

3.2. Decay data and gamma ray properties 

The table o f isotopes edited by Lederer et al [16] is the last comprehensive 

con çila tion o f decay data and gamma ray properties that includes 

a ll the fis s io n products o f in terest in our work. However, no


gamma ray measurements with semiconductor detectors are included in th is 

compilation fo r most o f the fis s io n products, as such m easurem ents w ere 

not available at that time. Due to the rapid development and increasing 

application o f high resolu tion semi-conductor detectors these data were 

o f l i t t l e value to users and superseded by more accurate measurements 

already shortly a fter the publication o f the la st ed ition o f the book. 

Decay and level scheme evaluations by the Nuclear Data group are 

published on a regular basis. However, they s t i l l have a large backlog 

and th eir la st compilations o f many important fis s io n products (mass 

numbers 97, 99. ЮЗ, 106, 131, 133, 134, 137, 140) date from 1959 to 1961. 

The situation is not so bad for h a lf liv e s and branching ra tio s as there 

are not so many measurements performed and the "Recent References" o f 

the Nuclear Data Group helps to find the pu blications. 

More recently a number o f evaluations and compilations were published 

[1 7 - 19]. E specially the detailed tables o f Martin and B lich ert-T oft [17] 

were very valuable for our work, although they do not contain a ll o f the 

important fis s io n products. However, no up-to-date compilations were available 

between 1967 and 1970, except for tables o f gamma ray energies for 

detector ca lib ra tion , and therefore com pilation a c tiv itie s started at the 

reactor center Seibersdorf fo r internal use. 

3 . 3. Neutron cross sections 

As with h a lf lives,measurements o f thermal neutron cross sections and 

resonance in tegrals are not very frequent. The comprehensive and w ell known 

compilation BNL-325 [29,30] contains a ll pre 1966 measurements. References 

fo r la ter measurements can be found in CINDA [3 1 ]. Also a number o f other 

compilations ex ist due to a world-wide in terest in neutron data. 

The main problems concerning neutron cross sections are the lack o f measurements 

fo r a number o f nuclides and p a rtia lly unresolved discrepancies between some 

measured values. Another strik in g fact is the lack o f information about 

world-wide compilation a c tiv itie s such as the litera tu re index CINDA [31] or 

retrieveable computer f i l e s o f experimental and evaluated data and the serv 

ices offered by data centers. 

3.4. Suggested improvements in compilation e ffo r ts 

Although a literatu re index to experimental data may be o f great value, 

a user would preferably not just adopt the resu lt o f a most recent measurement. 

Due to the lack o f decay data com pilations, esp ecially o f gamma ray 

energies and in te n sitie s, several unpublished com pilations have been prepared 

at our and other laboratories fo r internal use. A number o f these compilations 

have only recently been published or prepared for publication. In order to 

save world-wide p a ra llel e ffo r ts we would strongly support any means to 

make information about compilation a ctiv ity and existin g compilations 

commonly available. This could be achieved by issuing p eriod ica lly a comp 

ila tio n b u lletin or by the in clusion o f references to compilations and 

evaluations in indexes to existin g lite ra tu re, even i f unpublished. It 

would then be the resp on sib ility o f the compilers to supply th is information 

to indexers. 

In many application fie ld s only a lim ited number o f nuclear data 

types is needed. For example most applications need only gamma ray energies 

and absolute in ten sities rather than complete level schemes. During our 

own com pilation work i t proved convenient to maintain computer f i l e s o f 

experimental data for gamma ray energies and in te n sitie s, h a lf liv e s and 

branching ra tio s , which could be updated p eriod ica lly . A certain selection o f

IA E A -S M -1 7 0 /1 2 245 

data has to be made but th is selection causes not much additional e ffo r t. 

Some care is required on the part o f the compiler in calcu latin g absolute 

gamma ray in ten sities from supplementary information, but th is may not be 

necessary fo r every update. 

The situ ation is somewhat d ifferen t for neutron cross sections and fis s io n 

y ie ld s as these data require carefu l evaluation. However, these evaluated data 

could also be maintained in a computer f i l e . We would therefore recommend 

the in vestigation o f the generation o f such computer lib ra rie s o f important 

nuclear data which would be readily available to a ll users. 

4. RECOMMENDED NUCLEAR DATA 

Tabulations o f fis s io n prodout nuclear data are s t i l l rather rare 

and we have received some requests fo r our data. Therefore we present a 

recen tly updated set o f fis s io n product and fuel isotope nuclear data. 

D etails w ill be published elsewhere. 

4 .1 . Nuclear data o f fu el isotopes 

Table I contains the preliminary resu lts o f a new evaluation o f 

2200 m/s constants [ 32] which is a revision o f the e a rlie r publication 

[3 3 ]. Only minor changes o f these values are expected for the fin a l 

version , except, perhaps, ^ 9 p u and 241pu> д carefu l réévaluation o f the 

h a lf liv e s o f these two isotopes is in progress. The S values were ca lculated 

by us from W estcott's data [34] ( Sg values) according to : 

Snew = Sold + n/ 4 T /7 J -T 0' I ( R I /


T A B L E I. P R E L I M I N A R Y 2 2 0 0 m / s C O N S T A N T S 

Quantitya 

LAEA-SM-170/12 

T A B L E II. N U C L E A R D A T A O F H E A V Y ISO TO PES 

neutron cross sections (barn)a 

capture fi ssion 

Isotope maxw RI fiss maxw RI fiss half life 

232Th 7.313b 82 0.262 0.072 

233Pa 39 860 0.39 27 d 

234ц 

99 600 0.14 1.3 

236u 5-4 415 0.14 О.69 

237„ 370° 0.07 2 0.68 6.75d 

238u 2.73 269 О.О85 0.310 

234 169 870 0.17 O.OI9 6 1.28 

238n p 43 10 0.12 2200 510 1.3 50.8 h 

239n p 60° 2.35 d 

238Pu 588 I64d 0.03 16.3 16.7 2.3 

240Pu 288 8220 0.06 1.5 

a maxw = maxwellian average (g x ® 0 ) cross section, 

RI = reduced resonance integral (l/v part subtracted) 

fiss = fission spectrum (235u) avercige cross section. 

b s; = 7.3449 ъ, g o = 0.99562 [21]. 

с pile neutron cross section 

d includes l/v part of cross section 

Half lives for many fission products were taken from the evaluation 

of Martin and Blichert-Toft [17]. "Recent References" issued by the 

Nuclear Data group in Oak Ridge were scanned regularily for new measurements. 

A computer fit was made whenever data more recent than those included 

in [17] were found and use was made of the tables of experimental 

data in [ 17]. In some cases, where one value was considered superior to 

others,this was adopted. Up to now for most of the fission products contained 

in [ 17] more recent data were available. 

The most extensive compilation of fission product thermal cross 

sections and resonance integrals is that of Walker [36]. Therefore his 

values for experimentally determined cross sections were adopted by us 

and only updated for some new measurements. Stable nuclides, for which 

no new measurements were found, are not included in our tables and 

Walker's data [36] are recommended. 

For nuclides where no experimental results are available the 

Australian fission product point cross section library [22,23] is used 

which is based on more sophisticated calculations than Walker's estimates. 

247

248 EDER and LAMMER 

TA B L E III. FISSION PRODUCT NUCLEAR D A TAa 

f i s s i o n 

p r o d u c t 

h a l f - l i f e c r o s s - s e c t i o n s ( b a r n ) 

2 2 0 0 m / s m a x w e l l i a n r e s i n t . p i l e 

7 7 A s 3 8 . 8 3 + O . O 5 h 1 2 . 5 Ъ 2 0 ° 

8 l B r 

8 2 B r 3 5 - 3 4 + 0 . 0 2 h 1 8 Ъ 

2 . 7 + 0 . 2 

5 5 + 5 

S 3 K r 2 0 0 + 1 0 1 5 0 + 3 0 

8 4 K r 0 . 1 8 

8 5 K r 1 0 . 7 3 + 0 . 0 6 a 8 

8 6 R b 1 8 . 6 5 + 0 . 0 2 d 

4 0 С 

0 . 4 9 b 0 . 5 ° 

8 9 S r 5 О . 5 2 + О . О 5 d 0 . 4 £ 

9 ° S r 2 8 . 6 + 0 . 4 a 0 . 8 

9 1 S r 9 . 4 8 + 0 . 0 2 h 0 . 1 4 Ъ 0 . 1 5 ° 

9 1 y 

5 8 . 5 1 + 0 . 1 2 d 1 . 0 ъ 1 . 4 

9 4 Z r 0 . 0 6 + 0 . 0 1 0 . 3 7 + 0 . 0 4 

9 5 z r 6 3 . 9 8 + О . 1 2 d 0 . 4 8 Ъ 1 С 

9 5 m w b 3 . 6 1 + 0 . 0 4 d 

9 5 N b 3 5 . О 4 5 + О . O l O d 1 . 4 3 ъ 4 

9 6 Z r О . О О 6 + О . О О ] 5 . 0 + 0 . 5 

9 7 Z r 1 6 . 8 + 0 . 2 h 0 . 2 0 Ъ 0 . 4 ° 

9 8 M o 

9 9 M o 6 6 . 7 + О . 5 h 1 . 7 ъ 

0 . 1 3 + 0 . 0 1 

1 0 3 R u З 9 . З 5 + О . 1 О d 7 . 6 Ъ 1 0 е 

^ E h 3 5 . 5 + 0 . 2 h 1 7 0 0 0 + 2 0 0 0 1 7 0 0 0 + 3 0 0 0 

1 0 6 D 

R u 3 6 8 . 3 + 2 . 0 d O . I 5 + O . O 5 2 . 0 + 0 . 6 

1 0 9 p d I 3 . 4 6 + O . O 2 h 

Note: for footnotes a > c< d, e< ^ see below last portion of this table. 

2 е 

5

T A B L E III (con t. ) 

fission 

product 

half life 


cross-sections (harn) 

2 200 m/s maxwell iar¡ res int. pile 

IO9 Ag 93+5 1500+200 

110m, Ag 252.2+0.3d 82 

U4 7.45 +0.01 d 3+2 105+20 

112P01 20.12+0.06 h 1 

1 1 2 л Ag 

3.16+0.02h 

115"‘c d 44.6+ 0.2 d 3 1 ъ 5 0 d 

n 5Cd 53.38+О.О4 h 5 . 4 b 2 0 d 

b" 

121mSn 50 + 10 a 

12.4 Ъ 

1 21Sn 27.O5+O.IO h J 

121Sb 6.2+0.1 200+10 

122Sb 64.34+0.06 h 21 Ъ 

123Sn I29.3+ O .5 d о.оз ъ 

123Sb 4.2+0.2 120+10 

124Sb 60.20+0.02 d 6.5 

12^Sn 9.64+О.ОЗ d 0.55 Ъ 

125sb 2.75+О.О4 a 1.56 

12^mTe 58+1 d llb 20 d 

126Sn 0.3 Э. 12 

126Sb I2.4+O.I d 5.8Ъ 

127 Sb 9I.2+O .3 h 0.9Ъ 

127I\ a 109 + 2 d 9-4 20 d


T A B L E III (con t. ) 

fission 

product 

half life cross-sections (barn) 

1 2 9 ^ е 33.6+ 0.2 d 1.1 

131"Ve' 30 h 0.1 

2200 m/s maxwellian res int. pile 

131I 8.05*0.02 de 0.94Ъ » 8 

131mXe 11.98+0.05 d 50 

132Te 78+ 1 h 0.0024^ 

132I 2.285+O.OIO h 

X33i 

20.9+0.I h 0.0035Ъ 

133mXe 54+2 h f 

133Xe 5 .29+0.Old I9O+9O 

133Cs 29.5+2.О 450+20 

134c s 2.05+0.02 a 133* 140+12 

135, 6.585+О.ОО2 h 0. 02Ъ 

135 X e 9. I 72+O.OO5 h 2.65xl06 3.1xl06 

136C S 13.00j0.02 d 1.9Ъ 

137Cs 30.0+0.2 a 0.11 

1 4 °Ba 12.79+0.Old 1.57+0.03 13+2 

140La 4О.27+О.О5 h 2»7 +0.3 69+4 

141Ce 32.55+0.02 d 29+З 

142Pr 19.I+O.I h 20+3 

143Ce 33 + 1 h 6

T A B L E III (cont. ) 

f i s s i o n 

p r o d u c t 

1 4 3 p r 

h a l f l i f e 

I 3 . 5 8 + O . O 3 d 

IA E A -S M -1 7 0 /1 2 251 

c r o s s - s e c t i o n s ( b a r n ) 

2 2 0 0 m / s m a x w e l l i a n r e s , i n t . p i l e 

» "1 

1 0 0 + 1 0 1 5 О + З О 

1 4 4 C e 2 8 4 . 5 + О . 4 d 1 . 0 + 0 . 1 2 . 2 + 0 . 3 

1 4 7 N d 1 1 . 0 0 + 0 . 0 3 d 5 0 b iood 

1 4 7 P m 2 . 6 2 3 + O . O O I a 1 8 2 + 2 0 2 4 О О + З О О 

1 4 7 S m 6 1 ± 7 6 4 6 ± 6 0 

1 4 4 m 4 О . 9 + О . 2 d 2 5 0 0 0 + 2 0 0 0 

1 4 8 P m 5 . 3 7 + O . O I ' d 3 0 0 0 + 2 0 0 0 

148Sm 3 . 5 ± 1 . ' 2 2 7 ± 1 4 

1 4 9 P m 5 3 . 0 8 + 0 . 0 5 h 1 4 O O + 3 O O 

1 4 9 S m 

4 2 1 0 0 + 4 0 0 

^ P m 2 8 . 4 + 0 . 1 h 4 0 0 

^ S m 9 3 + 5 a I 5 O O O + I 8 O O ( 3 1 0 0 ) 

^ a n 4 6 . 9 + 0 . 2 h 3 3 5 Ъ 

4 5 0 + 2 0 

5 0 0 d 

8 . 5 + 0 . 2 a 1 5 O O 

4 . 9 + О . l a 4 0 4 0 + 1 2 5 

^ E u 1 5 . l 6 + 0 . 0 2 d 4 8 0 Ъ 5 0 0 d 

^ B u I 5 . I 5 + O . O 8 h 1 9 0 Ъ 2 0 0 d 

a F o r b r a n c h i n g r a t i o s a n d c r o s s s e c t i o n r a t i o s t o m e t a s t a b l e s t a t e s 

s e e t a b l e V I . 

b I n t e r p o l a t e d f r o m A u s t r a l i a n f i s s i o n p r o d u c t p o i n t c r o s s s e c t i o n l i b r a r y 

[ 2 2 , 2 3 ] . E s t i m a t e d e r r o r 1 0 0 % [ 2 2 ] . 

с R o u g h e s t i m a t e f r o m 2 2 0 0 m / s c r o s s s e c t i o n b y c o m p a r i s o n w i t h n u c l e i 

o f s i m i l a r c h a r g e a n d m a s s n u m b e r c o m b i n a t i o n s 

d O r d e r o f m a g n i t u d e e s t i m a t e d f r o m p o i n t c r o s s s e c t i o n l i b r a r y d a t a [ 2 2 , 2 3 ] 

e M o r e r e c e n t m e a s u r e m e n t s q u o t e d i n [ 2 4 - 2 6 ] a r e n o t i n c l u d e d , a s 

t h e y a r e e i t h e r d i s c r e p a n t [ 2 4 , 2 6 ] o r n o t y e t p u b l i s h e d [ 2 5 ] 

f C r o s s s e c t i o n n o t m e a s u r e d n o r c a l c u l a t e d . M e a s u r e m e n t s o f R e y n o l d s 

a n d E m e r y [ 2 7 ] ( o n d e c a y s c h e m e s ) s u g g e s t , t h a t t h i s c r o s s s e c t i o n 

m i g h t b e o f t h e o r d e r o f 1 0 ^ b .


О . О 2 5 З e V c r o s s s e c t i o n s w e r e o b t a i n e d f r o m t h e s e d a t a b y i n t e r p o l a t i o n a n d 

p i l e n e u t r o n c r o s s s e c t i o n s e s t i m a t e d a s i n d i c a t e d i n T a b l e I I I . I n 

c a s e s w h e r e t h e c r o s s s e c t i o n i s i n s i g n i f i c a n t g e n e r a l l y o n l y t h e 2 2 0 0 m / s 

v a l u e i s l i s t e d . 

E s t i m a t e d e r r o r o f t h e c a l c u l a t e d v a l u e s i s + 1 0 0 $ [ 2 2 ] . T h e e s t i m a t e d 

c o n t r i b u t i o n t o t h e p i l e n e u t r o n c r o s s s e c t i o n s h o u l d h a v e e v e n g r e a t e r 

u n c e r t a i n t y a n d i n d i c a t e o n l y t h e o r d e r o f m a g n i t u d e . G e n e r a l l y n o e r r o r s 

a r e a s s i g n e d t o m e a s u r e d p i l e n e u t r o n c r o s s s e c t i o n s a s t h e v a l u e d e p e n d s 

o n t h e n e u t r o n s p e c t r u m . O t h e r e r r o r s s h o w n a r e f r o m s i n g l e m e a s u r e m e n t s 

o r a s s i g n e d a c c o r d i n g t o t h e d i s p e r s i o n o f s e l e c t e d v a l u e s . 

T a b l e I V s h o w s s o m e i s o m e r i c r a t i o s f o r m o r e i m p o r t a n t f i s s i o n 

p r o d u c t s w i t h m e t a s t a b l e s t a t e s . 

4. 3. T a b le o f gamma r a v s 

T h e c o m p l e t e t a b l e o f f i s s i o n p r o d u c t g a m m a r a y e n e r g i e s a n d a b s o l u t e 

i n t e n s i t i e s c a n n o t b e i n c l u d e d i n t h i s p a p e r . A l s o , t h e l a s t u p d a t e w a s m a d e 

i n 1 9 7 1 . 

E n e r g i e s a n d r e l a t i v e i n t e n s i t i e s a r e f i t t e d b y c o m p u t e r . T h e c o n 

v e r s i o n o f r e l a t i v e t o a b s o l u t e i n t e n s i t i e s i s d o n e b y h a n d a n d g i v e n a s 

i n p u t . E x a m p l e s f o r t w o f i s s i o n p r o d u c t s a r e s h o w n i n T a b l e V . T h e f i t t e d 

e n e r g i e s a n d a b s o l u t e i n t e n s i t i e s a r e p u n c h e d o n c a r d s a s w e l l a s t h e 

r e f e r e n c e n u m b e r s . 

T h e s e c a r d s a r e i n p u t t o a n o t h e r c o m p u t e r p r o g r a m . T h i s p r o g r a m p r i n t s 

o u t a t a b l e o f g a m m a r a y s s o r t e d b y f i s s i o n p r o d u c t s , a t a b l e o f g a m m a 

r a y s s o r t e d b y d e s c e n d i n g e n e r g y a n d s u b d i v i d e d i n t o t h r e e h a l f l i f e g r o u p s , 

a n d a l i s t o f r e f e r e n c e s . E x a m p l e s a r e g i v e n i n T a b l e V I . T h e h a l f l i f e 

v a l u e s s h o w n a r e s u p e r s e d e d n o w b y t h o s e i n T a b l e I I I . A l l t h e s e t a b l e s a r e 

s t o r e d o n d i s c a n d c a n b e r e c a l l e d f o r p r i n t o u t b y a n o t h e r p r o g r a m . T h e 

" O r d e r e d t a b l e o f e n e r g i e s " s e r v e s t o f a c i l i t a t e t h e i d e n t i f i c a t i o n o f 

g a m m a r a y s i n c o m p l e x s p e c t r a f r o m b u r n t f u e l e l e m e n t s . 

5 . UNCERTAINTIES IN GAMMA SPECTROMETRIC MEASUREMENTS AND FORWARD CALCULATIONS 

T h e a c t i v i t y o f a f i s s i o n p r o d u c t a t t h e t i m e o f m e a s u r e m e n t , A , i s 

c a l c u l a t e d f r o m a m e a s u r e d g a m m a s p e c t r u m f r o m t h e f o r m u l a : 

. vj __________________ 1 + D C __________________ / . \ 

P = P h o t o p e a k a r e a 

I y ~ . E F ( E ) . T . G A ( E ) ' ' 

D C = D e a d t i m e c o r r e c t i o n 

I^>*= G a m m a r a y i n t e n s i t y 

E F ( e ) = p h o t o p e a k e f f i c i e n c y f o r g a m m a l i n e w i t h e n e r g y E i n 

p o s i t i o n o f m e a s u r e m e n t ( o r s c a n n i n g e f f i c i e n c y ) 

T = M e a s u r i n g t i m e ( s e c ) 

G A ( e ) = E n e r g y d e p e n d e n t g a m m a r a y a b s o r p t i o n f a c t o r .

T A B L E IV. B R A N C H I N G R A T I O S 

f i s s i o n 

p r o d u c t 

h a l f 

l i f e a 

$/J- 

d e c a y a 

IA E A -S M -1 7 0/1 2 253 

b r a n c h i n g 

( $ ) 0 

p r e c u r s o i c r o s s s e c t i o n ( b ) ^ 

m a x w r e s . i n t . 

8 2 B r 3 5 h 1 0 0 2 . 7 + 0 . 2 e 5 5 + 5 0 

_85fiKr 

OO 

i f 

4 - 4 h 7 8 . 8 + 0 . 9 f 1 0 0 f 8 5 B r 0 . 0 9 j p . 0 1 7 

1 0 . 7 a 1 0 0 of 8 5 B r 0 . 0 3 ® 2 e 

9 5 m N b 3 . 6 d 0 1 . 8 + 0 . 5 9 5 Z r 

9 9 щ Т с 6 h 0 8 6 . 3 + 1 . 0 9 9 M o 

1 1 0 m . 

A g 2 5 2 d 9 8 . 6 + 0 . 1 3 4 . 6 7 + 0 . 0 7 7 0 + 2 

1 2 ^ е 5 8 d 0 2 2 . 3 1 2 5 s b 

1 2 7 m T e 1 0 9 d 2 . 4 + 0 . 2 1 7 . 4 1 2 7 S b 

1 2 9 " * e 3 3 . 6 d 3 6 + 7 1 6 . 6 1 2 9 S b 0 . 0 1 6 + 0 . 0 0 1 О . О 7 7 + О . О О 5 

1 3 1 m X e 1 2 d 0 1 . 3 5 + 0 . 1 1 

1 3 3 m X e 5 4 h 0 2 . 8 + 0 . 1 

148V 4 1 d 9 3 . 2 + 0 . 7 8 6 + 1 0 1 1 3 0 + 1 0 0 

1 4 8 g P m 5 - 4 d 1 0 0 6 . 8 + 0 . 7 1 4 8 n V m 9 6 + 2 1 2 7 O + I O O 

Р о г e x a c t v a l u e s e e t a b l e I I I . T h i s f i g u r e i s o n l y g i v e n t o d i s t i n g u i s h 

b e t w e e n i s o m e r i c s t a t e s . 

U n l e s s o t h e r w i s e n o t e d j l O O $ m i n u s t h e v a l u e g i v e n i s i s o m e r i c t r a n s i t i o n 

t o g r o u n d s t a t e . 

1 3 1 ! 

! 3 3 i 

0 . 0 4 

P e r c e n t a g e o f ß - d e c a y s o f r a d i o a c t i v e p r e c u r s o r ( c o l u m n 5 ) t o t h e 

f i s s i o n p r o d u c t l i s t e d i n c o l u m n 1 . 

C r o s s s e c t i o n o f i s o t o p e w i t h m a s s n u m b e r A - l f o r p r o d u c t i o n o f f i s s i o n 

p r o d u c t w i t h m a s s n u m b e r A ( c o l u m n l ) . 

S h o r t l i v e d i s o m e r i c s t a t e n e g l e c t e d . P r o d u c t i o n c r o s s s e c t i o n l i s t e d 

i n c l u d e s f r a c t i o n f r o m i s o m e r i c t r a n s i t i o n . 

I f a 1 0 0 $ d e c a y o f ° 5 ß r t o б Э г о к г i s a s s u m e d , t h i s v a l u e i s s l i g h t l y h i g h e r 

c o m p a r e d t o t h e f r a c t i o n o f 8 5 g K r o b s e r v e d i n f i s s i o n y i e l d m e a s u r e m e n t s 

( 2 1 . 6 $ - 2 2 $ [ 2 8 ] ) . T h i s m i g h t b e d u e t o d i r e c t f o r m a t i o n o f ° 5 l C r i s o m e r s 

i n f i s s i o n , b u t i s u n l i k e l y f o r 2 3 5 u f i s s i o n . T h e p o s s i b i l i t y o f a 

f r a c t i o n o f ® 5 в г d e c a y i n g d i r e c t l y t o 8 5 é f t r s h o u l d b e i n v e s t i g a t e d . 

T h e r a t i o s o f f i s s i o n y i e l d s [ 1 5 , 2 8 ] a r e r e c o m m e n d e d f o r u s e i n 

c a l c u l a t i o n s . 

0 . 2


T A B L E V . E X A M P L E S O F E V A L U A T E D G A M M A -R A Y E N E R G IE S AND 

IN T E N S IT IE S 

58 CE 141 

32.38 (+/- 0.02) DAYS HALFL IfE 

100 PERC. REL = 100. (+/- 0. ) PERC. ABS. 

ENERGY (KEV) INTENSITY (PERC.) REF 

145.49 +/- 0.03 3 

145.43 +/- 0.02 125 

145.443 +/- 0.006 125 

145.44 +/- 0.05 148 

145.41 +/- 0.03 149 

145.450 +/- 0.005 150 

145.4498 +/- 0.0049 156 

145.441 +/- 0.003 193 

49. +/- 1. 73 

ADOPTED VALUE 

1 145.444 +/- 0.002 REL 49. +/- 1. 

A8S 49. */- 1. 

SEE REF. 73 

ABSOLUTE VALUE FOR 100 PERC. REL. INTENSITY 

LIST OF REFERENCES 

3 NUCL.PHYS.. A 1 0 7 I 1968)177 

73 NUCL.DATA, A 8 / 1 - 2 U 9 7 0 ) 

82 J.NUCL.SC I.TECHN.,3/51 1966)200 

125 NUCL. DATA, A4-3-301 (1968) 

148 NUCL.PHYS., A90(1967)650 

149 NUCL.PHYS., A 9 K 1967)453 

150 NUCL.PHYS., A 1 2 9 (1969)1 

156 COO-1112-167 (1967)50 

193 NUCL.1NSTR.METH., 77(1970)141

T A B L E V (cont. ) 

IA E A -S M -1 7 0 /12 255 

63 fcU 155 

1770. (+/- 36 . ) DAYS h a l f l i f e 

100 P£RC. REL = 32.58 (+/- 1.03 ) PERC . ABS. 

NR ENERGY (KEV) INTENSITY (PERC.) REF 

1 

2 

3 

4 

18.776 +/- 0.035 0.162 +/- 0.038 212 

ADOPTED VALUE 

18.776 +/- 0.C35 REL 

ABS 

* 26.53 

26.513 +/- 0.021 

ADOPTED VALUE 

26.513 +/- 0.021 REL 

ABS 

31.55 +/- 

31.43 +/- 

0.10 

0.05 

ADOPTED VALUE 

31.45 +/- 0.05 REL 

ABS 

« 45.29 

45.299 +/- 

45.2972 +/- 

45.299 +/- 

0.002 

0.0013 

0.013 

ADOPTED VALUE 

45.2977 +/- 0.0011 REL 

ABS 

0.162 

0.053 

1. 

1.03 

1.03 

0.34 

# 0.03 

0.023 

0.023 

0.0075 

« 2.8 

3.6 

4.18 

4.1 

1.35 

+/- 0.038 

+/- 0.012 

+ /- 1. 

+/- 0.04 

+/- 0.04 

+/- 0.02 

+/- 0.02 

+/- 0.005 

+/- 0.005 

+/- 0.0016 

+/- 0.7 

+/- 0.7 

+/- 0.17 

+/- 0.2 

+/- 0.07 

79 

212 

99 

212 

79 

99 

192 

212 

* 38. 0.20 +/- 0.03 79 

57.970 +/- 0.026 0.22 +/- 0.05 99 

57.9805 + /- 0.0020 192 

57.983 +/- 0.030 0.217 +/- 0.011 212 

ADOPTED VALUE 

57.980 +/- 0.002 REL 0.215 +/- 0.010 

ABS 0.070 +/- 0.004 

* NOT USED FOR AVERAGE


T A B L E V (cont. 

NP 

10 

ENERGY (KEV) INTENSITY (PERC.) REF 

О 

• 

* 60. 3.8 + /- 0.2 79 

60.006 + /- 0.004 * 4.3 + / - 0.3 99 

60.0100 + / - 0.0018 192 

60.019 + / - 0.015 3.60 + /- 212 

ADUPTED VALUE 

60.0094 + /- 0.0016 REL 3.61 + /- 0.04 

ABS 1.18 + /- 0.04 

» 86.05 0.50 + /- 0.05 79 

86.062 + / - 0.023 0.49 + / - 0.05 99 

86.0621 + / - 0.0051 192 

ADOPTED VALUE 

86.062 + / - 0.005 REL 0.50 + / - 0.04 

ABS 0.16 + / - 0.01 

86.541 + / - 0.003 100. 99 

86.5452 + / - 0.0033 192 

86.539 + / - 0.015 100. 212 

ADOPTED VALUE 

86.5428 + / - 0.0022 REL 1 0 0 . 

ABS 32.58 + / - 1.03 

* 105.3 65. 7 + / - 6.5 76 

* 105.32 67.9 + / - 3.4 79 

105.302 + / - 0.004 68.3 + / - 2.7 99 

105.308 + / - 0.003 192 

105.315 + / - 0.015 66.8 + / - 1.3 212 

ADOPTED VALUE 

105.306 + / - 0.002 REL 67.1 + / - 1.1 

ABS 21.9 + / - 0.8 

146.2 + / - 0.2 0.16 + / - 0.05 76 

146.061 + / - 0.015 0.19 + / - 0.02 99 

0.167 + / - 0.060 254 

146.05 + / - 0.09 0. 169 + / - 0.008 212 

ADOPTED VALUE 

146.06 + / - 0.01 REL 0.172 + / - 0.007 

ABS 0.056 + / - 0.003 

* NOT USED FOR AVERAGE 

С

T A B L E V (con t. ) 

ABSOLUTE VALUE FOR 100 PERC. REL. INTENSITY 

GROUND STATE BETA TRANSITION OF 13 PRC. ASS. WAS TAKEN FROM 

B.N. SUBBA RAO, NUOVO CIM., 16(1960)283 

AS THE BETA INTENSITIES GIVEN THERE AGREE BEST WITH THOSE CALCULATED 

IN REF 212 FROM REL. GAMMA INTENSITIES ANO CONVERSION COEFFICIENTS. 

THEREFORE THE GROUND-STATE TRANSITIONS OF 60,86.5,105 AND 146 KEV HAVE TO 

TOTAL 87 PERC. THE CONV. COEFF. USED WERE THOSE GIVEN IN REF. 212,WHICH 

WERE CALCULATED FROM THE REL. К AND L C E - INTENSIT IE S OF REF. 254 NORMALIZED 

TO THE THEORET. VALUE OF ALPHA-K FOR THE 105 KEV TRANSITION (PURE El). 

THE REL. M AND N C E - I NTENSIT IE S WERE TAKEN FROM NUCL. DATA SHEETS. 

LIST OF REFERENCES 

76 NUCL.PHYS., 'A 96(1967)190 

79 NUCL.PHYS-., A 108(1968)145 

99 IS-T-290 AND NUCL.PHYS., A 153(1970)109 

192 NUCL . INSTR.METH., 87(1970)7 

2 12 NUCL.PHYS., A132I 1969) 177 

254 J .PHYS. (PARIS ) , 28( 1967)861


T A B L E V I. E X A M P L E S F R O M G A M M A LIN E T A B L E 

55 CS 134 

LIT.REF. 

8 9 

55 CS 136 

LIT.REF. 

39 40 

55 CS 137 

KEV 

749

T A B L E VI (con t. ) 

IA E A -S M -1 7 0 /1 2 259 

HALFLIFE BETWEEN 10 ANO 100 DAYS 

ORDERED TABLE OF ENERGIES 

KEV DAYS PERCENT 

818.3000 55 CS 136 12.900 100.0000 

817.2000 52 TE 129 G M 33.000 0.1470 

816.5900 51 SB 124 60.200 0.0700 

815.7680 56 BA 140 D 12.800 23.3000 

811.7000 63 EU 156 15.110 9.8000 

802.1700 52 TE 129 G M 33.000 0.2120 

794.9000 52 TE 129 G M 33.000 0.0023 

790.7600 51 SB 124 60.200 0.7400 

768.9000 52 TE 129 G M 33.000 0.0090 

765.8300 40 ZR 95 D 65.500 99.8000 

765.8300 41 NB 95 35.108 99.8000 

756.7800 40 IR 95 65.500 54.5000 

751.7700 56 BA 140 D 12.800 4.3800 

741.1000 52 TE 129 G M 33.000 0.0810 

735.7000 51 SB 124 60.200 0.1300 

729.6200 52 TE 129 G M 33.000 1.1800 

725.6500 61 PM 148 M 41.800 31.0000 

724.2300 40 ZR 95 65.500 44.2000 

723.4000 63 EU 156 15. 110 5.4000 

722.7800 51 SB 124 60.200 11.1000 

716.8000 52 TE 129 G M 33.000 0.0016 

713.8200 51 SB 124 60.200 2.5000 

709.9000 63 EU 156 15.110 1.0000 

709.3400 51 SB 124 60.200 1.3700 

705.6000 52 TE 129 G M 33.000 0.0080 

701.8000 52 TE 129 G M 33.000 0.0300 

695.9800 52 TE 129 G M 33.000 4.9600 

695.0000 51 se 126 12.500 100.0000 

685.8000 60 ND 147 11.020 0.5600 

679.4000 60 ND 147 11.020 0.0000 

672.0300 52 TE 129 G M 33.000 0.0390 

665.0000 51 SB 126 12.500 100.0000 

646.2500 63 EU 156 15.110 6.9000 

645.8400 51 SB 124 60.200 7.3000 

632.2600 51 SB 124 60.200 0.1300 

629.9000 61 PM 148 M 41.800 87.5000 

624.4000 52 TE 129 G M 33.000 0.0930 

618.2000 56 BA 140 D 12.800 0.0400 

611.5300 44 RU 103 39.600 

611.2600 61 PM 148 M 41.800 6.0000 

610.3700 , 44 RU 103 39.600 5.5000 

602.7100 51 SB 124 60.200 98.2000 

599.5000 61 PM 148 M 41.800 8.5000 

599.5000 63 EU 156 15.110 2.8700 

594.7000 60 ND 147 11.020 0.1680 

589.3000 60 ND 147 11.020 0.0290 

559.7000 52 TE 129 G M 33.000 0.0080 

557.1000 44 RU 103 39.600 0.7900 

556.6500 52 TE 129 G M 33.000 0.1780 

551.5000 52 TE 129 G M 33.000 0.0120


I n a f o r w a r d , c a l c u l a t i o n t h e a c t i v i t y A . ( T m ) o f a f i s s i o n p r o d u c t i 

( n e g l e c t i n g a l l s h o r t l i v e d p r e c u r s o r s ) a t t i m e o f m e a s u r e m e n t T m i s g i v e n 

b y t h e f o l l o w i n g f o r m u l a : 

T ir r 

j к t=0 к 

X ^ = 0 . 6 9 3 / T V . . . . d e c a y c o n s t a n t 

T i ...................... h a l f l i f e o f f i s s i o n p r o d u c t i 

. 0k(t).exp[ -(>-i-ôrfk .k). (Tm-t)] dt 

N j ( t ) . . . . n u m b e r o f a t o m s o f f i s s i l e i s o t o p e j a t t i m e t . 

f 

a .................. f i s s i o n c r o s s s e c t i o n o f f i s s i l e i s o t o p e j i n n e u t r o n g r o u p к 

с 

............... n e u t r o n f l u x i n g r o u p к 

. . . . c a p t u r e c r o s s s e c t i o n o f f i s s i o n p r o d u c t i i n n e u t r o n g r o u p к 

у. ... c u m u l a t i v e f i s s i o n y i e l d o f f i s s i o n p r o d u c t i f o r f i s s i l e i s o t o p e 

1 *' j i n n e u t r o n g r o u p k . 

( l ) a n d ( 2 ) i l l u s t r a t e h o w d i f f e r e n t s o u r c e s o f e r r o r e n t e r t h e e q u a t i o n 

u s e d f o r c a l c u l a t i o n . T h e r e q u i r e m e n t f o r n u c l e a r d a t a u n c e r t a i n t i e s i s 

t h a t t h e y s h o u l d n o t e x c e e d u n a v o i d a b l e e r r o r s a r i s i n g f r o m m e a s u r e m e n t 

c o n d i t i o n s o n t h e o n e h a n d a n d s i m p l i f i e d n e u t r o n f l u x r e p r e s e n t a t i o n i n 

c a l c u l a t i o n s o n t h e o t h e r h a n d . I n t h e f o l l o w i n g s o u r c e s o f e r r o r s a r e 

d i s c u s s e d a n d t h e a d v a n t a g e o f r a t i o m e a s u r e m e n t s i s s h o w n . 

5 . 1 . S o u r c e s o f e r r o r i n m e a s u r e m e n t s 

S o u r c e s o f e r r o r s i n g a m m a s p e o t r o m e t r i c m e a s u r e m e n t s a r e d i s c u s s e d b e l o w a n d 

s u m m a r i z e d i n T a b l e V I I . 

5 . 1 . 1 . D e t e c t o r c a l i b r a t i o n 

E n e r g y c a l i b r a t i o n o f t h e d e t e c t o r s e r v e s o n l y f o r i d e n t i f i c a t i o n 

o f f i s s i o n p r o d u c t g a m m a l i n e s . T h e g a m m a r a y e n e r g i e s o f c a l i b r a t i o n 

s t a n d a r d s a n d m a i n f i s s i o n p r o d u c t s a r e s u f f i c i e n t l y w e l l k n o w n f o r t h i s 

p u r p o s e a n d t h e i r u n c e r t a i n t i e s h a v e a n e g l i g i b l e e f f e c t o n t h e e n e r g y 

d e p e n d e n c e o f d e t e c t o r e f f i c i e n c y . 

T h e p h o t o p e a k e f f i c i e n c y o f a d e t e c t o r ( c o u n t s i n t h e p h o t o p e a k p e r 

у - q u a n t e m i t t e d f r o m t h e s o u r c e ) i s c a l i b r a t e d w i t h t h e a i d o f g a m m a 

e m i t t i n g s t a n d a r d s . P r i m a r y s t a n d a r d s w i t h w e l l k n o w n d e c a y s c h e m e s a n d 

k n o w n d é s i n t é g r a t i o n r a t e s a r e u s e d t o d e t e r m i n e t h e a b s o l u t e d e t e c t o r 

e f f i c i e n c y f o r d i f f e r e n t e n e r g i e s . A b s o l u t e g a m m a r a y i n t e n s i t i e s a r e 

k n o w n t o b e t t e r t h a n 1 $ f o r t h e m a j o r i t y o f p r i m a r y s t a n d a r d s . 

T h e s p e c i f i e d a b s o l u t e d i s i n t e g r a t i o n r a t e s o f s t a n d a r d s o u r c e s a r e 

g e n e r a l l y d e t e r m i n e d i n d e p e n d e n t o f a k n o w l e d g e o f d e c a y s c h e m e s . T h e 

a c c u r a c y o f a v a i l a b l e s t a n d a r d s r a n g e s f r o m b e t t e r t h a n V¡> ( v e r y t h i n s o u r c e s ) 

u p t o s e v e r a l p e r c e n t . 

T h e e n e r g y d e p e n d e n c e o f t h e d e t e c t o r e f f i c i e n c y c a n b e d e t e r m i n e d w i t h 

t h e a i d o f s e c o n d a r y s t a n d a r d s e m i t t i n g a n u m b e r o f s t r o n g g a m m a r a y s w i t h 

a c c u r a t e l y k n o w n r e l a t i v e i n t e n s i t i e s ( b e t t e r t h a n 1% f o r a n u m b e r o f

IA E A -S M -1 70/12 261 

T A B L E VH. E R R O R S O F M E A SU R E M E N T S O F FISSIO N 

PR O D U C T A C T IV IT IE S 

A b s o l u t e e f f i c i e n c y c a l i b r a t i o n 

( s t a n d a r d s o u r c e ) 

M i n i m u m ' A v e r a g e 


5 . 1 . 3 . D e a d t i m e c o r r e c t i o n 

S e r i o u s e r r o r s c a n b e i n t r o d u c e d i n s c a n n i n g m e a s u r e m e n t s o f f u e l r o d s , 

i f t h e a c t i v i t y v a r i e s s t r o n g l y a l o n g t h e r o d a n d d e a d t i m e c o r r e c t i o n s 

a r e l a r g e a t p o i n t s o f h i g h a c t i v i t y . A s a l s o a r e a s o f l o w a c t i v i t y a r e 

m e a s u r e d t h e m e a s u r e d t o t a l a c t i v i t y o f t h e f u e l r o d w i l l b e t o o l o w . 

E r r o r s i n d e a d t i m e c o r r e c t i o n s a r e e s t i m a t e d t o b e l e s s t h a n 1 % t o 5 $ 

[ 1 2 , 3 7 ] , d e p e n d i n g o n t h e m a g n i t u d e a n d v a r i a t i o n o f d e a d t i m e . 

5 . 1 . 4 . G a m m a r a y a b s o r p t i o n 

T h e a b s o r p t i o n o f g a m m a r a y s i s e n e r g y d e p e n d e n t . T a b u l a t e d g a m m a r a y 

a b s o r p t i o n c o e f f i c i e n t s a r e d e r i v e d m a i n l y t h e o r e t i c a l l y a n d h a v e a n u n 

c e r t a i n t y o f a b o u t 1 C $ > [ 3 8 , 3 9 ] . A d d i t i o n a l e r r o r s a r i s e f r o m i n h o m o g e n i t y 

o f a b s o r b i n g m a t e r i a l i n f u e l e l e m e n t s . T h e m a g n i t u d e o f t h e e r r o r d e p e n d s 

o n s i z e a n d t y p e o f t h e f u e l e l e m e n t a s w e l l a s o n t h e w a y t h e c o r r e c t i o n 

i s c a l c u l a t e d ( c o m p u t e r o r b y h a n d ) a n d i s a b o u t 2 - 2 C $ [ 1 2 ] . I t s h o u l d 

b e p o s s i b l e t o r e d u c e t h i s e r r o r b y d e t e r m i n i n g t h e a b s o r p t i o n e x p e r i m e n t a l l y 

w i t h u n i r r a d i a t e d f u e l e l e m e n t s a s a b s o r b e r s . 

5 . 1 . 5 * D e t e r m i n a t i o n o f p e a k a r e a . 

T h e a c c u r a c y o f t h e d e t e r m i n a t i o n o f p e a k a r e a s d e p e n d s m a i n l y o n t h e 

n u m b e r o f c o u n t s a c c u m u l a t e d ( w h i c h i n t u r n d e p e n d s e n t i r e l y o n t h e t i m e 

a v a i l a b l e f o r a m e a s u r e m e n t ) , t h e b a c k g r o u n d c o r r e c t i o n s a n d t h e i n t e r 

f e r e n c e o f o t h e r p e a k s . 

T h e b a c k g r o u n d i s i n c r e a s e d b y s c a t t e r i n g o f p h o t o n s i n c o l l i m a t o r a n d 

s u r r o u n d i n g . I t c a n b e g r e a t l y r e d u c e d b y a p p l i c a t i o n o f c o m p t o n s u p r e s s e d 

s p e c t r o m e t e r s o r C o m p t o n c o i n c i d e n c e s p e c t r o m e t e r s . B e s t r e s u l t s a r e o b t a i n e d 

b y p e a k s h a p e a n d b a c k g r o u n d f i t w i t h c o m p u t e r s , w h i c h i s i n d i s p e n s a b l e 

f o r r e s o l u t i o n o f c o m p o s i t e p e a k s . 

5 . I . 6 . A d v a n t a g e s o f a c t i v i t y r a t i o s 

T h e a d v a n t a g e s o f t h e u s e o f a c t i v i t y r a t i o s f o r i n t e r p r e t a t i o n b e c o m e 

o b v i o u s f r o m t h e s o u r c e s o f e r r o r d i s c u s s e d a b o v e . F i r s t O f a l l a c t i v i t y 

r a t i o s d e p e n d o n l y o n t h e a c c u r a c y o f t h e r e l a t i v e e f f i c i e n c y o f t h e 

d e t e c t o r . T h e c o m b i n e d e f f e c t o f g a m m a r a y a b s o r p t i o n a n d e d g e e f f e c t o f 

c o l l i m a t o r s n e e d s o n l y t o b e a c c o u n t e d f o r a s c h a n g e o f t h e r e l a t i v e 

e f f i c i e n c y a n d c a n b e d e t e r m i n e d b y i n t e r c o m p a r i s o n o f a c t i v i t i e s c a l c u l a t e d 

f r o m g a m m a r a y s o f t h e s a m e f i s s i o n p r o d u c t , w h i c h a r e d i f f e r e n t i n 

e n e r g y ( m u l t i l i n e e v a l u a t i o n ) . U n c e r t a i n t i e s c a n b e f u r t h e r r e d u c e d b y 

c o m p a r i s o n o f g a m m a l i n e s w i t h s i m i l a r e n e r g i e s . F u r t h e r a l l e r r o r s c a n c e l , 

t h a t a r e c o m m o n t o b o t h f i s s i o n p r o d u c t s s u c h a s f i n i t e s o u r c e a r e a o r 

d e a d t i m e c o r r e c t i o n . 

5 . 2 . U n c e r t a i n t i e s i n n u c l e a r d a t a 

I n t h e f o l l o w i n g w e c o n s i d e r t h e i n f l u e n c e o f e a c h t y p e o f n u c l e a r d a t a 

s e p a r a t e l y a n d a s s u m e t h a t t h e o t h e r n u c l e a r d a t a i n v o l v e d i n t h e s a m e e q u a t i o n 

c o n t r i b u t e n o e r r o r . F u r t h e r w e a s s u m e o p t i m a l e x p e r i m e n t a l c o n d i t i o n s . 

5 . 2 . I . G a m m a r a y i n t e n s i t i e s 

I t c a n b e s e e n f r o m e q u a t i o n ( l ) t h a t a n y a r r o r i n t h e g a m m a r a y i n t e n s i t y 

h a s a l i n e a r e f f e c t o n t h e r e s u l t . M i n i m u m e r r o r s i n t h e o t h e r f a c t o r s o f 

e q u a t i o n ( . l ) c o n t r i b u t i n g t o t h e d e t e r m i n a t i o n o f a b s o l u t e a c t i v i t i e s a r e : 

(see also Table VII)

a ) L e s s t h a n 1 $ f o r s m a l l s a m p l e s 

IA E A -S M -1 7 0 /1 2 

b ) I n r o u t i n e m e a s u r e m e n t s o f f u e l e l e m e n t s : 

- 1 ч Т С : l e s s t h a n 1 $ 

- E F ( e ) : 1 $ i f c l o s e t o g a m m a e n e r g y o f c a l i b r a t i o n s t a n d a r d w i t h 

a c c u r a c y й 1 $ . O t h e r w i s e 2 - 3 $ . 

- G A ( e ) : lf o f o r m u l t i l i n e e v a l u a t i o n , 2 $ f o r c a l c u l a t i o n [ 1 2 ] . 

c ) A c t i v i t y r a t i o s : 

- E F ( e ) : l e s s t h a n 1 $ t o 2 $ f o r t h e c a s e s l i s t e d i n b ) 

- C A C E ) m a y c a n c e l , o t h e r f a c t o r s c a n c e l . 

T h e r e f o r e t h e g a m m a r a y i n t e n s i t i e s s h o u l d h e k n o w n t o V fo b e t t e r . T h i s 

i s f u l f i l l e d o n l y f o r t h e m o s t i n t e n s e g a m m a r a y s o f ' ^ Z r , 95Nb, ^ l l , 134cs, 

1 3 ? C s a n d p a r t i a l l y l ^ O b a . T h e e r r o r o f l y - d i s a p p e a r s , i f s t a n d a r d s o u r c e s 

o f t h e f i s s i o n p r o d u c t s m e a s u r e d i n g a m m a s p e c t r a o f f u e l e l e m e n t s a r e u s e d 

f o r c a l i b r a t i o n . 

E q u a t i o n ( 2 ) i s l i n e a r i n t h e f i s s i o n y i e l d s . T h e r e f o r e t h e r e l a t i v e 

e r r o r o f t h e f i s s i o n y i e l d , w e i g h t e d b y N . ( t ) 6 ”^ ^ ( t ) , a p p e a r s i n t h e 

s a m e a m o u n t a s e r r o r o f t h e r e s u l t , w h i c h ( T ra) i n a f o r w a r d c a l c u 

l a t i o n a n d N j ( 0 ) , ¡6 ( t ) o r b u r n u p ( / N ( t ) 6 * " 0 ( t ) ) i n a b a c k w a r d c a l c u l a t i o n . 

E x c e p t f o r A . ( T m ) , N . ( t ) a n d ( t ) a l l f a c t o r s i n e q u a t i o n ( 2 ) a r e 

n u c l e a r d a t a . T h e a c c u r a c y r e q u i r e d f o r t h e f i s s i o n y i e l d s d e p e n d s o n 

t h e k n o w l e d g e o f i r r a d i a t i o n h i s t o r y , n e u t r o n f l u x a n d f u e l c o m p o s i t i o n , 

w h e t h e r a c t i v i t y r a t i o s a r e c o n s i d e r e d a n d w h a t t h e a i m o f t h e i n t e r 

p r e t a t i o n i s . 

I f w e c o n s i d e r a c t i v i t y r a t i o s a n d a s s u m e t h a t f a s t f i s s i o n s a r e 

n e g l i g i b l e a n d t h e f i s s i o n y i e l d ’ r a t i o i s t h e s a m e f o r t h e r m a l a n d e p i 

t h e r m a l n e u t r o n s , t h e u n c e r t a i n t y o f t h e c a l c u l a t e d a c t i v i t y r a t i o 

d e p e n d s o n l y o n t h e a c c u r a c y o f t h e f i s s i o n y i e l d s ( k n o w n i r r a d i a t i o n 

a n d f u e l p a r a m e t e r s ) . 

I f o n e w a n t s t o d e d u c e i n f o r m a t i o n f r o m m e a s u r e m e n t s , t h e m i n i m u m 

e r r o r o f a n a c t i v i t y r a t i o i s l e s s t h a n Vfo t o 2 $ , o f a b s o l u t e a c t i v i t i e s 

( r o u t i n e m e a s u r e m e n t s ) 1 - 3 $ . 

- I f t h e i n f o r m a t i o n i s d e d u c e d f r o m k n o w n i r r a d i a t i o n h i s t o r y a n d f u e l 

c o m p o s i t i o n , t h e u n c e r t a i n t i e s o f f i s s i o n y i e l d s s h o u l d n o t e x c e e d t h e 

e r r o r o f m e a s u r e m e n t s . 

- I f t h e i n f o r m a t i o n h a s t o b e d e d u c e d f r o m u n k n o w n i r r a d i a t i o n h i s t o r y , 

t h e u n c e r t a i n t i e s i n v o l v e d e x c e e d e x p e r i m e n t a l e r r o r s . 

U n c e r t a i n t i e s o f a v a i l a b l e f i s s i o n y i e l d d a t a a r e n o t c l e a r a n d s h o u l d 

b e s u b j e c t o f a c a r e f u l a s s e s s m e n t . T h e r e a r e d i s c r e p a n c i e s a m o n g e x p e r i m e n t a l 

a n d a m o n g e v a l u a t e d d a t a a n d t h e p h i l o s o p h y i n a s s i g n i n g e r r o r s i s n o t u n i q u e . 

5 . 2 . 3 . N e u t r o n c r o s s s e c t i o n s a n d h a l f l i v e s 

F o r t h e f i s s i o n c r o s s s e c t i o n s t h a t a p p e a r i n e q u a t i o n ( 2 ) , t h e s a m e 

a r g u m e n t s a r e v a l i d a s f o r f i s s i o n y i e l d s , e x c e p t t h a t t h e i r v a l u e s 

c a n c e l i n r a t i o m e a s u r e m e n t s . 

A b s o r p t i o n crosB s e c t i o n s a n d h a l f l i v e s a p p e a r i n e x p o n e n t i a l 

f u n c t i o n s . T h e i n f l u e n c e o f t h e i r u n c e r t a i n t i e s o n r e s u l t s i s t h e r e f o r e 

a f u n c t i o n o f t i m e a n d w i l l b e i l l u s t r a t e d b y s o m e e x a m p l e s . 

263


5.3. Examples of calculated errors 

5 .З.1 . Errors due to incorrect half life. 

For some of the most important fission products errors in forward 

and backward calculation arising from errors in half lives were calculated 

for typical irradiation conditions and cooling time. The errors were calculated 

relative to the half lives shown in Table III. 

Errors in forward calculation are given in Table Villa. They are 

total errors including irradiation time. Table VUIb lists the errors 

of decay corrections from the cooling time shown to reactor shutdown. 

The errors listed under zero cooling time arise only from correction 

for decay during irradiation and were calculated only for fission products, 

that serve as burnup monitor. The error of the calculated burnup is then 

the combined error from cooling time and irradiation time. 

All errors listed in Table Villa and b are relative to our recommended 

half lives or relative to activities calculated from these values. The 

half life values shown in these tables are either previously adopted 

values (95zr, 1 ° 3 r u , W e e ) or discrepant values included in the average 

(l°ÓRu, 137 Cs) or from a recent experiment (1311), Por 134cs the uncertainty 

of our recommended half life (Table III) was used. These half 

lives were selected to illustrate what errors can arise from their use or 

if some of these values were correct and not those shown in Table III. 

For Cel44 measured half lives are consistent and errors calculated in 

the same manner are well below 1%. The errors listed for 95Nb are only 

due to the 95Zr half life. 

Errors in shutdown activities do not change in magnitude from those 

listed in Table Villa, if the irradiation time is 1 year and approaches 

zero for longer irradiation time (equilibrium). Errors in correction for 

Hooay during cooling time can be estimated from a more general relationship. 

The ratio of the error in the result to the error in the half life varies 

linearily with the ratio of cooling time to half life for small ratios. 

This relationship holds approximately also for larger values of these 

ratios. The line goes through zero and the error of the result is equal 

to the error of the half life if the cooling time is about 1 .5 half lives. 

The percent uncertainties of our recommended half lives are: 

0*2 (95zr), O.25 (103Ru), 0.55 (106Ru), O.25 (131l), 1 (134Cs), 

O.67 (!37cs)i 0.O6 (14lce) and 0.14 (l44Ce). A comparison with Tables VIII 

a and b shows that they introduce no serious uncertainties at reasonable 

cooling times. However, some of these half lives have to be confirmed by 

further measurements ($5zr, 1®3rUj 141ce ) or might change after new 

measurements (^ “Ru, 131l). 

5.3 .2 . Errors due to incorrect neutron capture cross section. 

For most of the fission products measured gamma spectrometrically neutron 

capture is negligible under normal irradiation conditions. The only exceptions 

are 134cs and 5Êu which yield information about the neutron flux. For 

illustration we calculated the uncertainty of the 134qs/137Cs activity 

ratio at shutdown arising from the ifo uncertainty of the thermal neutron 

cross section of 133cs. The results for a neutron flux of 5 x 10^3 n/cm^s 

are: 

Error of ratio l.d fo after 1 year irradiation, l . j f o after 2 year irradiation.

IA E A -S M -1 7 0 /1 2 

T A B L E V illa . E R R O R S IN "F O R W A R D " C A L C U L A T IO N 

F i s s i o n 

p r o d u c t 

9 5 Z r 

H a l f L i f e e r r o r s i n r e s u l t (f>) a f t e r c o o l i n g t i m e o f 

v a l u e e r r o r s 0 1 0 d 3 0 d t a 1 a 2 a 

6 5 - 5 d 2 . 4 0 . 8 1 . 1 1 . 6 5 . 6 I O . 5 2 1 

9 5 M b f r o m 9 5 Z r 0 . 8 0 . 8 1 

265 

3 . 5 7 . 7 1 8 

1 0 3 R u 3 9 - 6 d 0 . 6 4 0 . 1 2 0 . 2 3 0 . 5 2 . 2 5 . 6 

106RU 3 7 1 d 0 . 7 - 0 . 1 6 - 0 . 1 5 - O . 1 3 + 0 . 0 7 + 0 . 3 + 0 . 8 

! 3 ! i 

7 . 9 7 d l . l 0 . 0 4 1 2 . 9 

1 3 4 C s 1 0 . 8 0 . 8 0 . 8 0 . 6 0 . 4 0 . 1 

1 3 7 C s 2 9 . 2 a 2 . 7 2 . 7 2 . 6 2 . 5 

1 4 1 C e 3 2 . 3 8 d 0 . 5 

0 . 0 8 0 . 2 0 . 4 2 

T A B L E V UIb. ER R O R S IN "B A C K W A R D " C A L C U L A T IO N 

Fission Half Life errors in result (fo) after cooling time of 

value error$ 0 lOd 3 0 d £a la 2a 

95Zr 6 5 - 5 d 2 . 4 3 . 1 О . 2 5 0 . 7 5 4 . 5 8 . 8 1 7 

95Nb from 95Zr 0 . 0 1 0 . 1 6 2 . 6 6 . 4 I 4 . 5 

103Ru 3 9 . 6 d 0 . 6 4 0 . 1 1 0 . 3 3 2 4 

106 Ru 3 7 1 d 0 . 7 0 . 5 0 . 0 1 0 . 0 4 0 . 2 3 О . 4 6 0 . 9 

1 3 ! i 

7 - 9 7 d 1 . 1 1 2 . 9 

1 3 4 Gs . 1 0 . 0 1 0 . 0 7 0 . 1 7 0 . 3 5 0 . 7 

137Cs 2 9 . 2 a 2 . 7 0 . 0 8 0 0 0 . 0 3 0 . 0 6 0 . 1 3 

141Ce 3 2 . 3 8 d 0 . 5 0 . 1 1 0 . 3 4 2.1 4 . 2 

^tot “ 5 x 10 3 nycm2 irradiation time = 2 years 

The error of this ratio increases with decreasing integrated neutron 

flux and approaches 7f> for (almost) zero irradiation time. The uncertainty 

of the resonance integral should have the same effect on the ratio hut 

the magnitude depends in addition on the neutron spectrum. 

Generally uncertainties in neutron cross-sections are rather large. 

Results of calculations depend on the neutron spectrum and thus on the flux 

model used. Here a comparison of calculations using point cross section data 

with integral measurements of fission product absorption in different neutron 

spectra should help to clarify what flux representations are to be used in 

calculations. Work in this drection is in progress at Petten, Studsvik and 

Idaho.


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M i c r o s c o p i c N e u t r o n D a t a , I A E A , V i e n n a ( 1 9 7 2 ) . 

[ 3 2 ] L E M M E L , H . D . , A X T O N , E . J . , D E R U Y T T E R , A . J . , L E O N A R D , B . R . , J r . 

S T O R Y , J . S . , D U N F O R D , C . H . , T h i r d E v a l u a t i o n o f t h e 2 2 0 0 m / s N e u t r o n 

C o n s t a n t s f o r f o u r f i s s i l e N u c l i d e s . 

L E M U E L , H . D . , I A E A , p r i v a t e c o m m u n i c a t i o n s D e c e m b e r 1 9 7 2 a n d F e b r u a r y 1 9 7 3 . 

[ 3 3 ] H A N N A , G . C . , W E S T C O T T , C . H . , L E M M E L , H . D . , L E O N A R D , B . R . , J r . 

S T O R Y , J . S . , A T T R E E , P . M . , A t o m . E n e r g y R e v i e w 7 ( 1 9 6 9 ) 3 . 

[ 3 4 ] B E S T C O T T , C . H . , A . E . o f C a n a d a r e p o r t A E C L - 1 1 0 1 ( i 9 6 0 ) . 

[ 3 5 ] F A B R Y , A . , D E C O S T E R , M . , M I N S A R T , G . , S H E P E R S , J . C . , V A N D E P L A S , P . , 

I n t . C o n f . N u c l e a r D a t a f o r R e a c t o r s ( P r o c . S ÿ n ç i o s . H e l s i n k i , 1 9 7 0 ) 

2 , I A E A , V i e n n a ( 1 9 7 0 ) 5 3 5 - 

' 3 6 ] W A L K E R , W . H . , A . E . o f C a n a d a r e p o r t A E C L - 3 0 3 7 t P a r t I ( 1 9 6 9 ) . 

" 3 7 ] H I C K , H . , p r i v a t e c o m m u n i c a t i o n . 

3 8 " D A V I S S O N , C . M . , " G a m m a - R a y A t t e n u a t i o n c o e f f i c i e n t s " , A p p . 1 , 

A l p h a - , B e t a - a n d G a m m a - r a y S p e c t r o s c o p y ( S I E G B A H N , K . , E d ) , _ 1 , 

N o r t h - H o l l a n d , A m s t e r d a m ( 1 9 6 5 ) 8 2 7 . 

[ 3 9 ] STORM, E . , I S R A E L , H . I . , N u c l e a r D a t a T a b l e s A 7 ( 1 9 7 0 ) 5 6 5 . 

DISCUSSION 

D. J . H O REN : Of th e ra d io is o to p e s th a t you c o n s id e r in y o u r w ork, 

how m an y h ave a b so lu te n o rm a liz a tio n s known to < 1%? 

M . L A M M E R : T h e ab so lu te in te n s itie s of th e s tro n g e s t g a m m a r a y s 

of 95Z r , 95Nb, 106R u -106R h , 134 C s , 137C s and 140B a - 140L a a r e known to 

b e tte r than 1%, but not th o se of 141C e and 144C e - 144P r . 

B . G R IN B E R G : I think you a r e rig h t in em p h a siz in g th at the a c c u r a c i e s 

c la im e d by th e a u th o rs of p ublished m a te r ia l should be su b je cte d to s e rio u s 

c r i t i c a l e x a m in a tio n , s in c e th e e r r o s a r e g e n e ra lly c o n sid e ra b ly g r e a te r 

th an s ta te d . 

M . L A M M E R : W hat I said w as th a t the e r r o r s a s quoted by the a u th o rs 

a r e v e r y often m u ch s m a lle r than th ey r e a lly a r e , s o the m a t t e r , indeed, 

n eed s in v e stig a tio n . 

D. J . H O REN : A s P r o f e s s o r G rin b e rg h a s pointed out, the e x p e rim e n 

t a l i s t s a r e s o m e tim e s o v e rly o p tim is tic , and th is o p tim ism m a y exten d to 

th e ir h a lf-life m e a s u re m e n ts . H ow ev er, the c r i t i c a l ev alu atio n of h a lf- 

liv e s is often v e r y d ifficu lt b e ca u se a u th o rs u su a lly do not give su fficie n t 

in fo rm a tio n in th e ir p a p e rs to p e rm it su ch an ev alu atio n to be m ad e. 

D. B E R É N Y I: W hat is the o rig in of the h a lf-life d ata in T a b le II, and 

w hat d a ta w e re in clu d ed ? 

M . L A M M E R : W e u sed a ll a v a ila b le r e f e r e n c e s in clu ded in N u cle a r 

D a ta , P a r t В " R e c e n t R e f e r e n c e s " , p ublished up to the autum n of 1 9 7 2 . 

C. B E E T S : I would m e r e ly lik e to e m p h a siz e th e v alu e of the m eth od 

p re s e n te d fro m th e point of view of s a fe g u a rd s . Its p o s s ib ilitie s a r e b eing 

a n a ly se d at p re s e n t in an e x p e rim e n t on ir r a d ia te d p ow er r e a c t o r fuel fo r 

the p u rp o se of exten d in g the c o r r e la tio n tech n iq u e to a m o re im p o rta n t p a rt 

of the fuel c y c le , n a m e ly , fro m th e end of irra d ia tio n (s to ra g e pool fo r 

irra d ia te d a s s e m b lie s at the r e a c t o r s ite ) to the d is s o lv e r of the r e p r o 

c e s s in g p lant. T h is e x p e rim e n t, w hich is known a s M O L IV, is b eing


c a r r i e d out by the E u ro p e a n A ss o c ia tio n fo r S a fe g u a rd s in co lla b o ra tio n 

w ith the A gen cy , the B a te lle M e m o ria l In stitu te and the U nited S ta te s A rm s 

C o n tro l and D isa rm a m e n t A gen cy (ACD A). 

C . W E IT K A M P : In co m p ilin g T a b le II of y o u r p a p e r, did you m e r e ly 

adopt fig u re s fro m the l i t e r a t u r e , o r did you m ak e a c r i t i c a l evalu atio n of 

y o u r own? In th e l a t t e r c a s e , how f a r did you go in th e evalu atio n o r r e - 

e v a lu atio n of p ublished h a lf-liv e s ? 

M . L A M M E R : F o r a ll p r e - 1 9 7 0 m e a s u re m e n ts , we re lie d on the 

s e le c tio n of M a rtin and B l ic h e r t-T o f t, a s in d icated in the full te x t of the 

p a p e r. We su b je cte d a ll sub seq u ent p u b licatio n s to a c r i t i c a l exam in a tio n 

and m ad e c e r ta in s e le c tio n s . We took w eigh ted a v e r a g e s w h ere a p p ro p ria te 

and a ssig n e d h ig h e r u n c e rta in tie s in c a s e s of d is c re p a n c ie s .

AN ANALYSIS OF CLAIMS AND AVAILABLE 

RADIOACTIVE DATA FOR SAFEGUARDS 

D. BERENYI 

Institute of Nuclear Research 

of the Hungarian Academy of Sciences, 

Debrecen, Hungary 

Abstract 

AN A N A L Y S IS OF C L A IM S A N D AVAILABLE R A D IO A C T IV E D A T A FOR SAFEG UARD S. 

IA E A -S M -170 /1 

O n th e o c c a s io n o f th e First M e e tin g o f th e In te rn a tio n a l W ork in g G rou p o n N u c le a r S tru ctu re and 

R e a c tio n D ata at th e IA E A , a n u m b er o f requests and p r io r ity lists w e r e p resen ted fr o m th e d iffe r e n t a p p lic a t io n 

fie ld s o f n u c le a r d a ta . O f th e s e , o n e o f th e r e la t iv e ly m o st d e t a ile d and c o n c r e t e on e s w as th e list o f n o n - 

n eu tron n u c le a r d a ta n e e d s for sa feg u a rd s d e v e lo p m e n t pu rp oses, w h ic h w as .p u b lish ed du rin g th e y e a r in a 

m o r e c o n c is e and m o d ifie d fo r m , as an IA E A R ep ort. 

O n th e basis o f th e a b o v e lists, a c o m p a r is o n o f th e re q u e ste d and a v a ila b le d a ta has b e e n c a r r ie d o u t. 

T h e m o st stro n gly ex p ressed c la im s a re fo r th e h a lf - li v e s o f 95 Z r , 106 Ru, 134 C s, 137 C s, 140 Ba and 144 C e as w e ll 

as th e g a m m a y ie l d p e r b e ta d e c a y f o r 5 5Z r , 106Ru, 134C s, l 3 1C s, 140L a a n d 144C e w ith an a c c u r a c y o f o n e p er 

c e n t , in g e n e r a l. 

T h e resu lts o f th e a n a ly sis a re g iv e n in ta b le s . C o n c lu s io n s a re draw n and s o m e su g g estion s are g iv e n for 

fu rth er e x p e r im e n t a l tasks, fo r th e use o f th e f a c i li t ie s o f th e O a k R id g e N u c le a r D ata C en ter (R e c e n t R e fe r e n c e s , 

N u c le a r D a ta S h eets, ta b le s o f s e le c t e d r a d io a c t iv e is o to p e s , c o m p u t e r iz e d f i l e o f re fe re n c e s ) and for th e req u est 

lists. 

1. Introduction 

As is well known, an International Working Group on 

Nuclear Structure and Reaction Data was convened by the IAEA 

in March, 1972, with the aim of promoting the compilation, 

evaluation and dissemination of nuclear structure and reaction 

data. During the first session of this group, a number of 

requests and priority lists were presented from the different 

fields of application of nuclear data. The relatively most 

detailed and concrete among these was the list of non-neutron 

nuclear data needs for safeguards [1]. In June, 1972, an even 

more clearly arranged but shorter list of the above claims 

was published [2], and this latter one is, first of all, the 

basis of the present analysis. 

The main goal is here to test the utility of the Nuclear 

Data Group /Oak Ridge, Tennessee/ data accumulation systems 

/data sheets, data tables, recent references, data file of 

references/ for safeguards purposes and to compare the accuracy 

269

270 BERENYI 

claims for radioactive data with the accuracy of the recent ex 

perimental data. At the same time we compile the recent radio 

active data necessary for safeguards. 

2. Results of the analysis 

The results of the present analysis are summarized in 

Tables I and II for the half-lives and gamma yields, respectively, 

of the radioactive nuclides in question. When compiling the 

tables, the Recent References issues of Nuclear Data Sheets 

published in the last two years [3-10], the Nuclear Data Sheets 

/for S5Zr/ [11], the computerized data file of the Oak Ridge 

Nuclear Data Center /for 134Cs/ tl2] and the Nuclear Data Tables 

for 105 radioactive atoms published by the Oak Ridge Nuclear 

Data Group [13] were used. In the last tabulation, the "best" 

values for half-lives, intensities etc. for each of the atomic 

and nuclear radiations emitted by the chosen 105 radioactive 

atoms are given in tabular form. The "best” values mentioned 

above are partly adopted, partly averaged data. 

In the present tables, besides the data and references, 

the priority, assignment from ref. [2] and the relative experi 

mental and claimed accuracy are also indicated. Where more 

than one datum is available for the requested quantity, the 

most accurate experimental value is underlined. 

3. Discussion and conclusions 

As can be seen from the tables, the claimed radioactive 

decay data are available in the recent literature with the 

necessary accuracy in the case of the half-lives. As regards the 

gamma yields, the situation is definitely worse. Especially for 

134Cs and 1ччСе, more accurate measurements are needed. The 

data, however, are nearly satisfactory in the case of 95Zr, 

106Ru(106Rh) and 140La /as to the most intensive gamma rays 

here/. The experimental gamma yield value perfectly meets 

the claims for 137Cs. 

On the basis of the present analysis, we can state the 

good utility of the facilities of the Oak Ridge Nuclear Data 

Group. The data obtained by this way are, in general, more 

recent and accurate or reliable /in the cases in which I was

IA E A -S M -1 7 0 /1 271 

able to check them/ than those suggested in the recent safe 

guards publication [2]. E. g. the gamma yield for the 661.64 

keV gamma ray of 137Cs is 84.2 /without any error/ in one of 

the suggested literature [33] and 85.7±0.9 in the other [3^3- 

Our corresponding value is 84.6+0.4 /see Table II/. The same 

quantity is 41.7 in [33], 43.7±1.0 in [3*0 and our datum is 

43.5±0.5 /in Table II/. In the case of 13i*Cs there is no 

reference to the 98.4±1 value in [3^3 and, in this way( the 

reliability of the accuracy of this datum is doubtful. 

Summing up the experiences in connection with the 

nuclear data accumulation system of the Oak Ridge Nuclear 

Data Group, from the point of view of the safeguards claims, 

one can say the following: The most complete and recent 

information in connection with the decay data of an actual 

nuclide can be obtained if the computerized file of references 

of the Group is used /in the present analysis e. g. for 

13“Cs/. In these files all the post-1959 literature is 

included. These practically do not contain more information 

than the Recent References issues of the Nuclear Data Sheets 

periodical except that the files are more concise and easy 

to survey. It means that the Recent References issues are 

usable in every respect beside the Oak Ridge file. If there 

exists a similar evaluated compilation of data as [13] or a 

recent Nuclear Data Sheets for the actual А-chain, then the 

use of the Recent References or the files is necessary only 

for the period after the completion of the compilation in 

question, i. e. the actual Sheets or specified tabulations. 

This is a reason why the following sources of in 

formation were used during the present analysis in detail. 

For 106R u ( 1 06Rh) , 1 37Cs , 1 40Ba, 1I*0La and 1 ““Ce the Martin 

and Blichert-Toft [13] table and the Recent References issues 

from 1970-72 [3-10] were used, for 13

T A B L E I. H A L F -L IF E O F R A D IO A C T IV E N U CLID ES F O R SA FEGUARDS 

Radioactive 

nuclide, 

Priority 

assignment 

131*Cs 

I. 

1 37Cs 

I. 

9 5 Z r 

IX. 

i°eRu(i°eRh) 

a D a ta w ith th e s m a lle s t error a re u n d e rlin e d . 

Recent experimental data® 

Half-life Reference Experimental 

accuracy, % 

2.058 ± 0.012 y 1972 [14] 0.6 1 

30.0 ± 0.5 y 

30.64 ± 0.43 y 

29.901 ± 0.045 y 

65.5 + 0.5 d 

63.98 ± 0.06 d 

1970.[13] 

1970 [15] 

1970 [16] 

1970 [13] 

1971 [17] 

1.7 

1.4 

0.15 

0. 8 

0.09 

369 ± 2 d (Ru) 1970 [13] 0.5 1 

30.4 ± 0.5 s (Rh) 1970 [13] 1.6 1 

Claimed 

accuracy, % 

1 

1

T A B L E I . CONTIN U ATIO N 

Radioactive 

nuclide, 

Priority 

assignment 

Recent experimental data* 

Half-life Reference Experimental 

accuracy, % 

1 “°Ba 12.8 ±0.1 d 1970 [13] 0. 78 1 

II. 

14 “Ce 

II. 

a D a ta w ith th e s m a lle s t error are u n d e rlin e d . 

12.789 ± 0.006 1971 [18] 0.05 

287.5 ± 3.5 d 1967 [19] 1.2 1 

284 ± 1 d 1970 [13] 0. 35 

Claimed 

accuracy, %

T A B L E II. Y IELD O F G A M M A Q U A N T A P E R B E T A D E C A Y E V E N T F O R SA F E G U A R D S a 

Radioactive 

nuclide, 

Priority 

assignment 

Energy of the 

gamma rays (keV)b 

R e с e n t e x p é r i m é n t a 1 d a t a° Claimed 

Gamma ray 

intensity (qu/100 d) 

Reference Experimental 

accuracy, % 

1 34Cs 475,355 ± 0.038 1.51 ± 0.16 1967 [20] 10.6 1 

I. 

1.4 ± 0.2 1968 [21]. 14. 3 

1.57 ± 0.08 1970 [22] 5.1 

563.325 ± 0.041 8.96 ± 0.84 1967 [20] 9.4 

8.7 ±1.0 1968 [21] 11.5 

8.86 ± 0.45 1970 [22] 5.1 

569.371 ± 0.047 15.81 ± 1.1 1967 [20] 7.0 

15.0 ±1.6 1968 [21] 10.7 

16.0 ±1.0 1970 [22] 6.3 

604.744 ± 0.027 98.04 1967 [20] 

98.0 1968 [21] 

98.1 ± 6.0 1970 [22] ff.l 

795.806 ± 0.050 87.79 ± 6.6 1967 [20] 7.5 

a O n ly g a m m a ra ys w ith an in ten sity h igh er than 1 p e r c e n t a re in c lu d e d . 

88.4 ± 9.1 1968 pi] 10.3 

86.0 ± 4.3 19 70 [22] 5.0 

k T h e e n e r g y v a lu e s a re , in g e n e r a l, ta k e n fr o m M a rtin and B lic h e r t -T o ft [ 1 3 ] , e x c e p t fo r ^ C s and ^ Z r w h e re th e d a ta o f R a e sid e e t a l. [ 2 0 ] and B rahm avar and 

H a m ilto n [ 2 4 ] are u sed , r e s p e c t iv e ly . 

c D ata w ith th e s m a lle s t error are u n d e rlin e d .

T A B L E Ha. CO N TIN U ATIO N 

Radioactive 

nuclide, 

Priority 

assignment 

Energy of the 


R e с e n t e x p e r i m e n t a 1 d a t aa 

Gamma ray 



accuracy, % 

801.86 ± 0.28 8.94 ± 0.8 1967 [20] 8.9 

9.2 ± 1.0 1968 [21] 10.9 

8.7 ± 0.44 1970 [22] 5.1 

1038.61 ± 0.49 1.02 ± 0.08 1967 [20] , 7 -8 

1.1 ±0.6 1968 [21] 54.5 

0.99 ± 0.06 1970 [22] 6.1 

1167.99 ± 0.39 1.96 ± 0.22 1967 [20] 11.2 

1.8 ±0.2 1968 [21] 11.1 

1.86 ± 0.10 1970 [22] 5.4 

1365.08 + 0.32 3.25 ± 0.32 1967 [20] 9.8 

3.3 ± 0.3 1968 [21] 9.1 

3.23 ± 0.17 1970 [22] 5.3 

Claimed 

accuracy,% 

13,7Cs 661.64 ± 0.8 85.1 ± 0.4 1969 [23] 0.5 1 

I. 84.6 ± 0.4 1970 [13] 0.5 


b T h e e n e r g y v a lu e s a re , in g e n e r a l, ta k en fr o m M artin and B lic h e r t -T o ft [ 1 3 ] , e x c e p t for m C s and æZ r w h e re th e d a ta o f R a e sid e e t a l. [ 2 0 ] and B rah m avar and 

H a m ilto n [ 2 4 ] a re u sed , r e s p e c t iv e ly . 

I A E A - S M -170/1 275

T A B L E lib . CONTIN U ATIO N 

Radioactive 

nucli'de 

Priority 

assignment 

Energy of the 


R e с e n t e x p e r i m e n t a 1 d a t a* 

Gamma ray 



95Zr 724.23 ± 0.04 44.2 ± 0.7 0 1969 [24] 1.6 1 

II. 43.5 ± 0.5 19 70 [13] 1.1 

756,74 ± 0.04 54.6 ± 0.5 0 1969 [24] 0.9 

54.3 ±0.5 1970 [13] 0.9 

1 ° 6 R u ( l ° 6 R h ) 511.8 ± 0.2 20.6 ± 0.6 1969 [25] 2.9 3 

II. 20.6 ±0.9 1970 [13] 4.3 

a D a ta w ith ch e s m a lle s t error a re u n d e rlin e d . 

622.1 ± 0.2 9.89 ± 0. 48 d 1968 [26] 4.9 

9.80 ± 0 . 5 3 d 1969 [27] 5.4 

9.83 ± 0.30 1969 [25] 3.1 

9.94 ± 0.11 1970 [13] 1 . 1 

1050.1 ±0.2 1.48 ± 0.11d 1968 [26] 7,1 

1.45 ± 0.09d 1969 [27] 6.0 

1.51 ± 0.08 1969 [25] 5.0 

1.48 ± 0.04 1970 [13] 2.7 

Claimed 

accuracy, % 

b T h e e n e r g y v a lu e s a re , in g e n e r a l, ta k e n fr o m M a rtin and B lic h e r t -T o ft [ 1 3 ] , e x c e p t for w C s and ^ Z r w h e re th e d a ta o f R a e s id e e t a l. [ 2 0 ] and B rahm avar and 

H a m ilto n [ 2 4 ] are used , r e s p e c t iv e ly . 

c C o m p u te d fr o m th e p u blish ed v a lu e a c c e p t in g ( 5 4 . 6 ± 0 .5 ) p er c e n t [ 2 4 ] for th e r e la t iv e in te n s ity o f th e b e t a g r o u p to th e 7 5 6 .7 4 le v e l , 

d C o m p u te d fr o m th e p u b lish e d v a lu e a c c e p t in g ( 2 0 . 6 ¿ 0 ,9 ) q u an ta p er d e c a y in te n sity [ 1 3 ] for th e 5 1 1 .8 k e V g a m m a ra y s. 

276 BERÉNYI

J. -tt.-D.LjIl/ Н С . V^V-/1N A UN U A i i\»/XN 

Radioactive 

nuclide, 

Priority 

assignment 

Energy of the 


R e c e n t e x p e r i m e n t a 1 d a t aa 

Gamma ray 



1 40La 328.77 ± 0.02 21 ± 2 1970 [13] 9.5 1 

II. 


18.5 ± 0.07 0 1970 [28] 0.4 

19.0 ± 1.2 c 1971 [29] 6.0 

432.55 ± 0.03 3.3 ± 0.2 1970 [13] 6.1 

2.7 ± 0.16 ° 1970 [28] 5.3 

2.9 ± 0.20 0 1971 [29] 7.0 

487.03 ± 0.02 45 ± 2 1970 [13] 4.4 

43.0 ± 0.22 c 1970 [28] 0.5 

46.8 ± 2.9 c 1971 [29] 6.1 

751.79 ± 0.06 4.4 ±0.1 1970 [13] 2^3 

4.2 ± 0.20 0 1970 [28] 4.6 

4.1 ± 0.29 c 1971 [29] 7.1 

815.83 ± 0.06 23.1 ±0.4 1970 [13] '1.7_ 

. 22.5 ± 0.67 c 1970 [28] 3.0 

21.4 ± 1.3 c 1971 [29] 6.3 

Claimed 

accuracy, % 

b T h e e n e rg y v a lu e s a re , in g e n e r a l, ta k e n fr o m M a rtin and B U c h e r t-T o ft [ 1 3 ] , e x c e p t f a “ c s and ® Z r w h e re th e d a ta o f R a e sid e e t a l. [ 2 0 ] and B rahm avar and 

H a m ilto n [ 2 4 ] a re w e d , r e s p e c t iv e ly . 

c C o m p u te d fr o m th e p u b lish e d v a lu e a c c e p t in g ( 9 5 .6 ± 0 .3 ) q u an ta p er d e c a y in te n sity [ 1 3 ] fo r th e 1 5 9 6 .6 k e V g a m m a ra y s. 

I A E A - S M -170/1 277

T A B L E lid . CO N TIN U ATIO N 

Radioactive 

nuclide 

Priority 

assignment 

Energy of the 



R e c e n t e x P e r i m e h t a l d a t aa 

Gamma ray 



867.84 ± 0.10 5.5 + 0.3 1970 [13] 5.5 

5.4 + 0.3 ° 1970 [28] 5.4 

5.4 ± 0.38° 1971 [29] 7.1 

919.6 ± 0.2 2.5 + 0.2 1970 [13] 8.0 

2.5 + 0.15d 19 70 [28] 6.1 

2.9 + 0. 26 d 1971 [29] 9.1 

925.2 ± 0.8 6.9 + 0.3 1970 [13] 4.3 

6.8 + 0. 29 d 1970 [28] 4.2 

7.5 + 0.55d 1971 [29] 7.4 

1596.6 ± 0.2 95.6 + 0.3 1970 [13] 0.3 

1970 

1971 

[28] 

[29] 

2522.0 + 0.4 3.3 + 0.2 19 70 [13] 6.0 

3.4 + 0.17d 19 70 [28] 5.0 

3.6 + 0. 21d 1971 [29] 5.8 

Claimed 

accuracy, % 

b T h e e n e r g y v a lu e s a re , in g e n e r a l, t a t e n fr o m M a rtin a n d B lic h e r t -T o ft [ 1 3 ] , e x c e p t fo r m C s and ^ r w h e re th e d a ta o f R a e s id e et a l. [ 2 0 ] and B rah m avar and 


c C o m p u te d fr o m th e p u b lish ed v a lu e a c c e p t in g ( 9 5 .6 ± 0 .3 ) q u an ta per d e c a y in te n sity [ 1 3 ] fo r th e 1 5 9 6 .6 k e V g a m m a ra y s. 

^ C o m p u te d fr o m th e p u b lish e d v a lu e a c c e p t in g ( 2 0 .6 ± 0 . 9 ) qu an ta per d e c a y in te n sity [ 1 3 ] for th e 5 1 1 .8 k e V g a m m a ra y s. 

278 ' BERÉNYI

T A B L E lie. CO N TIN U ATIO N 

Radioactive 

nuclide 

Priority 

assignment 

Energy of the 


R e c e n t e x p e r i m e n t a 1 d a t a a 

Gamma 

intensity 

ray 

(qu/100 d) 


i‘*‘*Ce 80.12 ± 0.3 2.38 ± 0.24 c 1969 [30] 10.2 

II. 1.54 ± 0.15 1970 [13] 9.7 


1.60 ± 0.11 c 19 70 [31] 6.9 

1.73 ± 0 . 11 c 1970 [32] 6.4 

133.53 ± 0.3 10.8 ± 0.5 1970 [13] 4.6 

Claimed 

accuracy, % 

b T h e e n e rg y v a lu e s a re g e n e r a lly ta k e n fr o m M a rtin and B lic h e r t -T o ft [ 1 3 ] , e x c e p t fo r c a s e o f “ C s and ® Z r w h e re th e d a ta o f R a e sid e e t a l. [ 2 0 ] a n d B rahm avar and 


c C o m p u te d fr o m th e p u b lish e d v a lu e a c c e p t in g ( 1 0 . 8 ± 0 .5 ) qu an ta p er d e c a y in te n sity [ 1 3 ] for th e 1 3 3 .5 3 k e V g a m m a ra y s. 

I A E A - S M -170/1 279

280 BERÉNYI 

future: it would be very useful, in view of the various applica 

tions, if the file of references in Oak Ridge would be the file 

of nuclear data. 

Finally, I should like to summarize our experiences in 

connection with the request lists for safeguards purposes [1-2]. 

First of all( the real claims are much more numerous than they 

could be analysed now here, but these requests are not concrete 

enough, e. g. there is no figure about the requested accuracy 

• • 

/ cf. [1]/. Even in the case of the second, more precise request 

list [2] there are some insufficiencies. Thus, there is no 

hint for the intensity limit up to which the gamma quanta per 

decay data are necessary. /It is obvious, that the gamma rays 

of low intensity are of no interest for safeguards./ In the 

present analysis this limit was arbitrarily chosen as 1 % /i. e. 

1 quantum per 100 decays/. 

Furthermore, in the request list [2] only 9sZr, 106Ru, 

etc. are indicated, although it is very probable that the gamma 

rays from the corresponding daughter nuclides / 95Nb, 106Rh etc./ 

are also important. E. g. in the case of 106Ru we were obliged 

to include the decay of 1°6Rh in the analysis because the 106Ru 

itself is only a beta decaying nuclide without any monoenergetic 

gamma rays. Some of the nuclides in question have an isomer 

state too /e. g. 106mRh/, the decay characteristics of which 

might be important in safeguards tasks, but such claims are 

not indicated in the lists. 

As a final conclusion, it can be stated that further 

thorough and detailed request lists are badly needed. 

The author is obliged to Professor D. J. Horen, Director, 

Nuclear Data Project, Oak Ridge, Tennessee, for sending the 

necessary list from the computerized file of references and 

the Nuclear Data Sheets for A=95 mass chain before the official 

publication. 

REFERENCES 

[1] BYER, T. A . , „Draft Working Paper for IWGNSRD on Non-Neutron 

Nuclear Data Needs for Safeguards Development Purposes." 

1st Meeting of IWGNSRD, Working Paper No. 20, March, 1972 

[2] BYER, T. A., INDC(NDS)-44/G, IAEA, Vienna, June 1972 

[3] Nuclear Data Sheets, 4B 1-2 (1970)

Nuclear Data Sheets, 4B 5 (1970) 


Nuclear Data Sheets, 5B 4 (19 71) 

Nuclear Data Sheets, 6B 2 .(1971) 




MEDSKER, L. R. and HOREN, D. J . , Nuclear Data Sheets B8 (1972) 

29 

Computerized data files for 13^Cs, Oak Ridge Nuclear Data 

Group, Oak Ridge, Tennessee, USA. 

MARTIN, M. J. and BLICHERT-TOFT, P. H., Nuclear Data 

Tables 8A (1970) 1 

LAGOUTINE, F., LEGRAND, J., PERROT, C., BRETHON, J. P ._ and 

MOREL, J. , Int. J. Appl. Rad. Isotope, 23 (1972) 219 

HARBOTTLE, G., Radiochim. Acta 13 (1970) 132 

WALZ, K. F. und WEISS, H. M., Zeits. Naturf. 25a (1970) 921 

DEBERTIN, K., Zeits. Naturf. 26a (1971) 596 

BABA, S., BABA, H., NATSUME, H., J. Inorg. Nucl. Chem. 33 

(1971) 589 

WALKER, D. A. and EASTERDAY, H. T., Nucl. Instr. Meth. £8 

(1967) 277 

RAESIDE, D.E., REIDY, J. J. and WIDENBECK, M. L., Nucl. Phys. 

A98 (1967) 54 

ABDUL-MALEK, A. and NAUMANN, R.A., Nucl. Phys. A106 

(1968) 225 

HOFMANN, H., WALTER, H.K., WEITSCH, A., Z. Physik, 230 

(1970) 37 

HANSEN, H.H., LÖWENTHAL, G., SPERNOL, A., EIJK,van der W., 

and VANINBROUKX, Zeits. Phys. 218 (1969) 25 

BRAHMAVAR, S.M. and HAMILTON, J. H., Phys. Rev. 187 (1969) 

1487 

ODRU, P., Radiochim. Acta 12 (1969) 64 

HATTULA, J. and LIUKKONEN, E., Ann. Acad. Sei. Fennicae, 

Ser. A. VI. No. 274 (1968) 

STRUTZ, Kl.-D. and FLAMMERSFELD, A. Zeits. Phys. 221 

(1969) 231 

IA E A -S M -1 7 0 /1 281 

KALINNIKOV, V. G., RAVN, K. L., HANSEN, H. G., LEBEDEV, 

N. A., Izv. AN SSSR, Ser. Fiz. ¿4 (1970) 916

282 BERÉNYI 

[29] ARDISON, G. et MARSD, C., Rev. Roum. Phys. 16 (1971) 1043 

[30] MANGAL, P. C. and TREHAN, P.N., Journ. Phys. Soc. Japan, 

22 (1969) 1 

[31] ANTTILA, A. and PIIPARINEN, M. Zeits. Phys. 237 (1970) 126 

[32] POTNIS, V. R., A G I N , G.P., MANDEVILLE, C.E., J. Phys. Soc. 

Jap. 29 (1970) 539 

[33] HILLER, S., Kerntechnik 12 (1970) 485 

[34] MILLER, 0. A., DEMIDOV, A. M., OVCSINIKOV, F. Ja., GOLUBEV, 

L. I. and SUNCSUGASHEV, M. A., Atomnaya Energiya 27 (1969) 

281 

DISCUSSION 

C. W E IT K A M P : In con n ection w ith y o u r s ta te m e n t th at h a lf-liv e s a re 

u su a lly w ell enough known fo r sa fe g u a rd s p u rp o se s , I should lik e to give 

an e x a m p le of a c a s e in w hich th e y a r e n o t. T h e a c c u r a c i e s of s p e c ific 

p ow er v a lu e s of 239P u , 240 P u and 241P u fo r c o lo r im e tr ic plutonium a s s a y 

a r e at p re s e n t in ad eq u ate, and b e tte r h a lf-liv e s fo r th e f i r s t tw o would 

g r e a tly im p ro v e th e situ a tio n . Im p ro v e m e n ts can , of c o u r s e , a ls o co m e 

fro m o th e r m e a s u re m e n ts , su ch a s d ir e c t (i. e. c a lo r im e tr ic ) d e te rm in a tio n . 

D. J . H O REN : F i r s t , I would lik e to thank M r. B e ré n y i fo r m ak in g 

su ch good u se of ou r output. I would a ls o m en tion th at th e se ty p es of 

sp e c ia liz e d r e f e r e n c e lis t s a r e a v a ila b le to anyone on re q u e s t. The id ea 

of p ub lish in g cu m u la tiv e r e f e r e n c e l i s t s in ste a d of R e c e n t R e fe r e n c e s h as 

b een u n d er c o n sid e ra tio n fo r th e p a st y e a r and a h alf but we fe e l th at it is 

m o re e c o n o m ic a l to resp o n d to individual re q u e s ts . 

Y ou s ta r te d to g e t down to so m e of the d e ta ils of the handling of th e se 

d a ta . I think th is would le a d to a v e r y len gth y d iscu s s io n if we w e re to 

p u rsu e it. H ow ev er, I would like to m ak e a couple of co m m e n ts on the 

su b je ct. W e a g r e e th at it would be helpful fo r u s to ta b u la te ab solu te 

g a m m a in te n s itie s and we hope w ith som e of th e co m p u te r p ro g ra m m in g 

th at we a r e now doing, to s e t up a s y s te m by w hich we w ill be ab le to c a l 

cu la te the w hole d e ca y s ch e m e and then p ro d u ce tab u latio n s of ab solu te 

g a m m a in te n s ity , to ta l tra n s itio n s in te n sity o r c o n v e rs io n e le c tr o n s . T h e se 

p ro g ra m s h ave not y e t b een co m p le te d , but w e a r e w orkin g in th at d ire c tio n . 

K . W A Y : Did you m e a n to su g g e st a d a ta file of e x p e rim e n ta l d ata 

o r re co m m e n d e d d a ta ? 

D. B E R É N Y I: I think the m a in ta s k of a d a ta c e n tr e is to c o lle c t d ata 

and th a t is why a file of e x p e rim e n ta l n u c le a r d a ta is the m o s t im p o rta n t 

re q u ire m e n t. T h e evalu atio n of th e d a ta a c c o rd in g to d iffe re n t p oin ts of 

view s is , of c o u r s e , a ls o v e r y im p o rta n t and n e c e s s a r y but it is p o ssib le 

only if w e have a s co m p le te a c o lle ctio n (d ata file) of the o rig in a l 

e x p e rim e n ta l d ata a s p o ssib le . 

D. J . H O REN : I would lik e to follow up M iss W a y 's q u estion . I think, 

when it is a m a tte r of a ra w d ata file , i. e. d a ta put in to a co m p u te r file 

d ire c tly fro m e x p e rim e n ta l p a p e r s , th a t u ntil the e x p e rim e n ta lis ts adopt 

so m e of th e id e a s ad v o cate d by M iss W ay fo r m an y y e a r s now , th e r e a l 

valu e of su ch a file is som ew h at q u estion ab le.

IA E A -S M -1 7 0 /1 283 

С. B E E T S : T h e im p o rta n c e of the v a rio u s s a fe g u a rd s re q u ire m e n ts 

h as b een sp e cifie d in g r e a t e r d e ta il, a s fa r a s g a m m a m e a s u re m e n ts of 

irra d ia te d fuel a r e co n ce rn e d , in a p a p e r p re s e n te d at th e 1972 ANS m e e tin g 

in W ashin gton by C. B e e ts , T . D ra g n e v e t al.

Section IV 

LIFE SCIENCES

Chairman 

A.H.W. ATEN (ССЕ)

LE ROLE DES DONNEES NUCLEAIRES 

DANS L'UTILISATION DES INDICATEURS 

RADIOACTIFS EN MEDECINE 

C. KELLERSHOHN, D. COMAR 

CEA, Département de biologie, 

Service hospitalier Frédéric Joliot, 

Orsay, France 


TH E ROLE OF N U CLEAR D A T A IN TH E USE OF R A D IO A C T IV E TRACERS IN M E DICIN E. 

T h e n u c le a r d a ta , k n o w le d g e o f w h ic h is fu n d a m e n ta l fo r th e use o f r a d io e le m e n ts in m e d ic a l 

d ia g n o s tic s , a re r e v ie w e d . A fte r an in tr o d u c to ry part o n th e p r o d u c tio n o f r a d io e le m e n ts p r o b le m s 

IA E A -S M -П 0 /9 7 

c o n c e r n in g fu n c tio n a l e x p lo r a tio n , as, e . g . , k in e t ic stu d ies and d o s im e try , a re c o n s id e r e d . T h e last 

part o f th e p a p e r d e a ls w ith th e a n aly sis o f th e e le m e n ta r y c o m p o s itio n o f b io l o g i c a l m a te r ia ls using 

r a d io a c t iv a t io n a n aly sis in v itr o e t in v iv o , th e la tte r a lso c o n c e r n in g d o s im e t r ic p r o b le m s c o n n e c t e d 

w ith th e n a tu re o f th e p a r tic le s used fo r ir ra d ia tio n . 

LE ROLE DES DONNEES NUCLEAIRES D A N S L ’ U T IL IS A T IO N DES IN D IC A TEU R S R A D IO A C T IF S EN M EDECINE. 

Les auteurs passent e n re v u e le s d o n n é e s n u c lé a ir e s d o n t la c o n n a is s a n c e est fo n d a m e n ta le pou r 

l'u t ilis a t io n des r a d io é lé m e n ts dans le d ia g n o s tic m é d ic a l. A p rès un e x p o s é sur la p r o d u c tio n des r a d io 

é lé m e n ts ils é tu d ie n t le s p r o b lè m e s r e la tifs â l'e x p lo r a t io n fo n c t io n n e lle , te ls q u e .le s étu d e s c in é tiq u e s 

e t la d o s im é tr ie . La d e r n iè r e p a rtie du m é m o ir e tr a ite d e l'a n a ly s e d e la c o m p o s itio n é lé m e n t a ir e d es 

m a té r ia u x b io lo g iq u e s p ar a n a ly se par r a d io a c t iv a t io n in v itr o e t in v iv o , c e t t e d e r n iè r e fa isan t é g a le m e n t 

a p p e l à d es p r o b lè m e s d o s im é triq u e s lié s à la n a tu re d es p a rticu le s u tilis é e s p ou r l'ir r a d ia t io n . 

Les données nucléaires dont la connaissance est fondamentale 

pour l'utilisation des radioéléments en diagnostic médical 

s'appliquent à trois domaines principaux : 

- la production des radioéléments, 

- l'exploration fonctionnelle comportant les études cinétiques, 

l'imagerie, et leurs conséquences dosimétriques, 

- l'analyse de la composition élémentaire des matériaux biologiques 

par analyse par radioactivation in vitro et in vivo, cette 

dernière faisant également appel à des problèmes dosimétriques 

liés à la nature des particules utilisées pour l'irradiation. 

1. PRODUCTION DES RADIOELEMENTS 

Quoique le nombre des radioéléments connus à l'heure actuelle 

soit voisin de 1300, bien peu sont utilisés en médecine 

diagnostique soit en raison de la difficulté de leur production 

soit que leurs caractéristiques nucléaires ne sont pas souvent 

convenables. 

L'irradiation par les neutrons dans les réacteurs nucléaires 

est la méthode de choix de production d'un certain nombre 

d'entre eux. A côté du rendement de fission qu'il est utile de 

287

288 KELLERSHOHN et COMAR 

connaître pour déterminer la proportion des radioéléments produits 

au cours de la fission de 1 'uranium-235, les deux paramètres 

nucléaires qui gouvernent les réactions avec les neutrons 

sont la section efficace et la période. 

A partir des neutrons thermiques les réactions par capture 

radiative sont les plus fréquentes conduisant à l'isotope radioactif 

d'une unité de masse supérieure. La quantité de radioactivité 

produite sera, à flux de neutrons constant et pour un temps 

d'irradiation long par rapport à la période, directement proportionnel 

à la section efficace d'activation. Sa connaissance est 

donc fondamentale si l'on veut prévoir la radioactivité spécifique 

du produit fabriqué. Il est important que la masse d'entraîneur 

associée aux radioéléments soit aussi faible que possible, 

sinon nulle. En effet les études cinétiques fondées sur l'emploi 

des indicateurs supposent au préalable que la masse de produit 

injectée soit négligeable par rapport à celle contenue dans le 

système. 

La toxicité de l'espèce chimique utilisée est également un 

facteur limitant de l'emploi des indicateurs nucléaires en diagnostic 

médical et ici aussi la connaissance de la section efficace 

permettra de décider de la possibilité d'utilisation du radioélément 

chez l'homme. Les éléments lourds en sont un bon exemple 

: le produit par réaction (n,y) à partir du !96нд malgré 

sa grande section efficace d'activation suppose pour avoir 

une radioactivité spécifique suffisante, l'enrichissement de l'isotope 

stable et l'irradiation dans un flux de neutrons important. 

Un autre élément lourd, le thallium, dont l'intérêt pour 

l'exploration fonctionnelle du rein a récemment été mis en évidence, 

ne possède qu'un seul radioisotope (204T1) produit par 

capture radiative. La faible section efficace d'activation, associée 

à la période de 204t i (38 ans) et du schéma de désintégration 

défavorable pour la détection "in vivo" rendent ce radioélément 

inutilisable chez l'homme. 

La connaissance des données nucléaires relatives aux paramètres 

d'activation en fonction de l'énergie des neutrons sont également 

très utiles pour déterminer les conditions les meilleures 

de production. Ainsi le cuivre-67 de période 2,44 j et émetteur 

d'une raie gamma à 184 keV est produit par réaction n,p sur le 

zinc enrichi. Il constituera donc un radioélément sans entraîneur 

d'intérêt beaucoup plus grand en médecine que n'est le ®^Cu 

T = 12,8 h et émetteur de positrons produit avec entraîneur lors 

de l'irradiation du cuivre naturel par les neutrons thermiques. 

Dans la plupart des cas oû le radioélément a une période 

suffisamment longue pour être transporté du lieu de sa production 

à celui de son utilisation, le médecin connaissant la radioactivité 

indiquée par le fabricant doit à partir de la période du 

radioélément calculer la radioactivité réelle qu'il sera amené à 

injecter au patient. Il pourra également comparer la radioactivité 

de la source à celle d'un standard commercial. 

Le cas particulier des générateurs de radioéléments plus 

communément appelés "vaches à radioéléments" suppose la 

connaissance simultanée de la part du médecin de la période et 

du schéma de désintégration. Le générateur de radioélément le 

plus généralement utilisé à l'heure actuelle est la "vache à 

technétium" dont le fonctionnement se déduit facilement du schéma 

de désintégrations du 99Mo et 99ттс présenté sur la figure 1. De 

la radioactivité connue en 99m 0 à un instant donné, l'application 

des équations de la filiation radioactive permet à chaque instant

IA E A -S M -1 70/97 289 

FIG. 1. S c h e m a d e d é s in té g r a tio n du m o ly b d e n e - 9 9 (6 7 h ) et du t e c h n é t iu m -9 9 m ( 6 h ). 

de déterminer la radioactivité en produit fils 99ттс à condition 

de connaître avec précision les périodes physiques des deux radioéléments 

. 

Une alternative consiste bien entendu à mesurer la radioactivité 

du 99mijic séparé du З^Мо à l'aide d'un détecteur spectro- 

mêtre gamma convenablement étalonné et de déduire du taux de 

comptage le taux de désintégrations, donnée pour laquelle le 

pourcentage d'émission par désintégration de la raie gamma mesurée 

est le paramètre nécessaire. 

Depuis quelques années l'apparition sur le marché de cyclotrons 

compacts à usage médical ouvre des perspectives nouvelles 

quant à la disponibilité des radioéléments (1). Une dizaine de 

cyclotrons de ce type sont installés à l'heure actuelle dans 

différents instituts médicaux ; une de leurs principales caractéristiques 

est de pouvoir produire des isotopes radioactifs de période 

très brève inaccessibles par d'autres méthodes. Les trois 

principaux sont I'ISq^t = 2,05 min), le ^ c f T = 20,4 min) et l'-^N 

(ï = 10 min^ Utilisés directement sous forme gazeuse (C>2 , CO2 , СО, 

N 2 ) ces radioéléments sont particulièrement intéressants pour 

l'étude de la ventilation pulmonaire. Combinés à des molécules 

plus complexes ils permettent d'étudier les composantes rapides 

de certains métabolismes (médicaments ou produits naturels). Ces 

études doivent dans certains cas se poursuivre pendant un temps 

correspondant à plusieurs périodes de désintégration du radioélément. 

La précision avec laquelle cette période sera connue conditionnera 

la précision des données biologiques mesurées.


Courbes d'activation du 11C 

et des éléments interférants 

1 1 , 

Rendement obtenu en С 

1— A partir des deutons de nMev 

B20 3 + Не i5oml/min _____¿ 2 ,5 mCi^tA.h 

2 _ A partir des protons de 12 Mev 

B2 C^ + Не i5om l/m in ----------» 3omCj/Û.A.h 

N2 (1 bar] i5 omJ/min ----------» eomCjû. A h 

FIG . 2. P ro d u ctio n d e n C à partir d es r é a c t io n s 10 B (d ,n )n C , ‘ 'B f p . n f 'c e t l4N ( p , a ) u C . 

En h a u t: c o u r b e s d 'a c t iv a t io n du “ C e t d es é lé m e n ts in te rfé ra n ts pou r le s trois ré a ctio n s c o n s id é r é e s 

sous fo r m e d e la r a d io a c t iv ité e x p r im é e e n fo n c t io n d e l'é n e r g ie . 

En bas: r e n d e m e n t d e s tro is r é a c tio n s e n m illic u r ie s p ar m ic r o a m p á r e -h e u r e . 

En ce qui concerne la production de ces radioéléments un des 

paramètres fondamentaux qu'il est nécessaire de connaître et qui 

malheureusement fait encore défaut dans bien des cas est la variation 

de la section efficace en fonction de l'énergie des particules. 

Celle-ci permettra de prévoir l'énergie optimale pour 

obtenir le meilleur rendement tout en évitant certaines réactions 

parasites conduisant à la fabrication d'un autre radioélément. 

La figure 2 illustre les problèmes posés par la fabrication 

du Н С ainsi que quelques résultats préliminaires obtenus dans 

notre service. 

Les courbes d'activation du 1J-C à partir des réactions 

(d,n) IIç, IIß (p, n) 4 c et 14N (p, ) H c sont empruntées à 

Engelmann (2). Pratiquement la méthode la plus intéressante consiste 

à irradier par des protons d'énergie voisine de 12 MeV de

C IB L E 

Hg 

PARTICU LES 

iA E A -S M -1 7 0 /9 7 291 

198" ’ T l T = 1 , 8 7 h C E = 4 5 % 

198 

199 

200 

201 

T l T = 5 , 3 h C E = 1 0 0 % 

T l T = 7 , 4 h C E = 1 0 0 % 

T l T “ 1 , 0 4 j C E = 1 0 0 % 

T l T = 3 , 0 8 j 

C E = 1 0 0 % 

202 

T l T - _ 1 2 j 

C E = 1 0 0 % 

RENDEMENT heure 

,9 8 T I 199 T l 200 T l 501 T l S 0 S T I 

H g O d ( l 5 M e v ) 3 6 5 4 1 0 i 2 3 3 8 4 2 1 

H g O p ( 5 0 M e v ) 5 4 5 0 2 6 0 0 7 3 0 1 2 3 7 , 6 

H g O p ( 1 6 M e v ) 

- 

2 5 0 6 0 4 5 - 

H g p ( 1 6 M e v ) 6 6 0 9 0 0 2 3 0 1 8 0 7 

F IG .3 . R a d io is o to p e s du th a lliu m p rod u its par c y c lo t r o n . 

En h a u t: R a d io is o to p e s p rodu its a v e c le u r p é r io d e e t le u r m o d e d e d é s in té g ra tio n . 

En bas: R e n d e m e n t d e p r o d u c tio n e n fo n c t io n d e la n a tu re des p a r tic u le s , d e le u r é n e r g ie e t d e la n ature 

d e la c i b l e . 

l'azote gazeux contenant 2 à 3 % d'oxygène, ce dernier ayant pour 

effet de réagir directement avec les atomes de 1]-C pour donner du 

H C C ^ . Les courbes présentées en haut et à droite de la figure 

mettent bien en évidence que l'oxygène présent dans le gaz cible 

conduira à la formation d'azote-13 contaminant le ^ C . La conséquence 

logique d'une telle observation aboutira soit à modifier 

le mode de préparation, soit à effectuer une séparation chimique 

des deux gaz radioactifs. 

Dans la plupart des cas la fonction d'excitation étant inconnue, 

seule l'expérience permettra de déterminer le rendement 

de fabrication d'un radioélément et la contamination par les radioisotopes 

voisins, s'ils existent. La figure 3 illustre un tel 

cas. Il concerne la fabrication des thallium 198m à 202 par bombardement 

du mercure par les protons ou les deutons. La partie 

supérieure indique les radioisotopes produits ainsi que leur période 

et le mode fondamental de désintégration. Le tableau inférieur 

illustre les rendements de fabrication en fonction de la 

nature chimique de la cible de la particule incidente et de son 

énergie. Il apparaît que le bombardement par les protons conduit 

à un mélange de radioisotopes plus riche en radioéléments de 

courte période.


FIG . 4 . S c h é m a d u p r in c ip e d e S te w a r t-H a m ilto n . 

S: S y s te m e b io lo g iq u e é tu d ié 

qo: R a d io a c t iv it é in je c t é e 

a (t): R a d io a c t iv it é s p é c ifiq u e à l'in s ta n t t d e la su b sta n ce é tu d ié e a la s o r tie d e S 

R: D iè t e ou flu x d 'e n t r é e d e la su b sta n ce é tu d ié e dans S 

t: T e m p s m o y e n d e transit d e la su b sta n ce é tu d ié e â travers S 

O s : M asse o u p o o l d e la su b sta n ce é tu d ié e dans le s y stè m e . 

2. DONNEES NUCLEAIRES DANS LE CADRE DES ETUDES CINETIQUES ET 

DE L'EXPLORATION FONCTIONNELLE 

2.1. Procédures 

Que ce soit pour l'exploration fonctionnelle d'un organe, 

l'étude d'une fonction physiologique et de ses anomalies ou plus 

généralement l'étude du métabolisme d'un élément ou d'une substance 

à différents niveaux d'une structure vivante en état sta- 

tionnaire vis-à-vis de cet élément ou de cette substance, l'utilisation 

des indicateurs nucléaires se ramène à trois types de 

procédures : 

2.1.1. Le principe de Stewart-Hamilton 

La figure 4 schématise ce principe dans le cas oû l'excrétion 

de l'indicateur se fait par une seule voie. C'est par exemple 

le cas de toutes les substances qui sont excrétées par la 

seule voie urinaire. Le flux de substances à travers l'organisme 

S

IA E A -S M -1 7 0/9 7 293 

ou système S considéré, la diète quotidienne R ;est égale au quotient 

de la radioactivité injectée qg par la surface limitée par 

la courbe représentant la variation de la radioactivité spécifique 

de l'excréta en fonction du temps a(t) 

R = q° 

Г а (t)dt 

L'application la plus connue de cette procédure est la mesure 

du débit cardiaque F au moyen de l'expression 

f-4 - 'o > 

q° 

c(t)dt 

oü qg est la radioactivité injectée en amont du coeur et c(t) la 

concentration radioactive à l'instant t d'échantillons sanguins 

prélevés en aval du coeur. 

L'injection de la radioactivité étant effectuée en "equivalent 

supply", c'est-à-dire que dans le cas où la substance étudiée 

pénètre dans l'organisme par plusieurs portes d'entrée, la 

radioactivité de l'indicateur est injectée simultanément dans 

chaque porte d'entrée dans les mêmes proportions que les flux de 

substance-mère, le temps moyen de transit t de la substance considérée 

à travers le système S est donné par l'expression 

_ jj2 ta (t) dt 

t = 

0 a(t)dt 

Я 

valable si la durée de l'injection est brève par rapport à t. 

La masse totale ou pool Qs de la substance considérée dans 

le système est alors donnée par la relation 

Qs = R.t. 

2.1.2. Le principe d'occupation 

Il constitue au fond une généralisation du principe de Stewart-Hamilton. 

Si qg représente la radioactivité totale injectée, 

qgi(t) la radioactivité, à l'instant t après le début de l'injection, 

dans une portion arbitraire S' du système S et Qgi la masse 

totale ou pool de la substance considérée dans S', le flux constant 

R de cette dernière dans S (Figure 5) est donnée par l'ex- 

Elle a été établie pour la première fois par Bergner (3) qui 

désignait le ternes 

■qs .(t) 

(*)s i = J — - dt sous le vocable de temps moyen 

de séjour de la 0----g 0-------substance considérée dans la


FIG . 5. S c h é m a du p r in c ip e d 'o c c u p a t io n . 

S: S y ste m e b io lo g iq u e é tu d ié 

S ', S " : P ortion s arb itra ires d e S 

q j: R a d io a c t iv it é i n je c t é e dans S 

q s '( ') . q s ''( t ) : R a d io a c t iv it é á l'in s ta n t t dans S 'e t S " 

R: D iè t e ou flu x d 'e n t r é e d e la su b sta n ce é tu d ié e dans S 

S 

( -> S '. (■)$••: O c c u p a tio n d e S ' e t S " par la su b sta n ce é tu d ié e . 

Q g ', Qs " : C a p a c it é d e S ' e t S " pou r la su b sta n ce é tu d ié e . 

région arbitraire S'. Elle a été reprise et largement développée 

dans ses applications pratiques par Orr et Gillespie (4) sous le 

nom de principe d'occupation. Ces auteurs appellent le temps C-) s ' 

occupation de S' par la substance étudiée et le pool Qs i capacité 

de S' pour cette substance. Ils énoncent alors le principe : le 

quotient de la capacité d'une région arbitraire d'un organisme S 

en état stationnaire par l'occupation de cette dernière, est égal 

au flux ou diète de la substance considérée pour cet organisme. 

(•)s' est mesuré par l'étude de la cinétique de la radioactivité 

dans S'. Si d'autre part Qg< peut être déterminé par une 

quelconque technique analytique, on en déduit la diète quotidienne 

moyenne R du sujet S. La région arbitraire S' est souvent 

constituée par un certain volume, un litre par exemple, de plasma. 

S'il est possible expérimentalement de mesurer la radioactivité 

au niveau d'un organe s", on détermine son occupation (-)" et 

par suite son pool Qg" pour la substance étudiée puisque : 

Si on prend pour région S' le système S lui-même, l'occupation 

se confond avec le temps de transit moyen t.

IAEA -SM -1 7 0 /9 7 295 

Le principe d'occupation est une méthode très puissante pour 

l'étude des métabolismes dans un organisme en état stationnaire. 

Il a été notamment utilisé dans le cas du métabolisme de l'iode 

(5), du brome (6), du rubidium (7), du calcium (8), du sélénium 

(9) . 

2.1.3. L'analyse compartimentale 

Elle constitue un mode de représentation bien connu du métabolisme 

d'un élément ou d'une molécule dans un organisme en état 

stationnaire. Sur la base de données anatomiques, physiologiques 

et biochimiques, ce dernier est divisé en "compartiments" représentant 

l'ensemble des atomes ou molécules étudiés se trouvant dans 

un même volume spatial, un même organe, ou un même état chimique. 

Les paramètres d'un tel système compartimentai sont constitués 

par les pools des compartiments, ainsi que les taux d'échange et 

de transfert entre eux. Après injection d'une radioactivité q 0 

d'un indicateur dans l'un de ces compartiments, en général celui 

W . 

5 10 15 20 25 J 

Compartiment iodure 

X x Valeurs expérim entales 

■— Modèle 

5 10 15 20 25 J 

* X 

Compartiment T4 plasmatique 

Compartiments thyroid iens M odè le final 

FIG. 6. A n a ly s e c o m p a r t im e n t a le du m é t a b o lis m e d e l 'i o d e c h e z le rat n o rm a l. 

D iè t e : 6, 8 8 f i g /j . P o o l io d u re : 3 , 1 p g . P o o l th y r o ïd ie n fo r m é d e 2 c o m p a r tim e n ts d e p o o ls 3 , 5 et 

9 , 8 p g , P o o l d ’ io d e o r g a n iq u e fo r m é d e 2 c o m p a r tim e n ts d e p o o ls 1 ,4 5 e r 1 ,4 2 jig . Les ta u x d e transfert 

e n tre c o m p a r tim e n ts sont e x p r im é s e n j i g /j.


a u q u e l a p p a r t i e n t l e p la s m a , l a r a d i o a c t i v i t é q ¿ (t) ou l a r a d i o 

a c t i v i t é s p é c i f i q u e a^(t) du ièm e c o m p a r tim e n t s o n t d e s f o n c 

t i o n s du tem p s o b é i s s a n t à un s y s tè m e d e n é q u a t i o n s d i f f é r e n 

t i e l l e s l i n é a i r e s du p r e m ie r o r d r e d o n t l e s c o e f f i c i e n t s c o n s 

t a n t s s 'e x p r i m e n t en f o n c t i o n d e s p a r a m è t r e s du s y s t è m e . I l e s t 

p o s s i b l e d a n s c e r t a i n e s c o n d i t i o n s d e d é t e r m i n e r c e s p a r a m è t r e s 

en r é s o l v a n t l e s y s tè m e d e f a ç o n q ue l'une ou p l u s i e u r s d e s 

f o n c t i o n s q i ( t ) ou a ¿ ( t ) c o r r e s p o n d e n t à l e u r v a l e u r e x p é r im e n 

tale. C e c i e s t a u j o u r d 'h u i e f f e c t u é s u r o r d i n a t e u r au m oyen de 

p ro g ram m es c o n v e n a b l e s . 

La figure 6 représente les courbes expérimentales de radioactivité 

dans les compartiments thyroïdiens, piodure plasmatique 

et thyroxine plasmatique chez le rat normal recevant une diète 

quotidienne de 5 ^g d'iode, après injection plasmatique d'iode- 

125 sous forme d'iodure, ainsi que le schéma compartimentai qui 

s'adapte le mieux à ces courbes. De tels schémas compartimentaux 

sont très utiles pour mettre en valeur le caractère normal ou pathologique 

d'un métabolisme. Ils permettent notamment de classer 

différents états pathologiques suivant ceux des paramètres du 

système (pool et taux de transfert) qui présentent des valeurs 

anormales. Une telle méthode d'analyse est employée pour de nombreux 

éléments tels que l'iode, le calcium, le fer, etc... etc... 

Finalement les trois procédures qui viennent d'être passées 

en revue et qui représentent l'essence actuelle des applications 

biologiques et médicales de la méthode des indicateurs se ramènent 

à des mesures de radioactivité en valeur relative à la radioactivité 

injectée ‘Здц et à leurs variations en fonction du 

temps. Ces dernières bien entendu doivent être corrigées de 

la perte de radioactivité par le mécanisme de désintégration, de 

façon à ce que les variations observées correspondent aux seuls 

processus métaboliques. La seule donnée proprement nucléaire nécessaire 

est en toute rigueur la constante radioactive, ou la 

demi-vie de l'indicateur utilisé. Encore est-il que, eu égard au 

caractère aléatoire des processus métaboliques, une très grande 

précision n'est pas nécessaire sur cette donnée. Ajoutons d'ailleurs 

que dans la plupart des cas cette correction est effectuée 

automatiquement par comparaison des activités des échantillons à 

une partie aliquote de la dose injectée et qu'alors cette unique 

donnée nucléaire n'est même plus nécessaire. Font exception les 

cas d'emploi d'éléments à vie très courte comme l'oxygène-15 (T = 

2,5 min) et le baryum-137m (T = 2,5 min) pour lesquels la mesure 

alternée sur un échantillon et un standard est difficilement réalisable. 

Une connaissance détaillée du spectre de rayonnement du radioélément 

utilisé n'est pas nécessaire si les mesures sur les 

échantillons et le standard sont effectuées dans les mêmes conditions 

de géométrie et de détection. Les données d'un schéma de 

désintégration simplifié donnant les énergies maxima des spectres 

béta et leur pourcentage ainsi que la répartition des principales 

raies gamma ou X et leur pourcentage par 100 désintégrations sont 

suffisantes. Ces dernières données sur les rayonnements électromagnétiques 

sont particulièrement importantes pour la détëction 

externe et les techniques d'imagerie (scintigraphie, caméra) qui 

jouent un rôle majeur dans les applications cliniques. 

2.2. Dosimétrie 

Si l'on met à part certaines techniques d'avant-garde, qui 

appartiennent essentiellement à des perspectives d'avenir et que

IA E A -S M -1 70/97 

nous examinerons plus loin, nous voyons que les résultats que 

l'on peut obtenir dans le domaine du diagnostic médical au moyen 

des indicateurs nucléaires ne nécessitent que peu de données nucléaires 

précises. Il n'en va pas du tout de même de l'appréciation 

des doses de radiation délivrées à l'organisme au cours de 

leur utilisation, appréciation de première importance dans le cas 

des applications sur l'homme. 

Le formalisme actuellement employé en dosimétrie (10) repose 

sur l'emploi d'un "modèle isotropique uniforme" pour lequel la 

source de rayonnement et la cible sur laquelle elle agit sont 

plongées dans un matériau absorbant homogène de dimensions suffisamment 

grandes pour négliger les effets de bord et tel que 

la radioactivité est distribuée uniformément dans la source. La 

dose absorbée moyenne D (v

R a y o n n e m e n t 

Stable 

KELLERSHOHN et COMAR 

197. 

79 

% par 

désintégration 

Energie de 

tran sition 

(MeV) 

Hg 65 h 

Autres 

para mètres 

Capture électronique-1 2 0,15 Première interdite 

Capture é(ectronique-2 98 0,34 Prem ière interdite 

Gamma-1 99,8 0,0773 M, 4 10 % e 2 

Gam m a- 2 1,8 0,1915 

a K=o,o a L=3,27 

M,* 30% e 2 

a K = o,8o 

K / (L+ M ) = üfi 

Gam m a-3 0,14 0,2680 M,#a K =0,375 (T) 

¿ L=0,0643 (T) 

D'après - L.T. OILLMAN, MIRD Pamphlet N•- i , J. Nucl.Med I0t supplement- 2 

FIG. 7. S ch é m a d e d é s in té g ra tio n du m e r c u r e -1 9 7 . 

T A B L E A U la . N O M BR E P A R D ESIN T EG R A T IO N E T E N E R G IE D ES 

PH OTONS GAMMA E T E L E C T R O N S D E CONVERSIO N D E 197Hg 

Rayonnement { i ) 

Nombre moyen 

par 


(ni) 

E nergie 

moyenne 

(ëi) 

Capture électronique -1 — — * 

Capture électronique-2 — — * 

fд-гасП 

V p C i- h J 

Ai 

Gamma - 1 0,186 0,0773 0,0306 

Electron con. int. L,gamma-1 0,609 0,0640 0,0830 

Electron con. int. M,gamma-1 0,203 0,0746 0,0323 

Gamma - 2 0,0090 0,1915 0,0037 

Electron con.int. K,gam m a-2 0,0072 0,1108 0,0017 

Electron con.int. L ,gamma-2 0,0014 0,1792 0,0005 

Electron con.int. M,gamma-2 0,0005 0,1888 0,0002 

Gamma - 3 0,0010 0,268 0,0006 

Electron con. int. K, gamma-3 0,0004 0,1873 0,0002

IA E A -S M -1 70/97 299 

T A B L E A U Ib. N O M BR E P A R D ESIN T EG R A T IO N E T E N E R G IE D ES 

PH O TO N S X D E 197Hg 

Rayonnement ( i ) 

l9,Hg (RAYONS X) 

Nombre moyen 

par 


N 

Energie 

moyenne 

( Ë i) 

fg-rad A 

V y C i-h J 

Rayons X K 2 -1 0,363 0,0688 0,0532 

Rayons X K 2 -2 0,199 0,0670 0,0284 

Rayons X Kß-1 0.126 0,0780 0,0209 

Rayons X K fl - 2 0,0338 0,0807 _ 0,0058 

Rayons X L| CL .0,252 0,0097 0,0052 

Rayons X li 13 0,236 0,0115 0,0058 

Rayons X Li T 0,0317 0,0134 0,0009 

T A B L E A U le . N O M BRE P A R D ESIN T EG R A T IO N E T E N E R G IE D ES 

E L E C T R O N S A U G E R D E 197Hg 

Rayonnement (i) 

,97Hg (ELECTRONS Auger) 

Nombre moyen 

par 


("0 

Energie 

moyenne 

(Ëi). 

Ai 

/'g-rad \ 

\|JCi-h ) 

Ai 

Electron Auger KLL 0.0191 0,0540 0,0022 

Electron Auger КЦХ 0,0108 0,0646 0,0015 

Electron Auger KXY 0,0018 0,0752 0,0003 

Electron Auger L,MM 0,903 0,0079 0,0152 

Electron Auger MXY 2,72 0,0027 0,0156 

Quoi qu'il en soit la fraction absorbée et la fraction absorbée 

spécifique ne sont pas des données nucléaires. Ce sont 

essentiellement les valeurs de nj_ et Ei pour chaque composante 

qui représentent les données nucléaires nécessaires au calcul des 

doses de radiation. Leur détermination exige une connaissance extrêmement 

précise du schéma de désintégration du radioélément utilisé 

sous peine d'erreurs d ’appréciation sur les valeurs des doses 

absorbées qui peuvent être importantes. 

A titre d'exemple la figure 7 représente le schéma de désintégration 

du mercure-197, radioélément assez utilisé en médecine 

nucléaire notamment pour l'exploration du rein et le diagnostic


des tumeurs. Ce schéma est emprunté à une monographie de Dillman 

(19) sur l'usage des schémas de désintégration et des paramètres 

nucléaires pour l'estimation des doses de radiation. Cet auteur 

a établi un programme d'ordinateur permettant d'obtenir à partir 

des données d'entrée les différentes valeurs de n¿ et E¿ pour les 

radionuclides d'intérêt médical. Les données des schémas de désintégration 

telles que celles présentées sur la moitié inférieure 

de la figure 7 pour le mercure comprennent le nombre, le pourcentage 

par désintégration, l'énergie et la nature des différentes 

transitions (i- , p + et par capture électronique, le nombre, le 

pourcentage par désintégration, l'énergie, la nature multipolaire 

magnétique ou électrique, les coefficients de conversion K, L, 

M . .. des différentes transitions gamma. 

Les Tableaux la Ib et le représentent dans le cas du mercure- 

197 les données de sortie, c'est-à-dire les valeurs de n^ et Ej_ 

respectivement, pour les photons У et les électrons de conversion, 

les photons X et les électrons Auger. On voit que 21 composantes 

sont à considérer, 9 pour les X et les électrons de conversion, 

7 pour les photons X et 5 pour les électrons Auger. La désintégration 

se faisant par capture électronique, il n'y a pas de particules 

K en jeu. 

Si nous considérons la seule dose délivrée au rein par les 

particules non pénétrantes, c'est-à-dire en l'occurrence les électrons 

de conversion et les électrons Auger, nous avons pour ces 

deux types de particules : 

I 45! Д 1 = j^soit respectivement 0,1179 et 0,0348 

puisque 1ф1 = 1. 

On voit que les électrons Auger représentent alors 

0 ï l 7 9 'fY 3'o \ ^ 4 8 so:i-t 23 % âe la âose âue aux radiations non pénétrantes, 

fraction dont la plus grosse partie est due aux électrons 

Auger LMM et MXY de très faible énergie par suite de leur nombre 

par désintégration élevé. Une appréciation précise de ces derniers 

exige une connaissance très détaillée des données nucléaires caractérisant 

le schéma de désintégration. Il faut dire qu'elle est 

surtout importante dans le cas des radionuclides décroissant par 

T A B L E A U II. C A R A C T E R IS T IQ U E S D ES G R O U PES D 'E L E C T R O N S 

PR O D U IT S AU CO U RS D E LA D ESIN T EG R A T IO N D E 125I 

(D 'a p r è s F e i g e e t a l. [20]) 

R a yonnem e n t E n e rg ie Ab o n da n ce Porco u rs T E L = E /R TEL.In 

(K«V) A ( •/• ) R(pm) K . V / r m K*V/Pm 

C o n v e r s io n in t e r n e M 1 

C o n v e r s io n i n t e r n e L + A u g e r j 

E l e c t r o n A u g e r K .L X î 

E le c t r o n A u g e r K .L L J 

C o n v e r& io n in te rn e K 1 

E le c tr o n A u g e r LM .M j 

3 2 / 1 9 ,6 2 0 ,9 1,55 0,93 

23.6 19,5 12,1 1 .9 6 1,12 

3 .2 22 0 0 . « 7 ,2 « , в 

o,e 360 0 ,0 5 6 K . 2 11.«

IA E A -S M -1 70/9 7 301 

capture électronique. Pour les émetteurs p - ou P+ , le nombre de 

particules |b par désintégration est en général plus élevé que celui 

des électrons Auger et surtout leur énergie est incomparablement 

plus grande. Aussi la fraction de la dose due aux électrons 

Auger est-elle beaucoup plus faible pour ces nuclides. 

Un autre exemple de l ’importance de l'appréciation précise 

des électrons Auger de faible énergie est fourni par l'iode-125, 

radionuclide décroissant par capture électronique, très utilisé 

en biologie et en médecine. 

Le Tableau II dû à Feige et al. (20) donne les caractéristiques 

des groupes d'électrons produits au cours de la décroissance 

de 125j . énergie, abondance, parcours et transfert linéaire d'énergie. 

Les électrons Auger LMM et MXY de très faible énergie ont 

une très grande abondance et présentent un transfert d'énergie 

linéique élevé pour un parcours très faible. On conçoit que ceci 

peut entraîner un dépôt d'énergie sur des structures subcellulaires 

comme l'interface colloïde-cellule de la vésicule thyroïdienne 

très supérieur à celui que la dose moyenne de radiation délivrée 

au tissu thyroïdien laisserait prévoir. D'autre part, il est 

possible que les ions à charges multiples consécutifs aux cascades 

d'électrons Auger aient quelque importance biologique (21). 

L'ensemble des considérations développées dans ce paragraphe 

montre que si des données nucléaires précises ne sont pas nécessaires 

pour étudier une fonction physiologique ou un métabolisme, 

une connaissance détaillée des caractéristiques nucléaires est 

indispensable pour apprécier les doses de radiation délivrées par 

les radionuclides utilisés chez l'homme à cette fin. 

3. DONNEES NUCLEAIRES DANS LE CADRE’DE LA MESURE DE LA COMPOSI 

TION ELEMENTAIRE DES MATERIAUX BIOLOGIQUES 

L'analyse des milieux biologiques a considérablement profité 

des propriétés particulières des radioéléments, en particulier 

grâce au concept de dilution isotopique. Celui-ci, d ' ailleurs connu 

avant la découverte des radioéléments, n'a pu trouver sa généralisation 

qu'à partir du moment oû n'importe quelle espèce chimique 

a pu être reconnue et mesurée après marquage par un indicateur 

nucléaire. Qu'il s'agisse de la dilution isotopique simple, double, 

de l'analyse par substoiechiométrie, par compétition, ou ra- 

dioimmunologique, le concept utilisé obéit à la formule générale 

M = masse de la molécule ou de l'élément à mesurer, 

A = radioactivité totale de la molécule ou de l'élément dans l'échantillon, 

a g = radioactivité spécifique de l'espèce chimique dans l'échantillon 

après dilution homogène de l'indicateur. 

La radioactivité spécifique, lorsqu'elle est définie comme 

étant le rapport du nombre de noyaux radioactifs au nombre total 

de noyaux présents suppose pour être mesurée la connaissance du 

schéma de désintégration de l'indicateur nucléaire. En fait, le 

chimiste n'a pas besoin de cette donnée car toutes les mesures 

qu'il pratique sont comparatives. A la rigueur il peut lui être 

utile de connaître le mode de désintégration (bé’ta et gamma) du 

radioélément concerné surtout si travaillant à la limite de sensibilité 

de son détecteur il cherche à obtenir le meilleur rapport 

signal/bruit de fond.


Il en est de même pour les méthodes de radioactivation appliquées 

à l'analyse des milieux biologiques "in vitro". Dans son 

principe cette méthode permet, à partir de la mesure de la radioactivité 

induite à la suite d'une réaction nucléaire, de déterminer 

la masse de l'élément présent dans l'échantillon soumis à 

l'irradiation. La loi gouvernant la production de cette radioactivité 

s'exprime par la relation suivante : 

A.des/s 

M = ----------------------------------------------r r ? -------------------- Z ï — 

ф . 6" • f (1-e 1) (e b2) 

dans laquelle 

M = masse à mesurer 

A = masse atomique de l'élément 

des/s = taux de désintégration du radioélément produit au moment 

de la mesure 

ф = flux de particules induisant la radioactivation 

6“ = section efficace de la réaction nucléaire 

f'= abondance isotopique de l'élément stable ayant subi la réaction 

mcléaire 

A = constante radioactive du radioélément produit 

t^ et t 2 = durée de l'irradiation et temps séparant la fin de 

celle-ci de la mesure de la radioactivité. 

Dans la plupart des cas cette formule approchée n'est pas 

utilisée pour convertir le taux de désintégration en masse de 

l'élément dans l'échantillon car les données nucléaires qu'elle 

contient, et en particulier la section efficace, ne sont pas connues 

avec suffisamment de précision. 

Le chimiste préfère éliminer tous ces paramètres en irradiant 

simultanément l'échantillon et un étalon contenant une 

quantité connue de l'élément à doser. 

La connaissance précise des données nucléaires de section 

efficace, de période et de schéma de désintégration permettrait 

de s'affranchir de cet étalon et présenterait un gros avantage en 

particulier au cours des analyses multiélémentaires lorsque l'on 

ne connaît pas au préalable la composition de l'échantillon. Ces 

remarques valables pour 1'activation par les neutrons thermiques 

s'appliquent bien évidemment aux irradiations par les neutrons 

épithermiques pour lesquels les sections efficaces de résonance 

permettent des activations sélectives ainsi qu'aux neutrons rapides 

. 

Un deuxième aspect de l'analyse par radioactivation neutronique 

qui s'apparente plus au domaine de la recherche qu'à celui 

de la routine concerne les analyses "in vivo". Celles-ci pratiquées 

depuis 5 ou 6 ans par quelques laboratoires spécialisés 

(22) utilisent l'irradiation par des neutrons de réacteurs lents 

ou épithermiques ou produits à partir d'accélérateurs. Le Tableau 

III indique les principaux éléments constituant les organismes 

vivants susceptibles d'être dosés par activation "in vivo", leur 

abondance respective, les éléments résultant des réactions, les 

réactions nucléaires qui leur ont donné naissance et les caractéristiques 

nucléaires utilisées pour leur mesure. Il apparaît que 

celles-ci peuvent être soit le résultat de la connaissance du 

schéma de désintégration du radioélément produit (gammas de désintégration) 

, soit le résultat de la connaissance de la réaction 

nucléaire (gammas de capture).

lA E A -S M -1 7 0 /9 7 303 

T A B L E A U III. C A R A C T E R IS T IQ U E S D 'IN T E R E T PO U R LA 

RA D IO A CTIV A TIO N "IN VIVO" D ES E L E M E N T S S U S C E P T IB L E S D 'E T R E 

D O SES P A R C E T T E M ETH O D E 

Elément % Radioélément Réaction Raie t 

stable du poids du corps produit neutronique â mesurer 

H 10 2H n, У capture 

N 3 13N n, 2n désintégration 

Ca 1,5 49Ca n, У 

.désintégration 

capture 

P 1 

( 28A1 

( 32P 

n, * 

n, x 


capture 

Na 0,15 24Na n, désintégration 

Cl 0,15 

( 38C1 

I T7 

( s 

n, гг 

n,p 

(désintégration 

( 

(capture 

Mg 0,05 

(26Mg 

Г 4 Na 

n, * 

n,p 



I 0,03 thyroïde 

I28r n,lT désintégration 

FIG . 8 . S p e c tre s d es g a m m a s d e ca p tu r e d 'u n t ib ia h u m a in ir ra d ié p ar d es neutron s th e rm iq u e s , m on tra n t 

d es ra ies c a r a c té r is tiq u e s du p h o sp h o re , d u s o d iu m , du c h lo r e e t du c a lc iu m .


Il apparaît dans ce Tableau deux éléments, l'hydrogène et l 

phosphore, qui après activation par les neutrons thermiques, conduisent 

à des éléments soit stable (2H) soit radioactif (32P) 

n'émettant aucun gamma de désintégration, seuls les gammas de 

capture permettront de les mesurer. 

Le spectre présenté sur la figure 8, obtenu au cours de 

l'irradiation "in vivo" par des neutrons thermiques^du tibia 

d'un sujet normal, montre les différents K de capture caractéristiques 

du phosphore,du sodium, du chlore et du calcium. L'identification 

de ces raies, si elle peut être faite par comparaison 

avec des étalons de composition connue, suppose cependant une 

connaissance préalable des données nucléaires de la réaction de 

capture. Les raies non identifiées sur le spectre correspondent 

aux pics d'échappement par production de paires de la raie de 

capture à 2,2 MeV de l'hydrogène. 

En raison de leur faible pouvoir de pénétration dans les 

tissus biologiques, les neutrons thermiques ne peuvent assurer 

l'irradiation homogène de la totalité d'un organisme humain. 

C'est la raison pour laquelle l'application de ce type d'activation 

est réduite aux irradiations localisées, desquelles on peut 

déduire cependant des paramètres biologiques intéressants tels 

les rapports en masse des éléments activés (23) . Il est un exemple 

cependant oû la masse totale d'un élément contenu dans un organe 

a pu être dosé par irradiation par les neutrons thermiques. 

Il s'agit de l'iode intrathyroïdien pour la mesure duquel la méthode 

de l'étalon interne a été employée (24). Une quantité connue 

d'iode-129 (T = 1,7.10^ ans) ayant été fixée dans la thyroïde 

et étant supposée avoir la même répartition anatomique que l'iode 

stable natif a été utilisée comme moniteur de flux. Des calculs 

F IG . 9. S p e c tre g a m m a e f f e c t u é a v e c un d é te c te u r G e (L i) o b te n u 6 , 5 m in u tes après u n e ir ra d ia tio n d e 

3 m in u te s aux n eu tron s th e rm iq u e s d e 129I (o r ig in e du c o m p t a g e : 6 , 5 m in ) . Les ra ies i 0. 587 e t 1 ,1 2 M e V 

sont ca r a c té r is tiq u e s d e l'é t a t is o m é r iq u e 130m i.

IA E A -S M -17 0 /9 7 305 

FIG. 10. S c h é m a d e d é s in té g ra tio n p ro p o s é p ou r l 'io d e - 1 3 0 m . 

préliminaires utilisant les caractéristiques de la réaction 129i 

(n, y) 130j et le flux de neutrons disponible avaient permis de 

déterminer la quantité d'iode-129 nécessaire à administrer pour 

obtenir une radioactivité de l'iode-130 mesurable dans les conditions 

expérimentales imposées. L'activation "in vivo" ayant été 

pratiquée, le spectre X enregistré quelques minutes après la fin 

de l'irradiation a montré une raie ¡f d'amplitude et de période 

très différentes de ce qui était attendu. Les analyses détaillées 

de ce spectre et d'autres tels que celui présenté sur la figure 9 

ont permis de mettre en évidence un nouveau radioélément, l’Omj 

de période 9,2 min isomère de 130j non encore décrit dans la littérature 

(25, 26). Le schéma de désintégration de ce nouveau radioélément 

(figure 10) montre que 85 % des désintégrations conduisent 

par transition isomérique au niveau fondamental de l'iode- 

130, et que 13,5 % se font par émission ß“ aboutissant à un niveau 

excité du 130Xe à 536 keV. C'est en fait cette raie qui a 

été mise en évidence sur les spectres enregistrés "in vivo". 

Un deuxième aspect de l'analyse par radioactivation "in vivo" 

concerne l'irradiation totale d'un individu en vue d'y doser 

la masse de calcium, de sodium, de phosphore, d'azote et de chlore 

qu'il contient. L'homogénéité de l'irradiation est obtenue en 

utilisant un flux de neutrons rapides émis par une cible de


FIG. 11, S p e c tr e g a m m a d 'u n rat après r a d io a c t iv a t io n in v iv o au m o y e n d e neutron s d e 14 M e V 

p a r t ie lle m e n t ra le n tis. U p e r m e t d e d é te r m in e r le c o n te n u d e l'a n im a l e n a z o t e (r a ie d ’ a n n ih ila tio n à 

0, 5 11 k e V d e 13N ), p h osp h ore (r a ie g a m m a à 1, 78 M e V d e 28A 1), c h lo r e (r a ie g a m m a à 2 ,1 6 M e V d e 

38C l ) , so d iu m (r a ie s g a m m a à 1, 3 6 et 2, 78 M e V d e 24N a) e t c a lc iu m (r a ie s g a m m a a 3 ,1 0 M e V ). Pour 

ch a c u n e d e s ra ies son t in d iq u é e s le s ré a c tio n s d 'in t e r fé r e n c e . Par e x e m p le le æC l p ré se n te à 1, 60 M e V 

u n e ra ie in d is c e r n a b le p ar s p e c tr o m é tr ie d e s c in t illa t io n d e la r a ie á 1, 78 M e V d e A l. 

béryllium ou de tritium bombardée par des deutons. Selon l'énergie 

des neutrons incidents, il est nécessaire de les ralentir 

partiellement par des matériaux hydrogénés avant lfeur pénétration 

dans le milieu biologique. Les radioéléments produits au cours 

d'une telle irradiation sont plus abondants que ceux obtenus dans 

le cas de l'irradiation par des neutrons thermiques, du fait du 

spectre neutronique complexe comme en témoigne le spectre K présenté 

sur la figure 11. Ce spectre a été obtenu après irradiation 

"in vivo" d'un rat par des neutrons de 14 MeV partiellement ralentis. 

Sous la réaction nucléaire principale conduisant au radioélément 

responsable des pics d'absorption totale présentés, 

ont été indiquées les différentes réactions d'interférence dont 

la connaissance a été nécessaire pour corriger le spectre (27). 

Les résultats obtenus à l'heure actuelle par la méthode 

d'activation "in vivo" sont suffisamment intéressants du point de 

vue médical pour que l'appréciation de la dose absorbée au cours 

d'un tel examen soit appréciée avec une grande précision. Nombreux 

d'ailleurs sont les auteurs qui l'ont calculée théoriquement 

et dans certains cas mesurée expérimentalement aussi bien 

lors de l'irradiation par des neutrons rapides (22) que par des 

neutrons thermiques (28) . Ces calculs généralement extrêmement 

complexes pour la résolution desquels les calculateurs sont nécessaires 

supposent la connaissance des sections efficaces de 

diffusion des neutrons dans la matrice biologique. 

Dans le cas du bombardement par les neutrons thermiques les 

deux sources principales responsables de la dose absorbée sont 

d'une part les Y de capture provenant de la réaction n, if sur 

l'hydrogène et les protons de recul issus de la réaction n, p

c o m p o s itio n du co r p s h u m a in . F lu x d e m u on s: 5 * 1 0 3/s * 10 c m 2 . D u ré e d 'e n r e g is tr e m e n t: 1 h. 

D iffé r e n te s tra n sition s m u o n iq u e s d e О , C e t N sont b ie n v is ib le s . D es ra ies m u o n iq u e s a p p a rten a n t au 

p h osp h ore et au c a lc iu m sont p r o b a b le m e n t présen tes.


sur l'azote-14 (29). Il a été montré que pour un tissu biologique 

de composition moyenne en azote, oxygène, carbone et hydrogène, 

la contribution des У de capture à la dose totale est de 20 %. 

Dans le cas des irradiations par neutrons rapides le processus 

principal de transfert d'énergie des neutrons au tissu biologique 

se fait par les protons de recul dont l'énergie est fonction de 

celle des neutrons incidents. 

Une méthode d'analyse élémentaire "in vivo" potentiellement 

très intéressante a été proposée récemment par L. Rosen et ses 

collaborateurs du Laboratoire Scientifique de Los Alamos (30, 

31, 32), ainsi que par Daniel au C.E.R.N. (33). Il s'agit de 

l'observation des rayons X muoniques produits au cours de l'irradiation 

d'un organisme par un faisceau de muons négatifs. Ces 

particules ayant une masse 207 fois plus grande que celle de 

l'électron, forment, quand elles sont stoppées dans la matière, 

des atomes muoniques d'une durée de vie de moins d'une nanoseconde 

et qui disparaissent en produisant des rayons X muoniques 

d'énergies discrètes 200 fois plus élevées que celles de leurs 

homologues ordinaires. Par exemple pour le carbone la raie XK 

muonique est à 75 keV. On conçoit qu'à ces énergies les rayons 

X muoniques de tous les éléments puissent faire aisément l'objet 

d'une détection externe dans un organisme. D'autre part le rendement 

de production est très élevé, c'est-à-dire que 90 % des 

muons stoppés dans les tissus doivent donner un photon XK . 

La figure 12 montre le spectre de rayons X muoniques que 

nous avons obtenu au cours d'une expérience préliminaire à l'Accélérateur 

Linéaire de Saclay sur un fantôme cubique de 10 cm de 

côté ayant la composition du corps humain pour les principaux 

éléments. L'intensité du faisceau de muons était de 5.10^ p ”/s 

sur une surface de 10 cm^ normale au faisceau. Il était produit 

par un faisceau d'électrons de 300 MeV de 27 mA de courant de 

crête à une fréquence d'impulsion de 2 OOO hertz et un cycle utile 

de 1 %. Tous les muons sont stoppés dans le fantôme. La détection 

était effectuée au moyen d'un détecteur Ge(Li) de 30 cm3 de 

volume utile et la durée d'enregistrement de une heure. Les raies 

du carbone de l'oxygène de l'azote et ce qui est plus intéressant 

une raie du phosphore et peut-être du calcium sont visibles. Si 

on dispose un jour de flux de p- 100 à 1000 fois plus élevé, la 

méthode peut devenir applicable pour l'analyse élémentaire "in 

vivo", mais nécessitera des données nucléaires plus précises sur 

la production des muons négatifs et de leur interaction avec la 

matière. 

Terminons en disant que nous avons éliminé systématiquement 

de cet exposé certains phénomènes nucléaires tels que la R M N , 

l'effet Mössbauer(34,35)et la corrélation angulaire (36) qui peuvent 

présenter de l'intérêt dans certains domaines biologiques et 

médicaux étroits. 


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G . A . K O L S T A D : T h i s i s a q u e s t i o n t h a t b e a r s o n t h e s t a t u s o f b i o m e d i c a l 

t h e o r y . A s y o u k n o w , w e h a v e t h u s f a r d i s c o v e r e d o n l y a b o u t 1 6 0 0 o f t h e 

6 0 0 0 r a d i o i s o t o p e s p r e d i c t e d t o e x i s t b e t w e e n t h e p r o t o n a n d n e u t r o n d r i p - 

l i n e s t h a t b o u n d t h e v a l l e y o f s t a b i l i t y . C a n y o u s p e c i f y , o n t h e b a s i s o f 

t h e o r e t i c a l l y o p t i m u m m o d e l s ( e . g . f o r t h e l i v e r , k i d n e y , b o n e , b r a i n , 

t h y r o i d , e t c . ) t h e c h a r a c t e r o f t h e r a d i a t i o n y o u n e e d f o r t h e d i f f e r e n t 

b i o m e d i c a l a p p l i c a t i o n s a n d t h u s s e n d o f f t h e n u c l e a r p h y s i c i s t s t o s e e k t h e 

p a r t i c u l a r i s o t o p e s y o u n e e d f o r t h e s e v a r i o u s a p p l i c a t i o n s ? 

C . K E L L E R S H O H N : S p e c i a l i s t s i n n u c l e a r m e d i c i n e a r e f u l l y a w a r e 

o f t h e p r o b l e m w h i c h y o u r a i s e . T h u s f a r , t h e i r c r i t e r i a f o r d e c i d i n g w h a t 

c o n s t i t u t e s t h e f a v o u r a b l e c h a r a c t e r i s t i c s o f a r a d i o e l e m e n t h a v e b e e n b a s e d 

o n t h e p o s s i b i l i t y o f r e d u c i n g t h e r a d i a t i o n d o s e t o t h e o r g a n i s m s o r o f 

i n c r e a s i n g t h e a c t i v i t i e s i n j e c t e d , f o r e q u i v a l e n t d o s e s , i n o r d e r t o i m p r o v e 

t h e a c c u r a c y o f m e a s u r e m e n t s , o r e l s e o n t h e e m i s s i o n o f g a m m a p h o t o n s 

o f e n e r g y e s p e c i a l l y f a v o u r a b l e f o r e x t e r n a l d e t e c t i o n , d u e a l l o w a n c e b e i n g 

m a d e f o r t i s s u e a b s o r p t i o n a n d f o r t h e p r o p e r t i e s o f t h e d e t e c t o r s u s e d . 

T h i s i s t h e r e a s o n w h y a n e l e m e n t l i k e 9 9 m T c , w h i c h w a s d e v e l o p e d b y 

P a u l H a r p e r , a n d w h i c h e m i t s a n i n t e n s e g a m m a l i n e a t 1 4 0 k e V a n d v e r y 

l i t t l e e n e r g y i n t h e f o r m o f c h a r g e d p a r t i c l e s , i s s o w i d e l y u s e d i n n u c l e a r 

m e d i c i n e e v e n t h o u g h i t i s n o t a n a t u r a l c o n s t i t u e n t o f t h e b o d y . D i s r e g a r d i n g 

t h e m a t t e r o f m e t a b o l i c s p e c i f i c i t y , i t d o e s n o t a p p e a r t h a t t h e n a t u r e o f t h e 

o r g a n u n d e r s t u d y h a s p l a y e d a n i m p o r t a n t r o l e i n t h e i r c o n c e r n s . F o r 

e x a m p l e , i t s e e m e d t o u s , i n t h e c a s e o f t h e t h y r o i d g l a n d , w h i c h i s a n 

o r g a n o f s m a l l v o l u m e c l o s e t o t h e c u t a n e o u s p l a n e s , t h a t i t m i g h t b e a d v a n 

t a g e o u s t o u s e a n e l e c t r o m a g n e t i c r a d i a t i o n o f l o w e n e r g y f o r o b t a i n i n g 

i m a g e s , s i n c e u s e c a n t h e n b e m a d e o f c o l l i m a t o r s w i t h v e r y f i n e s e p t a , 

w h i c h e n a b l e o n e t o g e t e x c e l l e n t r e s o l u t i o n . I n t h i s w a y , w e g e t p i c t u r e s 

o f t h e t h y r o i d i n o u r l a b o r a t o r y w i t h X k p h o t o n s o f 1 2 5 T e e m i t t e d b y 1 2 5 I b y 

m e a n s o f a s p a r k c h a m b e r p e r m i t t i n g a r e s o l u t i o n o f 1 m m . 

W h a t e v e r t h e c a s e m a y b e , I a g r e e w i t h y o u i n f e e l i n g t h a t i n t h e c a s e 

o f r a d i o i s o t o p e s w h i c h a r e s t i l l u n k n o w n , w e h a v e t o s e l e c t s e v e r a l o f t h o s e 

w h i c h a r e l i k e l y t o p r e s e n t m o r e f a v o u r a b l e c h a r a c t e r i s t i c s w i t h r e s p e c t 

t o t h e s e p r o b l e m s t h a n t h e n u c l i d e s k n o w n a t p r e s e n t . 

R . N I C K S : I n t h e p a p e r y o u u s e t h e M o n t e - C a r l o m e t h o d a n d t h e m e t h o d 

o f m o m e n t s c a l c u l a t i o n s t o d e a l w i t h t h e p r o b l e m o f t r a n s p o r t o f r a d i a t i o n 

( p h o t o n s , e l e c t r o n s ) i n t h e o r g a n u n d e r s t u d y . T h e l a t t e r t e c h n i q u e , h o w e v e r , 

i s a p p l i e d o n l y i n a n i n f i n i t e h o m o g e n e o u s m e d i u m a n d t h e r e f o r e i s n o t d i 

r e c t l y a p p l i c a b l e t o o r g a n s o f f i n i t e d i m e n s i o n s . H o w d o y o u m a k e a l l o w a n c e 

f o r f i n i t e d i m e n s i o n s ? 

C . K E L L E R S H O H N : T h e u s e o f t h e M o n t e - C a r l o m e t h o d s i n c o n n e c t i o n 

w i t h t h i s p r o b l e m h a s b e e n t h e s u b j e c t o f a n u m b e r o f s t u d i e s b y t h e B r o w n e l l 

g r o u p f o r o v e r t e n y e a r s , w h i l e t h e m o m e n t s m e t h o d ( S p e n c e r a n d F a n o ) 

h a s b e e n d e v e l o p e d a l o n g t h e s e l i n e s m a i n l y b y B e r g e r . T h e t w o m e t h o d s 

a r e c o m p l e m e n t a r y t o s o m e e x t e n t , s i n c e t h e y c a n b e u s e d f o r k e e p i n g a 

r e l a t i v e c h e c k o n o n e a n o t h e r . 

O f c o u r s e , I a g r e e w i t h y o u t h a t t h e m o m e n t s m e t h o d i s a p p l i c a b l e 

o n l y t o i n f i n i t e m e d i a . I t i s f o r t h i s r e a s o n t h a t t h e p r e s e n t t r e n d i n p h o t o n 

d o s i m e t r y i n m a n i s t o u s e t h e r e s u l t s o b t a i n e d b y t h e M o n t e - C a r l o m e t h o d , 

w h i c h a f f o r d a m e a n s o f t a k i n g b o u n d a r y e f f e c t s i n t o a c c o u n t .


NUCLEAR DATA REQUIREMENTS IN RADIOLOGICAL 

PROTECTION AND RADIOTHERAPY 

J. A. DENNIS, 

Head of Physics Department, 

National Radiological Protection Board, 

Harwell, Berks, 

United Kingdom 

Abstract 

NUCLEAR D A T A REQUIREMENTS IN RADIOLOGICAL PROTECTION A N D RADIOTHERAPY. 

The estimates of somatic and genetic risks arising from exposure to low levels of ionizing radiation are 

derived by linear extrapolation from the effects which have been observed when humans and animals were 

exposed to large acute doses of radiation for therapeutic or other reasons; this undoubtedly results in an over 

estimate of the risks, but no adequate theoretical basis exists for any other form of extrapolation. The 

dependence of the risk on the quality and type of the radiation is based by convention on the linear energy 

transfer (i.e . specific energy loss) of the ionizing particles in water. This convention is undoubtedly incorrect. 

While it must be considered that the present levels of allowable exposure to radiation give adequate protection 

to the individual and society, the existing uncertainties generate some unease. Although the main obstacle 

to the resolution of these uncertainties in the absence of a detailed understanding of the biological processes 

involved, an additional obstacle is the lack of adequate physical data and theories to fully describe the 

interaction of radiation with matter. This inadequacy effects the accuracy of radiation dosimetry and also 

makes it difficult to develop theoretical explanations to account for the dependence of biological effects on 

radiation quality. 

Similar difficulties exist in the field of radiation therapy, where there is a growing awareness of the 

advantages of using fast neutrons and accelerated heavy ions for the treatment of tumours. The absence of an 

adequate theoretical explanation for the dependence of effect on radiation quality makes it difficult to fully 

evaluate the advantages of using alternative types of radiation other than experimentally. 

Some of the current attempts at developing theoretical explanations of the dependence of biological 

effects on radiation dose and quality are described briefly in order to delineate those areas where additional 

physical data are required. 


The need for nuclear data arises in several different 

ways in Radiological Protection and Medicine* The most 

obvious which comes to mind is that for cross-section and 

build-up data for the calculation of the shielding of 

radiation sources, but this is no different from the 

present needs of the Nuclear Industry. Less obvious is the 

need for data on methods of producing different isotopes, 

and their half-lives and decay schemes* This data is 

required in the growing field of Nuclear Medicine for the 

use of isotopes in diagnostic techniques for various 

diseases and metabolic misfunctions of the human body; it 

is also required for radiological protection specification 

in the chemical plants of the Nuclear Fuel industry. Not 

only is the data required to be available, it also needs to 

be presented in a manner that is useful to the practical 

user who may not understand and care even less about 

theories of nuclear and atomic structure* 

313

314 DENNIS 

However, these aspects are not further discussed in 

this paper which is concerned with the nuclear data 

required to further our understanding of the dependence of 

the biological effects produced by radiation upon the 

quality of the radiation. One reason for concentrating on 

this requirement is that it throws up a demand not merely 

for an extension of the data on cross-sections to a much 

wider range of energies, but also for an extension of the 

way in which this data is provided. 

2. BIOLOGICAL EFFECTS OF RADIATION 

An obvious point to start an investigation of the 

fundamentals of the biological effects of radiation is 

by the irradiation of artificially cultured mammalian 

cells Г 1_7. The aim of such investigations being to 

uncover any general physical and biological effects which 

are relevant to radiation-therapy for cancer or to the 

prediction of the risks of somatic and genetic effects from 

low levels of radiation. 

D O SE (r a d s ) 

F IG .l . Survival of Chinese hamster cells (HI) after exposure to fast neutrons and X-rays after SCHNEIDER, D . 

WHITM ORE, G . F . , Radiat. Res. 18 (1963) 286 illustrating the RBE concept.


The typical results of such experiments are shown in 

Figure 1. Surviving cells are defined in this type of 

experiment as those which are capable of producing at 

least 50 daughter cells by further division. If instead 

of plotting the logarithm of the number of surviving cells 

against absorbed energy, the number of cells killed by the 

radiation had been plotted on a linear scale the result 

would have been that shown in Figure 2. It is this latter 

type of plot which encourages the belief that the risk 

estimates for occupation exposure to low doses of radiation 

derived /~2J from the exposure of human beings to large 

doses of gamma radiation for therapeutic reasons by linear 

extrapolation are over estimates. The therapist using 

radiation to cure a malignant disease has always to 

balance, of course, the risk of inducing further 

malignancies by his treatment against the possibility of a 

cure. 

Two further points must be made about dose-effect 

curves. 

Firstly, as shown in Figure 3» the efficiency for 

producing an effect increases as the specific energy loss 

or linear energy transfer, LET, of the radiation increases. 

D O S E ( ra d s) 

FIG. 2. Killing of Chinese hamster cells (HI) after exposure to fast neutrons and X-rays, illustrating the effect 

of linear extrapolation to low doses from the high results.

316 DENNIS 

D O S E ( K r a d s ) 

FIG .3. Effect of using radiations with different specific energy loss (LET) to irradiate cultured human kidney 

cells after ВARENDSEN, G . W . , WALTER, H . M . D . , FOWLER, J .F ., BEWLEY, D . K . , Radiat. Res. 18 (1963) 106. 

Moreover, relative to the effect produced by X-radiation 

the efficiency of high LET is greater at low levels of 

effect and small doses of radiation, Figure k. The 

relative biological effectiveness, RBE, of a radiation is 

defined as the ratio of the dose of from X-radiation to the 

dose from the specified radiation to produce the same level 

of effect, Figure 1. 

Secondly, the protection against damage afforded by 

depriving the biological material of oxygen decreases as 

the specific energy loss of the radiation increases, 

Figure 5* Since it is thought that many tumours are 

starved of oxygen due to a poor blood supply, this 

observation is one basis for proposals to use neutrons for

1Л 

UJ 

2 

( J 

ÜJ - 

ü. 5 

U. 

< 4 

U 

О о 

d 3 

со 

u j p 

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0*1 


I lililí -1— I—I II 1111 “I— I I I I I I I-1---1— Г Т 

I - > I 1 1 I I 1J_______ I 1 1 I 1 I I I 1_______ l_ ,J. .1 .L-LL_uJ___________I I I I I I I 

I 10 IO O 

IO O O 

L E T IN T IS S U E I K eV /jim ) 

FIG .4. Effect of estimating the RBE at different levels of effect, showing the increase in RBE for low levels of 

effect after BARENDSEN, G . W . , WALTER, FOWLER, J .F ., BEWLEY, D . K . , Radiat. Res. 18 

(1963) 106. 

D O S E ( K r a d ) 

FIG. 5. Effect of oxygen deprivation in protecting cells against the effects of radiation, illustrating the decrease 

in protection as the specific energy loss of the radiation increases.

318 DENNIS 

F IG .6. An illustration of the better depth dose characteristics of accelerated heavy ions and negative it-mesons 

for the treatment of deep tumours after Ref. [ 4 ] . 

radiation therapy, the other is that tumours may exhibit 

higher RBE values than normal tissues / 3J and therefore 

be more susceptable to treatment with neutrons than with 

X-radiation. 

One of the difficulties of treating deep lying 

tumours with X-rays, electron beams or neutrons is that 

the overlying healthy tissue receives greater doses than 

the tumour, and this can only be overcome to some extent 

by using multi-directional beams and higher energies. For 

this reason accelerated heavy ions beams have been used 

and negative pi-mesons are proposed for use in radiotherapy, 

since the depth dose charactaristics are more 

favourable /"”^_7, Figure 6. 

Now the dependence of biological effect on the 

specific energy loss demonstrated in Figure W has 

encouraged the belief that the RBE of radiation depends 

directly on the specific energy loss. This belief is now 

embodied in the Quality Factor which is used in 

radiological protection, Figure 7« The quantity used to 

estimate the hazards from radiation is the dose-equivalent 

of which the unit is the rem.


Ol l.o ю юо юоо 

L IN E A R E N E R G Y T R A N S FER lK eV у of tissue o r water) 

F IG .7. A comparison of the conventional quality factor with an experimentally determined RBE. 

Dose-equivalent in rem = Absorbed dose in rads x 

Quality Factor 

The ICRP recommendations for maximum permissible 

levels of dose-equivalent to guard against both somatic 

and genetic risks are given in Table I. 

The Quality Factor is most commonly involved in 

estimating the hazards from neutron and high energy 

accelerator radiations. 

Neutrons do not produce a single defined value for 

the specific energy loss in tissue, instead they produce 

distributions such as that shown in Figure 8. This 

distribution must be calculated from a detailed knowledge 

of the reactions produced by neutrons in the common 

elements of the body i.e. hydrogen, carbon, nitrogen, 

oxygen and calcium. At high neutron energies (>5MeV) not 

only are the details of the non-elastic and in-elastic 

reactions often uncertain but so are the cross-sections. 

Also involved in these calculations is the specific energy 

loss in biological tissue of the secondary particles 

produced and this is an additional source of uncertainty. 

If the calculated specific energy loss distributions 

from neutrons are combined with the apparent dependence of 

RBE upon specific energy loss determined experimentally, 

then it should be possible to predict the RBE of neutron 

radiation. Attempts to make this prediction have been 

unsuccessful •

TABLE I. SUMMARY OF I. C. R . P. RECOMMENDATIONS FOR MAXIMUM PERMISSIBLE 

LEVELS OF DOSE EQUIVALENT (I. C. R. P. PUBLICATION 9, PERGAM ON PRESS, 

OXFORD (1966) 

Organ 

Maximum Permissible Yearly 

Dose-Equivalent for adults 

exposed in the course of 

their work. 

Rem 

Maximum Permissible Yearly 

Dose-Equivalent for 

members of the public. 

Gonads 5 0.5 

Skin, bone and 

thyroid 30 3 

Hands, forearms, feet 

and ankles 75 7-5 

Other single organs 15 1.5 

Notes : 

1. One half the yearly permissible dose-equivalent may be accumulated in any 

period of a quarter of a year; with the limitation that the total 

accumulated dose at any age over 18 should not exceed 5(N - 1 8 ) rem, where 

N is the age in years. 

2. Women of reproductive age exposed in the course of their work should not 

accumulate dose-equivalent at a rate exceeding 1.3 rems in a quarter of a 

year. 

3. To guard against long term genetic consequences the total average dose to 

members of a population should not exceed 5 rems in a period of 30 years. 

Rem


LETœ MeV-cm2 g I 

F IG .8. Specific energy loss spectrum in fast-neutron-irradiated tissue after BEWLEY, D. K . , in Biophysical 

Aspects of Radiation Quality (Proc. Panel Vienna, 1967), IAEA, Vienna (1968) 65. 

The specific energy loss for a heavy ion, Figure 9, is 

not a single-valued function of the ion energy, moreover 

the energy loss processes may be quite different for the 

same specific energy loss value obtained at different 

energies. Intuitively it seems inherently unlikely that 

the different modes of energy loss should produce equal 

biological effects. When different ions are considered it 

seems even less likely that specific energy loss is an 

adequate parameter, since ions of the same energy loss may 

produce quite different distributions of delta-ray 

energies and energy deposition about their tracks. 

3. DOSE-EFFECT RELATIONSHIPS 

Perhaps the most obvious way of explaining the 

observed relationships between the dose to the tissue and 

the observed effect is in terms of hits on targets, in a 

conceptual framework that originated in the 1920's. The 

most widely used idea from this framework is that of m 

sensitive targets in the cell each of which must be hit in

322 DENNIS 

F IG .9. Specific energy loss of alpha particles in water. (DENNIS, J . A . , private compilation.) 

order to kill the cell, and the dose Do required to produce 

an average of one hit on each target. This gives rise to 

the following formula relating the N survivors of an 

original population No to the dose J). 

Apart from the study of cell killing, the other major 

study is that of chromosome aberrations. These are gross 

visible distortions in the genetic material, of the cell. 

The relationship between the number of aberrations, A, 

observed in the population No, and the dose can very often 

be represented by a combination of single and two target 

models i.e. 

2. 

A_ 

— = ^1 - exp( - D /jD 1 - exp - D/2D 0j) (2) 

N0 

which for very low doses can be usefully expanded as 

Nn 

D 

It must be said at this point that the problem is ill- 

conditioned in the sense that a large number of different 

expressions can be made to fit the experimental results 

(1) 

(3)


equally well /_ 6_7. In fact some biologists reject the 

whole hit and target concept in favour of explanations 

based on metabolic factors /"”7_7. It is certainly true 

that the dose-effect curves are changed by metabolic 

factors such as temperature, absence or presence of oxygen 

and the position of the cell within its cycle of growth and 

division at the time of irradiation. Also the ability of 

some cell systems to repair the damage caused by radiation 

has been demonstrated 1_J7. On the other hand it seems 

unlikely that purely metabolic factors can account for the 

dependence on radiation quality. 

k. MICRODOSIMETRY AND TRACK STRUCTURE 

The work of Lea Г 8_7 in the late 1930's and early 

19^0 's is seminal in attempts to provide a physical 

explanation for biological effectiveness, and in many ways 

his work anticipated the two current and contending 

theories. These theories are known as microdosimetry and 

track structure. 

4.1 Microdosimetrv 

------------------------------ ^ 

The basis of microdosimetry is the calculation or 

more often the measurement 9_/ of the energy event size 

distribution, f1(€) d£, in spherical volumes with 

effective dimensions of about 10“^ gram cm-^ Several 

considerations /"”10_J7 lead to the conclusion that there 

exist one or more loci or targets of dimensions about 0.6 

nanometers which must be activated in order to cause a 

chromosome aberration or kill a cell, and these locii must 

exist within a site of dimensions about 1.0 micrometer 

(i.e. 10“^ gram cm-2 in tissue). 

о 

It is assumed /”10_7 in microdosimetry that the 

probability of activating a locus is proportion to the 

size of the energy deposited in the site i.e. 

p = це (4) 

where ц is a constant of proportionality. 

These assumptions lead to the following expression for 

chromosome aberrations! 

Ao =J¿^- D - j j r e n - 2/u2 | + . . . etc. (5) 

¿P is the dose average event size. 

This theory has yet to be vigorously tested by 

exploration with a range of different radiations and 

biological systems. 

A difficulty in testing the theory is that of 

calculating the energy even size distribution, f^f) d£, 

as this requires a detailed knowledge of neutron cross- 

sections and reaction kinetics, as well as details of the 

energy loss in tissue by the secondary particles produced.

324 DENNIS 

Similar details are required for X-rays and electrons, and 

a point of investigation here is the influence of К and L 

shell effects and molecular b i n d i n i o n the energy loss 

processes of low energy electrons /”11_7. 

One might anticipate at this stage that the 

coefficient will not be independent of the mode of 

energy loss that produces the energy deposition £. This 

will open a new field of investigation requiring data on 

charge exchange processes, inner shell ionization 12_7 

and quasi-elastic nuclear scattering / ”13J * 

k .2 Track Structure 

Because of the ultimate influence of metabolic factors 

in governing the repair and recovery of cell populations 

that have suffered a large radiation insult it seems 

unlikely that the theory of microdosimetry can usefully be 

employed at this time in the field of radiotherapy. It is 

in this field that the track structure theory being 

developed by Prof. Katz 14_"7 may prove applicable. 

Briefly Katz takes the multi-target dose-effect 

survived curves, equation 1 above, obtained with X-radiation 

to represent the response function of the cells to 

electrons. From this response function he derives the 

dose-effect curves for heavy ions by regarding them as 

generating non-uniform distributions of electrons within 

tissue. 

After some manipulation a theoretical expression is 

obtained for the expected dose-effect relationship which 

has the plausible form for tissue irradiated by a fluence 

5. DISCUSSION AND CONCLUSION 


The importance of the theoretical explanations for the 

dependence of biological effect on radiation quality should 

not be over emphasized. One must assume that any 

responsible radiotherapist proposing to use something other 

than the conventional radiations will first have satisfied 

himself by means of a series of biological experiments 

that his treatment will be beneficial to his patient. On 

the other hand a 10% uncertainty in the level effect 

produced, or in the dosimetry, may make a significant 

difference to the cure rate in radiotherapy 7~15_'7. 

There is no evidence either from studies with plants, 

insects and animals or from the long term follow-up of the 

victims /”16J of the atomic bombing of Japan that the 

Quality Factors are seriously in error. Never-the-less any 

uncertainties in our understanding of the connection 

between radiation quantity and quality and the biological 

effects produced can be used to create public unease by 

those who are so minded /~17_7. 

The full understanding of the biological effects of 

radiation has been likened to digging a tunnel under a high 

mountain, not by starting at the ends and working towards 

the centre, but by sinking a series of vertical shafts and 

working outwards from the bottom of each. At one end are 

the biologists and medical practioners studying the somatic 

and genetic effects of irradiating animals and human 

beings, at the other end are the physicists studying the 

primary features of the interaction of radiation with 

matter. In between come the biologists studying the effects 

on cultured mammalian cells, bacteria and viruses; the 

radio-chemists studying radiation damage to and energy 

transfer within large micro molecules and enzymes ; and the 

physicists concerned with energy deposit in processes 

within tissue. It is the latter group that are now 

extending their requirements for nuclear data; I hope that 

resulting from this symposium will be data that is of 

some assistance to them in the next stage of investigation. 

REFERENCES 

j T l l ELKIND, M.M., WHITMORE, G.F., The Radiobiology of 

Cultured Mammalian Cells. Gordon and Breach, 

New York (1 9 6 7). 

/”2_7 ICRP Publication 14, Radiosensitivity and Spatial 

Distribution of Dose, Pergamon Press, Oxford (19 6 9). 

/"3_7 BROERSE, J.J., BARENDSEN, G.W. , FRERIKS, G., 

VAN PUTTEN, L.M., Europ. Journ. Cancer ¿ (1971) 171. 

£ " k j BEWLEY, D.K., Nature 2 37 (1972) 17. 

Г ъ 7 BEWLEY, D.K., Radiat. Res. 34 (1968) 446 

Г 6_7 ZIMMER, K.G. , Studies on Quantitative Radiation 

Biology. Oliver and Boyd, Edinburgh (1 9 6 1).

326 DENNIS 

C l J LAURIE, J., ORR, J.S., FOSTER, C.J., Brit. Journ. 

Radiol. 4¿ (1972) 36 2. 

/"8_7 LEA, D.E., Act ions of Radiation on Living Cells. 

Cambridge University Press (1946). 

Л 9 _ 7 ROSSI, H.H., Radiation Dosimetry. Vol. I (Ed. Attix, 

F.H., Roesch, W.C.) Academic Press, New York 

(19 6 8) 43. 

/”10 7 KELLERER, A.M., ROSSI, H.H., Radiation Research 

42. (1 9 7 1 ) 15. 

/~11_7 ARAKAWA, E.T., BIRKHOFF, R.D. , et. al. Oak & Ridge 

National Lab. Report ORNL - 4811 (1 9 7 2 ). 

/”12_7 METZ, W.M. , Sc ience 177 (I9 7 2 ) 1 5 6 . 

/_13_7 WATT, D.E., Phys. Med. Biol. ¿2. (1972) 409. 

/~14_7 KATZ, R., SHARMA, S.C., HOMAGOONFAR, M., Chapter 6. 

Progress in Radiation Dosimetry Ed. Attix F.H. - 

to be published. 

/”15_7 BARENDSEN, G. W ., BROERSE, J.J., First Sumposium on 

Neutron Dosimetry in Biology and Medicine. Commission 

of the European Communities. Luxemburg .1 (1972). 

/”l6_7 ICRP Publication l8. The RBE for High-LET Radiations 

with respect to Mutagenesis. Pergamon Press, Oxford 

(1 9 7 2 ). 

r i 7 j GOFMAN, J.W. , TAMPLIN, A.R., Poisoned Power. Rodale 

Press. Emmaus (I9 7I). 


L . HJÄRNE: W e have som etim es been given the im p ression that, o f 

all nuclear data, the neutron data are in fa irly good shape. T h erefore it 

is perhaps su rp risin g to many o f us that the attempts to p red ict RBE have 

not been v e ry su ccessfu l. R egarding the ela stic and in elastic data for 

neutrons above 5 M eV, the rea ctor p h y sicists, too, would agree that there 

is still a lot to be d esired . H ow ever, the fact that the situation is not good 

enough fo r dose calculations is disturbing. I would th erefore like to ask 

fo r you r opinion on w here the g reatest difficu lties lie . Is it a m atter o f 

the c r o s s -s e c tio n s and the angualr o r energy (secondary) distributions or 

does it have to do with the calculational m ethods? 

J .A . DENNIS: P articu la r d ifficu lties a rise in the n on -ela stic rea ction s, 

m ore s p e cifica lly the (n, a) reaction s with carbon and oxygen. Oxygen is a 

m a jor constituent o f b iolog ica l tissu e. A bove a neutron energy o f 5 MeV 

virtually all we have is the total c r o s s -s e c tio n fo r the (n ,a) reaction s with 

this elem ent. W e know that there are, at least, five o r six alpha groups 

from this reaction , and without details o f the c r o s s -s e c tio n s fo r each alpha 

group the d ose estim ates can be as much as 20% in e r r o r . When calculations


o f lin e a r e n e rg y t r a n s f e r d istr ib u tio n s a r e to b e m a d e , we r e q u ir e even 

g r e a t e r d e ta il, sin c e the e x a c t a lp h a sp e c tr u m p ro v id e d in e a c h a lp h a gro u p 

m u st be known. 

It i s m y im p r e s s io n th at c o m p ila tio n s o f c r o s s - s e c t i o n s h ave in the 

p a s t b een co n cern e d only w ith the fa te o f the n eu tron in r e a c t o r a p p lic a tio n s. 

In b io lo g y and m e d ic in e w e a r e c o n cern e d w ith the se c o n d a r y p a r t ic le s a s 

a r e s u lt o f the n eu tron r e a c t io n s .

IAEA -SM-170/64 

PROBLEMES POSES PAR LA FABRICATION DE 

PLUTONIUM-238 DE QUALITE BIOMEDICALE 

R. BERGER*, C. DEVILLERS*, F. GERVAISE*, G. LE C O Q ** 

Commissariat à l'énergie atomique, 

France 


PROBLEMS OF FABRICATING 238Pu OF BIOMEDICAL Q U A L IT Y . 

The biomedical quality of z38Pu presupposes the lowest possible 236Pu concentration, this being 

determined by irradiation methods. The results of the chemical analysis of !37Np samples irradiated in 

reactors have been compared with the results of calculation. A good knowledge of the cross-sections o y ,n et 

° n , 2n °f z37Np is necessary for calculating the 236Pu concentration and for optimizing the irradiation 

conditions. Evaluations having shown that it was difficult to estimate these data correctly in the present 

state of knowledge, oy , n was measured. By slightly adjusting the calculated results for the experimental 

results it may be possible to produce 238Pu of satisfactory quality. 

PROBLEMES POSES PAR LA FABRICATION DE PLUTONIUM-238 DE QUALITE BIOMEDICALE. 

La qualité biomédicale du 238Pu exige la plus faible teneur possible en 236Pu, celle-ci étant déterminée 

par les méthodes d'irradiation. L'analyse chimique d'échantillons de 237Np irradiés dans des réacteurs a 

pu être comparée avec les résultats de calcul. Une bonne connaissance des sections efficaces Oy n et 

°n 2n du 237Np est nécessaire pour le calcul de la teneur en 236Pu et l'optimisation des conditions d'irradiation. 

Les évaluations ayant montré qu' il était difficile d’ estimer correctement ces données avec les connaissances 

actuelles, une mesure de O y ,n a été effectuée. Un léger ajustement des résultats de calcul sur les résultats 

expérimentaux permet d'envisager la production d e 23!Pu de qualité satisfaisante. 

INTRODUCTION 

Le plutonium -238 est u tilisé com m e sou rce therm ique du con vertisseu r 

th erm o -électriq u e du stim ulateur cardiaque [1 ]. Cette application n écessite 

certain es p rop riétés de pureté du 238Pu. En effet, certa in es tra ces contenues 

dans le s descendants du 238Pu contribuent au ssi â l'a ctiv ité radiologiqu e soit 

en 7 pour le 236Pu, soit en neutrons par réaction (a, n) sur le s élém ents 

lé g e rs tels que F , O, A l, Ca. La fabrication du 238Pu par irradiation en 

p ile de 237Np peut produ ire du 236pu par réa ction (7, n) et réaction (n, 2n) 

sur le 237Np. La connaissance des sections e ffica ce s de ce s deux réaction s 

est n é c e s s a ir e au ca lcu l de la teneur en 236Pu fabriqué com pte tenu des 

conditions d 'irradiation . 

1. DOSE INDUITE PAR LES NEUTRONS E T LES RAYONNEMENTS 

GAMMA 

Nous rappelleron s ic i le s données n é ce ssa ire s au ca lcu l de la dose 

d'une sou rce de 155 m g de 238Pu dont la teneur isotopique est de 90%. 

L 'a ctiv ité due aux neutrons et aux gam m as provenant des isotop es su périeu rs 

au 238Pu est n égligeable. 

* Centre d ’ études nucléaires de Fontenay-aux-Roses. 

* * Centre d'études nucléaires de Saclay. 

329

330 BERGER et a l. 

1. 1. N eu tron s 

P our chaque fissio n spontanée le 238Pu ém et en m oyenne v = 2, 29 neutrons 

la p ériod e de fissio n étant d'environ 5, 0 • 1010 ans, la sou rce con sid érée 

ém et Sn = 355 n /s , le sp ectre énergétique étant de la form e 

N(E) = C • E 0> 5 exp ( - Е / 1, 23), E exprim é en MeV. Ce sont des neutrons 

ra p id es, donc ils ne sont pratiquem ent pas a rrê té s par le s m atériaux 

constituant le stim ulateur; la seule m anière de réd u ire la dose due aux 

neutrons est d 'éloig n er au m axim um la sou rce de la paroi. 

La dose m axim ale m oyennée sur un élém ent de surface due à ce s 

neutrons est égale à 0, 9 m rem /h [ 2 ]. Le nom bre de neutrons ém is par 

réaction (a, n) sur le s élém ents lé g e rs dépend de la concentration de ces 

élém ents dans le 238Pu (voir p aragr. 3). 

1. 2. Rayonnement gamma 

L es gam m as provenant du 238Pu sont ém is au cou rs de la désintégration 

a de p ériod e T = 87, 5 ans. Ces gam m as sont principalem ent de faible 

én ergie. P our une désintégration a il y a m oins de 2 • 10"5 gamma d 'én ergie 

supérieure â 150 keV. P our le 236Pu, l'a ctiv ité gamma est principalem ent 

due aux gam m as provenant de la désintégration ß~ des noyaux de fin de 

chaîne. Cette activité est donc variable dans le tem ps et présente un 

m axim um â 18 ans. C es gam m as ém is sont plus énergétiques; par rapport 

à une désintégration ß, 60% des y ont une én ergie supérieure à 200 keV, 

dont 14% ont une én ergie de 583 keV et 17% une énergie de 2, 6 M eV [ 2 ]. 

P our la sou rce de 238Pu contenant 0, 5 ppm de 236Pu, l'a ctiv ité gamma est 

la suivante (en désintégrations par secon de): 

T (ans) 0 1 2 5 10 20 

P u-238 8, 9 ■ 1010 8, 8 ■ 1010 8, 8 • 1010 8, 5 ■ 1010 00 

Pu-236 0 4, 2 • 103 1, 3 • 104 5, 0 • 104 

t>o 

I-» 

o 

o 

со 

00 

o 

тН 

7, 6 • 1010 

1, 0 • 105 

Quelques m illim ètres de platine ou de titane suffisent à ram en er la 

dose biologique des gam m as provenant du 238Pu au m êm e ord re de grandeur 

que la dose biologique due aux neutrons. Dans le s m êm es conditions une 

concentration d 'en viron 0, 5 ppm de 236Pu corresp on d à une dose moyenne 

sur 10 ans du m êm e o rd re de grandeur que la dose m oyenne y due a u 238Pu. 

Une réduction de 0, 5 ppm â 0, 3 ppm de la teneur en 236Pu ne rédu irait la 

dose totale que de 17%. Une teneur en 236Pu de 0, 5 ppm sem ble donc une 

pureté raisonnable du point de vue des dom m ages biologiqu es. 

2. PRODUCTION DE 238Pu DE QUALITE BIOMEDICALE 

P a r irradiation en pile de 237Np on souhaite obtenir du plutonium dont 

la com p osition isotopique est la suivante: § 90% de 238Pu, environ 9% de 

239Pu et 0 ,5 ppm de 236Pu. L es irradiation s faites, sans conditions particu -


liè r e s , dans des réa cteu rs à eau lourde fournissent un 238Pu contenant plus 

de 0, 7 ppm de 236Pu. On a donc ch erch é à sim u ler par ca lcu l la production 

de 236Pu. 

La production de 238Pu et de 239Pu est donnée par des cod es éprouvés 

d 'évolu tion de cœ u r de pile [ 3 ], m ais la production de 236Pu par d écroissa n ce 

ß - d e 236Np obtenu par réa ction (n, 2n) et (7 , n) ne peut être p rise en com pte 

dans ce s cod es. 

D es cod es de transport de neutrons rapides et de gam m as ont dû être 

u tilisés spécialem en t pour cette étude. 

2. 1. Etude de la réaction (n, 2n) 

Supposons une géom étrie cylindrique, la quantité de 236Pu produite 

par cen tim ètre de hauteur est donc: 

R » T 

f f 0 (E) (t )* (E ,r ,t )d r d E d t (1) 

0 0 0 

où T = tem ps d'irradiation 

a (E) = section effica ce (n, 2n) du 237Np 

Npu-236et Nnp-237 (t) = nom bre de noyaux par cm 3 de 236Pu et de 237Np 

respectivem en t. 

ф (E, r ,t ) = flux de neutrons, il dépend de la géom étrie du cœ u r de 

p ile et il est fourni par un code de transport de neutrons. 

2. 2. Etude de la réaction (7 , n) 

Le ca lcu l de la propagation gam m a susceptible de p rovoqu er une 

réa ction (7 , n) est presque rigou reu x ca r il peut être fait, sans grande 

e rre u r, en négligeant le s photons ayant subi une diffusion. 

La form ule (1) peut s'appliqu er pour le ca lcu l de la quantité de 236Np 

produite par réaction (7 , n) en prenant le flux de gam m as et la section 

e ffica ce Ст(п^ . Il faut tenir com pte de toutes le s sou rces de gam m as: soit 

de fission , soit provenant des m atériaux de stru ctu re, tels que bouchon, 

cuve et com p osé de l'a llia g e de l'ép rou vette. Un ca lcu l a été effectué sur 

une éprouvette NpOz A l irra d iée dans le réacteu r E L3: le tie rs du 236Np 

fabriqué était dû aux gam m as de capture dans l'alum inium du com posé [4 ]. 

2. 3. A justem ent des section s e ffica ce s 

L 'an alyse des irradiation s faites en pile de cib les de 237Np avec ou 

sans m a trice d'alum inium nous a p erm is de ch oisir la section effica ce 

E N D F-3 pour CT(nj 2n) (voir paragr. 3) et ainsi de ca lcu ler les contributions 

rela tives des d ifféren ts m ilieu x environnants. C eci a p erm is de fixer à 

environ 0, 014 b la section effica ce ^ du 237Np à 7, 72 M eV, én ergie de 

la raie prin cip ale des gam m as provenant de la capture d'un neutron par 

l'alum inium . Le but de l'étu de étant d 'é lim in e r les sou rces p rin cipales 

de form ation de236Pu, il est donc n é ce ssa ire d 'a v o ir plus de renseignem ents 

sur la section effica ce cr^

332 BERGER et al. 

3. MESURE ET EVALUATION DES CONSTANTES NUCLEAIRES 

3. 1. Données n u cléaires n é ce ssa ire s au calcu l de la form ation de 236Pu à 

partir de l'irra d ia tion en pile de 237Np 

a) Section effica ce de réaction (n, 2n) sur le 237Np. Une étude co m 

parative des évaluations de la section effica ce Ст(п 2n) contenues dans les 

deux bibliothèques KEDAK et E N D F /B III a p erm is de recom m ander la 

section effica ce contenue dans les bibliothèques E N D F /B III [ 5 ], résultat 

con firm é par le s irradiation s en pile. 

b) Section effica ce de réaction (7 , n) su r le 237Np. Une p rem ière 

évaluation de la section effica ce 0(r_êffectuée en septem bre 1971 n 'a pas 

p erm is de répon dre d'une m an ière satisfaisante aux besoin s. Aucune m esure 

expérim entale n'avait été faite et les valeu rs p rop osées avaient été ca lcu lées 

à partir de m od èles a ssez g r o s s ie r s ; ces valeurs avaient donc des b a rres 

d 'e rre u rs im portantes. 

Le groupe d'expérim en tateu rs sp écia listes des m esu res photonucléaires 

a effectué la m esu re de la section effica ce Ст(у_n)auprès de l'a ccé lé ra te u r 

lin éaire de 60 MeV de Saclay. L es m esu res n'ont pu être faites qu'à des 

én ergies de photons 7 quasi m onochrom atiques su périeu res à 9 M eV, c e ci 

étant dû essen tiellem en t à la radioactivité de l'éch an tillon de 237Np u tilisé [6] . 

A partir des m esu res, il a été p ossib le de d é crire la section effica ce totale 

d 'absorption photonique à toute énergie 

V =CTy ,n + 0 y .f +CTr . 2 n + ---- 

Le rapport o-y.n/^y.f = Ç /T f a été étudié pour des én ergies de 7 proch es du 

seu il d 'ém ission de neutrons. P ar réaction (7 , n) ou (n, 2n) il y a form ation 

de deux états du 236Np, l'un de p ériod e T > 5000 ans et de spin élevé 

(probablem ent 6‘ ), l'a u tre de p ériod e T = 22 h et de spin 1"; seul c e lu i-c i 

con tribu era à la form ation du 236Pu par ém ission ß~. Le rapport de 

form ation de l'éta t 1" du 236Np varie avec les én ergies des 7 incidents et 

est égal à environ 0, 7 - 0, 6 [7] . L es valeurs de cr^ njen fonction de l'én erg ie 

des 7 sont les suivantes: 

E (MeV) 6, 62 6, 7 

OO 

«0 

7 7, 5 7, 72 8 oo 

СЛ 

9 10 

ct (mb) 

y.n 

0 3 4 6 14 18 24 40 60 116 

CTy>n (mb)* 0 3 3 4 8, 5 11 14 24 36 70 

* Section efficace de formation de l 'état 1”. 

3. 2. Données n u cléaires n é ce ssa ire s au calcu l de la dose 

Outre l'évalu ation du nom bre m oyen v de neutrons ém is par fission 

spontanée et le sp ectre énergétique de ce s neutrons, nous avons étudié 

les neutrons et le s rayons 7 ém is par un échantillon de 238Pu contenant 

des tra ce s de fluor [ 8] . Le fluor peut ém ettre des neutrons et des rayons 7 

par réa ction a sur ce noyau: (a, a ' 7 ), (a, p 7 ) et (a, П7 ).

IAEA-SM- П О /64 333 

Le rendem ent neutronique, en cible ép aisse de flu or, a été déterm iné 

égal à 10 neutrons par m illion de a pour des én ergies de o de 5, 3 MeV 

provenant du 210P o [9] . 

P our le 238pu (E a = 5, 5 MeV) nous avons p ris: Rq = 14 ± 1 n /1 0 6. 

P our un m élange com p osé de n élém ents, le rendem ent neutronique Rn est 

défini par: 

où Rok est le rendem ent en cib le épaisse du kièm e élém ent, N^ est le 

n om bre re la tif d 'atom es et son pouvoir d 'a rrê t atom ique re la tif à l'a ir . 

P our une sou rce de 238p u contenant des tra ces de flu or, nous avons avec 

SPu = 4, 6 et SF = 1, 14 

Si nous avons une concentration de fluor de un ppm en m a sse, la sou rce de 

155 m g de 238Pu ém ettra 4, 3 n /s . L 'én erg ie m oyenne de ce s neutrons est 

de l'o r d r e de 1, 5 M eV, voisin e de l'é n e rg ie moyenne des neutrons de fission . 

CONCLUSION 

Cette étude a p erm is de sélection n er les conditions d 'irra d ia tion dans un 

réa cteu r afin d 'obten ir un plutonium -238 de qualité isotopiqu e biom éd icale: 

— u tilisation d'un réa cteu r qui p ossèd e un flux bien th erm alisé: réacteu r 

à eau lourde ou éventuellem ent à graphite, c e c i afin de dim inuer les 

réa ction s (n, 2n); 

— optim isation de la place de l'éch an tillon de 237Np dans le réa cteu r, a ssez 

loin des élém ents com bu stibles et surtout a ssez loin de la cuve du 

réa cteu r afin de dim inuer les réaction s (7 , n); 

— définition de la géom étrie et de la com p osition des cib les; un com posé 

Np 0 2C sem ble p référa b le à un com p osé N p 0 2Al. 

En outre, il est im portant de con sid érer le problèm e des tra ce s des 

élém ents lé g e rs dans le plutonium -238 et particulièrem en t les tra ce s de 

flu or dans l'évalu ation de la dose neutronique. 

[ 1] ALAIS, M . , BERGER, R ., BOUCHER, R ., LAURENS, P ., Générateur isotopique au plutonium-238 

pour stimulateur implantable electro -systolique (G .I. P. S .I .E .), Bull. Inf. Soi. Tech. (Paris) № 142 

(nov. 1969) 31-38. 

n 

R = 13 • 10+4 -| * - (n /s )/C i 

‘Pu 


[2] DEVILLERS, С . , Н ОТ, M . , « D o s e biologique autour d'un stimulateur cardiaque», Compt. Rend. 

2e Symp. Int. sur l'énergie d'origine radioisotopique (Madrid, 1972), O C D E (21 janv. 1973) 859-73. 

[3] BERGER, R . , DUCASSE, G . , K O EHLY, G . , PARADIS, G . , « L e programme de production du 238Pu 

et du 244C m au Commissariat â l'énergie atomique», Ibid., p . 31-47.

334 BERGER et a l. 

[4] GERVAISE, F ., DE SCHEEMA ECKER, J., Production de 238Pu de qualité médicale, Interprétation 

des expériences EL3 1972, CEA, Rapport interne D PR M A /SERM A/R n" 89 (sept. 1972). 

[5] RIBON, P ., Sections efficaces de la réaction 237Np (n;2n) !3sNp, C E A , Rapport interne DPhN/M F 

n° 533/72 (déc. 1972). 

[6] VEYSSIERE, A . et al., Nucl. Phys. A 199 (1973) 45. 

[7] LE C O Q , G . , VEYSSIERE, A . , Mesure des sections efficaces photonuclêaires pour le 237Np et évaluation 

de la section efficace de formation de l'état 1- du 23-6Np, CEA, Rapport interne D PhN/M F n° 532/72 

(déc. 1972). 

[ 8] KREBS, J., Neutrons et rayons gamma émis par un échantillon de 238Pu contenant des traces de fluor, 

CEA, Rapport interne D PhN/M F n° 880/71 (oct.1971). 

[9] SEGRE, E ., W IEGAND, C . , Los Alamos Scientific Laboratory Report MDDC- 185 (1944). 


A .H .W . ATEN (Chairm an): How long w ill the production o f 230Pu 

fro m 237Np be im portant and when w ill the production from 242 Cm take over? 

G. LE COQ: I shall ask M r. B erg er, one o f the co-a u th ors o f our 

paper, to rep ly to this question. 

R . BERGER: The production o f 238Pu by disintegration o f 242Cm , 

which is its e lf form ed by neutron irradiation o f 241A m , is still only in the 

experim ental stage. S everal y ea rs w ill be requ ired b efore it reach es the 

sem i-in d u stria l stage and it is not obvious that it w ill be able to m eet all 

future 238Pu requ irem en ts. M o reov er,it is lik ely that the 238Pu so obtained 

w ill be con sid erably m ore expensive than that provided by neutron irradiation 

o f 237Np.

NUCLEAR DATA AND 

NEUTRON ACTIVATION ANALYSIS 

OF BIOLOGICAL SAMPLES 

N.M. SPYROU 

Radiation Unit, Department of Physics, 

University of Surrey, 


Abstract 

NUCLEAR D A T A A N D NEUTRON A C T IV A T IO N ANALYSIS OF BIOLOGICAL SAMPLES. 


The application of activation analysis in the life sciences, environmental studies and industry has 

increased to such an extent that the technique has been introduced to undergraduates at this University 

in the form of short-term inter-disciplinary projects. Further it is predicted that the growth area of 

routine application will be in the bio-medical field and therefore activation analysis is included in 

certain postgraduate courses, e.g. Clinical Biochemistry, Radiation Studies and Medical Physics. However, 

this has highlighted several problems which arise mainly from the short period of time available for 

training in the technique and the multidisciplinary background of the students. 

It is suggested that part of the solution lies in a more suitable presentation of nuclear data which will 

enable the untrained analyst to reach a quick decision as to the procedure he is to follow for the determination 

of the required elements in a sample. 

An illustration is given in which nuclear data are used with particular reference to the analysis of 

biological material. Comments are included on the specific areas where uncertainties exist or greater 

accuracy is required in nuclear data. 

This paper therefore attempts, by looking to the future, where, for example, in a hospital department 

routine analyses are undertaken, to provide an approach which will facilitate use of the technique by those 

who are not radiation scientists. 

Introduction : 

The application o f activation analysis in the l i f e scien ces, 

environmental studies and industry, has increased to such an extent over 

the past few years that an attempt is being made at th is University to 

introduce the technique to students in several d is cip lin e s , at both 

undergraduate and postgraduate le v e ls. The short period available for 

training and the m ultidisciplinary background o f the students has highlighted 

several problems. The a c c e s s ib ility and presentation o f nuclear 

data is one. 

Although the remarks below are general, emphasis is la id on the 

application o f activation analysis to b io lo g ic a l samples. It is our b e lie f 

that th is is going to be the main growth area in the fie ld anl,in p a rticu lar, 

stimulated by concern with the problems o f environmental health, the 

measurement o f trace elements w ill be predominant. 

The m ajority o f the work with b io lo g ic a l media in neutron activation 

analysis has been concerned, from early days [ l , 2 ] , with evaluation o f the 

role o f trace elements in b io lo g ic a l metabolism and th eir relationship with 

deficien cy diseases and to x ic ity e ffe c ts . Schwarz has recen tly indicated 

[ 3] the elements which are lik e ly to come under consideration fo r essen tiality 

and thus require determination in b io lo g ic a l m atrices, table I . From 

a bibliogra p h ical survey compiled by J. De Donder [Ч-] , using published 

335

336 SPYROU 

TABLE I. TRACE ELEM ENTS UNDER CONSIDERATION FOR 

ESSENTIALITY IN THE MAMMALIAN ORGANISM AND THE NUMBER OF 

REFERENCES IN NEUTRON ACTIVATION ANALYSIS ASSOCIATED WITH 

THEIR DETERMINATION (TO 1968)a 

Bulk 

elements 

Essential 

trace 

elements 

(1972) 

H 

4/16 

S 

37/146 

F 

21/121 

Cu 

168/647 

С 

10/102 

Cl 

103/313 

Si 

15/185 

Zn 

127/357 

N 

22/102 

К 

61/173 

V 

58/190 

Se 

59/187 

0 

64/84 

Ca 

58/148 

Cr 

57/257 

Mo 

49/207 

Na 

134/381 

Mn 

144/452 

Sn 

12/85 

Mg 

37/121 

Fe 

78/325 

I 

64/145 

P 

91/256 

Co 

96/416 

Under Li Be В Al Ti Ge As 

sp ecial 1/55 0/87 6/111 45/128 20/99 2/27 113/433 

Br Rb Sr Ag Cd Sb Cs 

95/205 47/116 64/140 38/256 36/161 63/335 32/109 

Ba W Au Hg Pb Ni 

47/139 29/189 84/344 69/146 3/34 27/217 

« e ffe c ts demonstrated 1972 

figures indicate the numbers o f references the element has been 

determined in a b io lo g ic a l matrix to that in a ll other matrices. 

sources up to 1968, the number o f references associated with these elements 

in b io lo g ic a l and other matrices have been counted and included in the same 

table. Table li a shows a more recent survey (1969-1971), presented by 

Bowen [5 ], o f papers on activation analysis in Biology and table lib gives 

a breakdown o f these in to the number o f elements studied per paper. 

In the period 1969 to 1972, as we have reported elsewhere [6] , 27 

p r o je c ts , varying in length from a term 's work to over three years, have 

been carried out by our students ; these can be divided into subjects as 

shown in table I I I . A sim ilar pattern emerges, in a wider context, when 

irradiation c e r t ific a t e s , issued at the University o f London Reactor Centre 

over the past six years, are examined (see table IVa). The upsurge in the 

use o f irradiation f a c i lit ie s at the Reactor Centre fo r activation analysis 

(as opposed to say radiation damage stu d ies), has created a demand which, 

despite plans fo r another fast irradiation tube, may be d if fic u lt to meet 

i f a substantial proportion o f the time available fo r in -core irradiations 

continues to be allocated to "long irra d ia tion s". This surprisingly to me 

is the trend as seen in table IVb. The need fo r neutron irradiation 

fa c i lit ie s w ill not diminish. Therefore, we have decided to concentrate 

our e ffo r ts in measuring quantitatively sh ort-lived isotopes o f the elements 

o f in te re st, wherever p ossib le. This suggests the closer examination o f 

both rapid radiochemical and instrumental techniques o f analysis. We have 

gravitated p referen tia lly towards the la tte r and one facet we are in the 

process o f investigating [7] further is the technique o f c y c lic activation 

[8 ,9 ].


T A B L E lia . A C T IV A T IO N A N A L Y SIS IN B IO L O G Y , 196 9-1971 

Subject No. o f papers 

Animal tissu es • 47 

Plant tissu es 18 

Toxicology 9 

C lin ica l Medicine 9 

In vivo analysis 3 

Biochemistry 4 

Reviews 3 

Content o f 71 papers 

TABLE lib . NUMBER OF ELEMENTS STUDIED PER PAPER 

No. o f elements 0 1 2 3 4-24 to ta l 

No. o f papers 3 44 10 2 12 71 

TABLE III. NUMBER OF PROJECTS IN NEUTRON ACTIVATION A T 

THE UNIVERSITY OF SURREY (1969-1972) 

Subject No. o f p rojects 

Basic neutron physics 2 

Instrumentation 3 

Dosimetry 3 

Industrial m aterial analysis 3 

Geology survey 2 

Environmental p ollu tion (a ir + water) 2 

Trace elements in food 3 

Toxicology 1 

Mammalian (tis s u e , blood , excreta) 8 

Total 27 

337

338 SPYROU 

TABLE IVa. NUMBER OF IRRADIATION CERTIFICATES ISSUED 

BETW EEN 1967-1972“ AT THE UNIVERSITY OF LONDON REACTOR 

CENTRE 

Year_______________ 1967 1968 1969 1970 1971 1972 to ta l 

No. o f Irradiation 8 11 9 34 70 71 203 

C ertifica tes 

No. in B iologica l 3 2 1 11 24 29 70 

Work 

% in B iolog ical Work 37 18 11 32 34 41 34.5 

a Year ending January 1973 

TABLE IV b. DISTRIBUTION OF IRRADIATIONS REQUIRING LONG AND 

SHORT PERIODS 1971 and 1972 

Long irradiation s >_ 1 day or 8 hours ; short irradiation s


At th is stage most students have colla ted th eir own reference manual 

from the above and other sou rces, fo r ease o f a c c e s s ib ility to the relevant 

nuclear data. Such a document would then, p ossib ly, include (assuming 

gamma-ray spectrometry): 

(a) Tabular (or graphical) distribu tion o f radioisotopes with increasing 

h a lf - lif e ( t l ) , 

(b) Tabular (or graphical) d istribu tion o f radioisotopes with increasing 

gamma-ray energy (E y), and usually 

(c ) A nomogram (or nomograph) [1 6 ,1 7 ], fo r the calcu lation o f saturation 

a c tiv itie s o f each isotop e, achieved a fter thermal neutron 

irradiation . 

(Note: graphical distribu tion s o f (a ) and (b) have on occasion been very 

e ffe c tiv e in indicating quickly whether "bunching" and "in terferen ce" from 

other radionuclides occurs in the areas o f in t e r e lt .) 

However, i t is fe l t th at, with some m odification in parameters, (a ), 

(b) and (c ) can be combined into one table (or fig u re) which would cut out 

a lo t o f cross-referencin g when fin er d e ta il is not required. The fir s t 

steps towards th is have been taken by A liev et a l [18] where the d istribu 

tion o f radionuclides is p lotted on a x E^. frame o f reference (this 

combines (a) and (b )). 

To introduce the third parameter we shaid go to the equation 

representing the observed disintegration rate o f a radion u clide, after 

neutron irra d ia tion , 

D = ефгп, 

N f r, -Ati-, r -Xtw -X(tw + tc)-. 

о U - e j [e_____ - e____________ J_ 

A 0 Xtc 

where: 

e is 

Ф is 

" - 1 ) 

m is 

No is 

f is 

A is 

atom) 

a is 

X is the decay constant o f the nuclide ( s '1 ) 

t i is the irradia tion time (s) 

tw is 

COI 

tc is 

N f 

and £ = —— a(cm2 g- -*-) is the macroscopic cross-section o f the target 

nuclide (or equivalent to the saturation a ctiv ity per unit mass, 

per unit flu x fo r a 100% e ffic ie n t d etector). 

The parameter £ is not usually tabulated, the reasons are obvious when one 

considers the variation o f reaction cross-section with neutron energy and 

therefore the necessary correction to be made fo r the particular neutron 

spectrum used in the irra d ia tion . A liev et a l. do compute a macroscopic 

cross-section fo r thermal neutrons (2200 ms~l) fis s io n neutrons and 14 MeV 

neutrons.

T A B L E V a. IS O T O P IC SE N SITIVITIE S FOR E L E M E N T S IN M A M M A L IA N B L O O D 

\ M e V 

Ti X 

2 \ 

0.1s - lm 

0.02 - 0.04 0.04 - 0.06 0.06 - 0.08 0.08 - 0.1 0.1 - 0.2 

190 1 .6 K -9 ) 77mSe 6 .8 8 (-3 ) 

1 - 10m 82mBr 3 .12(-5 ) 79mSe 5.33C-5) 27Mg 5.0 7 (-7 ) 71Zn 4 .52(-8) 

10m - lh 60TnCo 4 .0 8 (-3 ) 113mSn 8 .77(-8) 

101Mo 3.02C-5) 81mSe 2 .4 3 (-5 ) 

lllm Cd 1 .9 9 (-5 ) 123mSn ? 

1 - 10h 80твг 4 .15(-3 ) 8°иВг 1.3 8( — 5) 71mZn 4 .22(-8 ) 

199mHß 2 .8 7 (-6 ) 125mSn 4 .0 9 (-5 ) 

10h - Id 42K 2 .87(-5 ) 197mHg 2 .15(-4 ) 

1 - lOd 

"M o 1 .52(-5 ) 197Hg 2 .3 И -3 ) **7Ca 2 .53(-7 ) 99Mo 5 .3 2 (-5 ) 

197Hg 2 .5 6 (-4 ) 

10 - lOOd 59Fe 1 .2 0 (-6 ) 117mSn 3 .77(-6 ) 

? indicates data incomplete or only rela tiv e in ten sity known, * isotope produced by reaction other than (n ,y) 

S en sitivity is followed by the power o f ten in parenthesis 

When more than one gamma-ray for the same isotope fa lls in the same box, the most intense is always quoted.

T A B L E V b . IS O T O P IC SEN SITIVITIES F O R E L E M E N T S IN M A M M A L IA N B L O O D 

v \ 

MeV 

0.2 - 0.4 0.4 - 0.6 0.6 - 0.8 0.8 - 1.0 

0 .ls-lm 20711^ * 38mCl 2 .0 8 (-5 ) 

10m-lh 

l-10h 

71Zn 6 .53(-8 ) 88Se ? 

125mSn 4 .0 9 (-5 ) 205Hr ? 

81 Se 1 .0 9 (-5 ) lllm Cd 6 .2 4 (-5 ) 

83Se 2 .90(-6 ) 199mHg 8 .1 2 (-7 ) 

71mZn 4 .4 0 (-7 ) 117mCd 2.1 9(-6) 

93raMo 3 .46(-6) 

71Zn 6 .53(-7 ) 

86n>Rb 3.0 5(-4) 

81 Se 6 .0 4 (-6 ) 128I 4 .1 2 (-3 ) 

101Mo 1.81( — 5) 128I 4 .12(-4) 

101Mo 2.54C-5) 

10h-ld 69mZn 1 .2 8 (-4 ) 197mHg 3.59(-5) 6kCu 1 .17(-2 ) 

10-100d 

99Mo 7 .6 0 (-6 ) 125Sn 3.62(- 11) 

115Cd 2 .78(-6 ) 197Hg 1 .92(-5 ) 

U5Cd 9 .2 8 (-6 ) 203Pb* 

51Cr 7 .2 5 (-5 ) 59Fe 1 .41(-7) 

82n>Br 1. 56 ( -5 ) 

83mse ? 

80Br 2 .6 9 (-3 ) 

81 Se ? 

101Mo 1 .33(-5 ) 

128I 5 .8 9 (-5 ) 

107Cd 3.6 6(-5) 71mZn 3,0 4 (-7 ) 

**7Са 2 .0 0 (-8 ) 115Cd 4 .6 4 (-5 ) 

82Br 7.36C-4) 115Cd 1 .2 K -4 ) 

99Mo 9 .12(-5 ) 198Au 2 .8 7 ( - l) 

125Sn 4.82C-11) 203Pb* 

107Cd 5 .23(-8) 

82Br 9 .2 5 (-4 ) 

^98Au 3 .0 2(-3) 

20 3Pb* 

27Mg 5 .6 4 (-5 ) 

71Zn 1 .5 K -7 ) 

■ 80Br 1.15(-5 ) 

81 Se 4 .0 3 (-6 ) 

88Rb 3.06(-5 ) 

101Mo 1 .8 K -5 ) 

56Mn 1 .44(-1 ) 

71mZn 3 .7 5 (-8 ) 

lt7Ca 2.00 ( - 8 ) 

82Br 2 .7 9 (-4 ) 

125Sn 1 .81(-10) 

2Q3Hg 2 .7 6 (-4 ) 1J5mcd 1 .92(-7 ) U5raCd 1.18C-6)

T A B L E V c . IS O T O P IC SENSITIVITIES F O R E L E M E N T S IN M A M M A L IA N B L O O D 

'\MeV 

Ti \ 

2 X 

1.0 - 1.2 1.2 -. 1.4 1.4 - 1.8 1.8 - 2.5 >2.5 

0 .ls-lm 207mPb* 190 9 .5 K -1 0 ) 20F 3 .1 7 (-4 ) 16N 3 .7 7 (-ll) 

l-10m 

27Mg 2 .4 8 (-5 ) 66Cu 5.00С-Ц). 

52V 5 .7 8 (-2 ) 8 3mSe 9 37S 3 .4 6 (-7 ) 

71Zn 6.53С — 8) 83mSe ? 

82mBr 9 .3 6 (-8 ) 

“♦â 2. 72(-5 ) 

10m-lh 

l-10h 

101Mo 3 .0 2 (-5 ) 

101Mo 1.33(—5) 

50mCo 4 .8 5 (-4 ) 

80Br 1 .92(-5 ) 

88Rb 3 .23(-6 ) 

38C1 1 .0 7 (-3 ) 

101Mo 1.3 3( — 5 ) 

71mZn 1 .87(-8) 31Si 4 .6 4 (-8 ) 117mCd 7 .3 K -7 ) 

10h-ld 24Na 3 .4 K -3 ) 

ld-10d 

82Br 3.2 3(-4) 125Sn 1 .6 9 (-9 ) 

198Au 6 .04(-8) 

6l*Cu 1 .5 4 (-4 ) 

1*7Ca 2.57C-7) 

82Br 2 .90(-4) 

10-100d 59Fe 2.39C-5) 86Rb 1 .7 9 (-4 ) 59Fe 1.88C-5) 

93mMo 5 .97(-6 ) 

38C1 7 .1 5 (-4 ) 

88Rb 4 .95(-5 ) 

101Mo 1 .8 K -5 ) 

56Mn 2 .19(-2 ) 

117mCd 1 .83(-6 ) 

49Са 3.06(-6) 

88Rb 2.47C-6) 

88Rb 5.42C-5) 

88Rb 7 .54(-7 ) 

56Mn 1 .4 6 (-3 ) 

**2K 2 .8 7 (-3 ) “ 2K 7.98C-6) 21*Na 3 .4 K -3 ) 

82Br 1 .90(-4) 

125Sn 1 .69(-11) 

125Sn 7 .2 3 (- ll) 

82Br ? 

125Sn 6 .03(-12) 

342 SPYROU

IAEA-SM-ИО/З 343 

TABLE VI. ELEM ENTS PRESENT IN MAMMALIAN WHOLE BLOOD [19] 

INCLUDING NON-ESSENTIAL ELEMENTS WITH TOXIC E F F E C T S , 

SOMETIMES FOUND IN BIOLOGICAL MEDIA 

Bulk 0 С H N Cl S Na 

.-1 

mgl 775000 94200 98000 33000 2900 2040 1990 

Bulk К P Ca Mg 

-1 

mgl 1690 370 62 41 

Trace Fe Zn Si Cu Other Br Rb 

>mgl 1 475 6.5 4.0 1.07 >mgl 4.6 2.7 

Trace I Mn Mo Со Cr V F 

-1 

T A B L E V II. D A T A F O R T H E R M A L N E U TR O N A C T IV A T IO N A N ALYSIS: AN E X A M P L E 

Isotope f% a(barns) £(cm2g 1 ) Daughter T t 

2 

58Fe 

26 

59Co 

27 

E (keV) 

Y 

0.33 1.2 4 .2 7 (-5 ) 59Fe 45d 143 

; 100 19 

18 

1 .9 4 (-1 ) 

6 0mCo 

99%J- 

60Co 

Note: Only (n ,y) reactions have been considered 

10.47m 

5.258a 

Eg is the internal conversion electron energy 

192.5 

335 

1098.6 

1291.5 

58.5 

1332.4 

1173.1 

1332.4 

=1 % 

Y 

0.8 

2.8 

0.3 

56 

44 

2.1 

0.25 

100 

100 

S Y 

3.42(-7) 

1. 20 ( - 6. ) 

1 .4 K -7 ) 

2. 39 (--5 ) 

1 .88(-5 ) 

4 .0 8 (-3 ) 

4.85C-4) 

Ee (keV) 

I and Ie are the approximate absolute in te n sitie s o f gamma-rays and conversion electrons 

S e n sitiv ities fo r gamma-spectrometry, S , are not calculated fo r "long liv ed " isotop es. 

51 

58 

~T 9- 

- V 

86 

19

IAEA-SM-ПО/З 345 

The follow ing points have been taken into account in drawing up the 

data sheets fo r the radionuclides formed by neutron capture. 

( i ) The tables are fo r (n,y) produced radionuclides and the thermal 

neutron cross-section s quoted are fo r neutrons with a v elocity o f 

2200 ms- 1 , unless otherwise indicated. 

( i i ) The main gamma-ray energies o f the radionuclide as w ell as those o f 

less intense gamma-rays are lis te d and the c r ite r ia fo r inclusion o f 

a particular gamma-ray energy is it s iso to p ic s e n s itiv ity , S, and 

it s p osition in the Ey x tJ frame o f reference. (Under certain 

conditions the signal to background ra tio may be more favourable 

fo r the less intense gamma-ray.) 

( i i i ) Although we expect the data to be used with Ge(Li) and Nal d etectors, 

the recent emergence o f low-energy photon detectors has allowed us 

to include certain energies which may be more suitably measured by 

the la tte r thus extending the range o f instrumental a n aly sis, 

despite sp ecia l requirements in the preparation o f samples to overcome 

self-a b sorp tion . (Perhaps one should sta rt constructing tables 

for low energy gamma-rays and X-rays arisin g from neutron 

a c tiv a tio n .) 

(iv ) Due to reasons set out in the in trodu ction, very lon g-liv ed isotopes 

are excluded unless the product o f iso to p ic s e n s itiv ity , corrected 

fo r saturation, and concentration in the b io lo g ic a l matrix is 

s ig n ific a n t. 

(v) Gamma-rays o f radioactive species with unknown in ten sities or only 

rela tiv e in ten sities are i f considered important clea rly id e n tifie d , 

otherwise they are excluded. 

The follow ing references were used fo r the compilation in addition to 

[11] , [12] , [14] and [18]: 

(a) Neutron A ctivation Analysis by D. De. Soete et a l. [20] 

(b) ( i ) Table o f p rin cip al gamma-rays from radioactive species. 

( i i ) Table o f radioactive species arranged according to h a lf - lif e . 

Both lis te d by Tannila and Kantele [2 l] , [22]. 

The format o f the information required fo r neutron activation analysis is 

illu stra te d in table VII. Here only iron and cobalt are used as examples. 

Tables V a,b and с indicate on a Ey x rl matrix th.e radioactive species 

formed and th eir is o to p ic s e n s it iv it ie s . Finally in table VIII we have 

lis te d those radioactive isotopes which emit internal conversion electrons. 

The reason fo r th is is tw ofold: (1) th is provides an alternative spectro- 

metric method o f measuring radioactive species and (2) since some gamma-ray 

in ten sities are in d ire ctly determined from the measurement o f the internal 

conversion e le ctro n s, th is may highlight an area fo r improvement in the 

search fo r greater accuracy in the data. We have measured with a modest 

s ilic o n , lithium d rifte d , semiconductor detector o f 50 mm2 sen sitive area 

and thickness 3 mm, low le v e l a c tiv itie s o f 137Cs on f i l t e r paper down to 

about 8pCi fo r a 30 hour run [23] , which compares very favourably with more 

complex Ge(Li) -Nal coincidence systems. 

Discussion : 

Although the introduction o f isoto p ic s e n s it iv it y , S, w ill fa c ilit a te 

the reading o f nuclear data in activation a n alysis, the lo g ica l extrapolation 

is to replace th is fa cto r by a detection lim it fo r each gamma-ray

346 SPYROU 

TABLE VIII. ISOTOPES EMITTING INTERNAL CONVERSION 

ELECTRONS. (ELEMENTS IN TABLE VI ONLY CONSIDERED WITH 

tj < lOOd) 

Isotope Tl 3 

Ee(keV) Ie% Isotope Tn 2 

Ee(keV) Ie% 

51 Cr 27. 8d 315 4 

69raZn 13. 7h 429 5 123mSn 40. 3m 130 ? 

77mSe 17.7s 148 40 

160 10 198Au 2 .696d 329 3 

79raSe 3. 5m 83 63 398 1 

95 22 197mHg 23.8h 51 21 

8imSe 57m 90 72 82' 

102 20 120 

8 0mBr 4 .42h 24 58 197Hg 64. lh 64 ? 

36 ? 74 ? 

47 ? 19 9mHg 43m 75 21 

®2mßr 6.1m 33 80 144' 

44 35 285 

93mMo 6 .95h 244 29 354 

261 10 2°3Hg 46.6d 194 13 

1 0 °тм о 14.6m 170 9 264 5 

11lmcd 48.6m 123 50 ' 275 

146 24 гозрь* 52'. lh 193 14 

? eith er in su fficie n t data or only rela tiv e in ten sities known 

* isotope produced by reaction other than (n,-y) 

52 

36 

264 3 

energy o f the radionuclides in question. There are various interpretations 

o f the term detection lim it [24] but none should be considered unless the 

background matrix due to gamma-rays from other radioactive species present 

(and other gamma-rays from the same radionuclide) are taken into account. 

The main background matrix when measuring trace elements in b io lo g ica l 

samples (blood , urine, tissu e e t c .) arises from the radiations o f sodium and 

chlorine (to a lesser extent from phosphorus). These bulk elements have 

concentrations in b io lo g ic a l samples which are w ell known. "Background 

spectra" (eith er generated by computer or recorded in a p ra ctica l situ ation )

IAEA-SM- ПО/З 347 

TABLE IX . DETECTION CHARACTERISTICS OF A 100 cm 3 G e(Li) AND 

A 7. 5 cm BY 7. 5 Nal (TI) INSIDE A 15 cm STEEL SHIELD 

Characteristic Energy 

Resolution 

(keV) 

Absolute 

Efficiency 

Background 

500-2500 keV 

Minimum 

Detectable 

Activity 

Ge(Li) 662 keV 2.2 0.014 108 counts 9.5 cpm 

1333 keV 2.8 0.0071 24 counts 14.5 cpm 

Nal(Tl) 662 keV 49 0.118 9920 counts 10.5 cpm 

1333 keV 99 0.063 3600 counts 12.1 cpm 

tc = 600 minutes and precision 0.2 

can then be constructed, for the specific irradiation and counting 

conditions, and used for the determination of detection limits. A useful 

definition for the latter is the one suggested by Walford and Gilboy [25] 

called the minimum acceptable activity which is that source activity which 

just allows the desired precision to be achieved in a given counting time. 

The quantity is obviously both background dependent and energy dependent. 

This can be seen in table IX where a 100 cm^ Ge(Li) and a 7.5 cm dia by 

7.5 cm Nal(Tl) are compared, albeit for a low level counting experiment 

inside a 15 cm steel shield with long counting times, 600 min, and 0.2 

precision. (Precision is defined as the ratio of the standard deviation 

of the net peak counts of interest to the net peak counts.) This result 

applies only to isolated peaks on a smooth background continu and any 

increase in spectral complexity or variation of background matrix with 

time would alter significantly the value of minimum acceptable activity. 

Conclusions : 

In conclusion therefore the following points are made : 

(i) University students are being trained in techniques of activation 

analysis because application of these has become common in biomedical 

and environmental fields. There is a need therefore for a manual 

which incorporates the salient features of present publications in a 

more accessible form. This publication must be directed at the user 

who is not interested in nuclear data per se. 

(ii) Economic necessity demands the determination of elements, wherever 

possible, by the measurement of short-lived isotopes. Long 

irradiations and handling will still be necessary and important in 

specific areas of research but for routine analyses one must be 

realistic and set practical detection limits and turn-around times 

for each sample. 

(iii) The sensitivity factor has been calculated here for a small number of 

isotopes undergoing (n,*y) reactions. Sensitivities for other neutron 

reactions and other neutron energies should be computed wherever 

these are significant.

348 SPYROU 

(iv) Detection limits for less intense radiations may be lower than for 

those for the main radiation energy. Thus it is important to have 

accurate data for absolute intensity of both gamma-rays and internal 

conversion electrons. 

(v) A likely development in the future with the advent of mini-reactors, 

greater quantities of 252Cf and larger numbers of accelerating 

machines used in hospitals is the provision of routine analytical 

services by regional hospital centres. Here with a section 

specifically treating the activation analysis of biological samples a 

manual of the type mentioned above will come into its own. 

Finally it is to examine, amongst other things, such topics that a 

Nuclear Activation Group is being formed in the U.K., constituted of 

members from universities, medical schools and other institutions of 

higher education. 

Acknowledgements : ^ 

I would like to thank my colleague, Dr. W.B. Gilboy, for his willingness 

to be drawn into lengthy discourses and his critique of the work; Mr. 

G. Burholt, Reactor Manager, for supplying the reactor users' raw data of 

the University of London Reactor Centre ; and all the students, too numerous 

to mention, who one way or another influenced the content of this paper. 

References : 

[1] SMALES, A.A., Neutron activation analysis, Symposium on Trace 

analysis, New York Academy of Medicine, ed. J.H. Yoe and J.H. Koch, 

John Wiley and Sons, Inc. (1955). 

[2] MEINKE, W.W., Trace element sensitivity: comparison of activation 

analysis with other methods, ibid. 

[3] SCHWARZ, K., The role of trace elements in health and disease 

processes in man and animals, IAEA Symposium on Nuclear Activation 

techniques in the Life Sciences, Bled, Yugoslavia (April, 1972). 

[4] DE DONDER, J., Bibliographical Survey of Neutron Activation Analysis, 

Chapter 12, Neutron Activation Analysis - D. De Soete, R. Gijbels and 

J. Hoste, Wiley-Interscience (1972). 

[5] BOWEN, H.J.M., The biochemistry of trace elements, IAEA Symposium on 

Nuclear Activation techniques in the Life Sciences, Bled, Yugoslavia, 

(April, 1972). 

[6] GILBOY, W.B. and SPYROU, N.M., Applications of Neutron Activation 

Analysis, Reactor Technology and Training Conference, University of 

Aston, Birmingham (April, 1972). 

[7] OZEK, F., Cyclic activation and its applications, M.Sc. thesis, 

University of Surrey (January, 1973). 

[8] CALDWELL, R.L. , MILLS, W.R. , ALLEN, L.S., BELL, P.R. and HEATH, R.L., 

Science, 152, 457 (1966). 

[9] CALDWELL, R.L., MILLS, W.R. and GIVENS, W.W., Nuclear Instruments 

and Methods, jtö, 95 (1969).


[10] SEELMANN-EGGEBERT, W., PFENNIG, G. and MÜNZEL, H., Chart of the 

Nuclides, Der Bundesminster für Wissenschaftafliche Forsehung, Bonn, 

2nd edition (1968). 

[11] LEDERER, C.M. , HOLLANDER, J.M. and PERLMAN, I., Table of Isotopes, 

Sixth edition, John Wiley and Sons, Inc. (1968). 

[12] KOCH, R.C., Activation Analysis Handbook, Academic Press (1960). 

[13] HEATH, R.L., Scintillation Spectrometry, gamma-ray spectrum 

catalogue, Vols. I and II, 2nd edition, USAEPCRep,ID0-16880-l, (1964). 

[14] STEHN, J.R. et al., Neutron Cross Sections, USAEAC Rep. BNL-325, 

2nd edition (1965). 

[15] CROUTHAMEL, C.E. , Applied gamma-ray spectrometry, Pergammon Press, 

Oxford, 1960; 2nd edition by F. Adams and R. Dams, 1970. 

[16] FREILING, E.C. , Nomogram for radioactivity induced in irradiation 

Nucleonics, Nucleonics, _18, 12 (1966). 

[17] ROUTTI, J.T. , Graphical technique for estimating activity levels 

produced in thermal and fission neutron irradiations, Analytical 

Chemistry, 40, 3, p.593, (March, 1968). 

[18] ALIEV, A.I., et al. Handbook of Nuclear Data for Neutron Activation 

Analysis, Israel Program for Scientific Translations, Jerusalem (1970). 

[19] BOWEN, H.J.M., Trace elements in biochemistry, Academic Press (1966). 

[20] DE S0ETE, D., et al., Neutron Activation Analysis, Vol. 34 on 

Chemical Analysis, ed. P.J. Elving and L.M. Kolthoff, Wiley-- 

Interscience C1972). 

[21] TAMILA, 0., and KANTELE, J. , Table of Principal Gamma-rays from 

Radioactive species, University of Jyväskylä, Research Report 

3/1969 (August, 1969). 

[22] TAMILA, 0., and KANTELE, J. , Table of Radioactive Species, 

Increasing half-life, University of Jyväskylä, Research Report, 

2/1969 (February, 1969). 

[23] LAMBERT, R.A. and GILB0Y, W.B., private communication. 

[24] CURRIE, L.A., Limits for qualitative detection and quantitative 

determination, Analytical Chemistry, 40, 3, (.March, 1968). 

[25] WALFORD, G., and GILB0Y, W.B., Fundamentals of sensitivity limits 

in low level counting, International Conference on the Natural 

Radiation Environment II, Houston, Texas (August, 1972).

LES CONSTANTES NUCLEAIRES 

DANS LES PHARMACOPEES 

Leur utilité pour la normalisation 

des substances pharmaceutiques 

Y. COHEN 

CEA, Centre d’études nucléaires 

de Saclay, France 



NUCLEAR C O N S T A N T S IN PHARMACOPOEIAS; THEIR USEFULNESS IN T H E S TA N D A R D IZ A TIO N OF 

PHARM ACEUTICAL SUBSTANCES. 

The radioelements administered to man are considered by national and international authorities 

(Council of Europe, World Health Organization) to be medicinal preparations. As such, they appear in 

national, regional and international pharmacopoeias under the heading "radiopharmaceutical substances". 

The preparation of monographs by groups comprising physicists, doctors and pharmacists has shown that it 

is often necessary to refer to precise nuclear constants, for pharmacopoeias are acquiring regulatory and 

legislative force, whereby they may be quoted in courts of law. Mention is made in such monographs of 

national radioactivity metrology laboratories which provide standards to which reference is made in the 

standardization of "radiopharmaceutical substances" as regards the radionuclide purity, concentration of the 

principal radionuclide and radioactive concentration. These monographs indicate the radioactive half-life, 

the nature of the radioactive emissions and the most characteristic radiations (with their energies). They 

also indicate what parasitic radionuclides accompany the principal radionuclide and establish upper limits 

for the concentration of such parasites. Such information requires the establishment of tables of generally 

accepted nuclear constants, which will be possible only if metrology laboratories collaborate. Such 

laboratories could furnish the authors of monographs with physical data for inclusion in the pharmacopoeias 

when periodic revisions are made. A standardization of nuclear constants and co-ordination of the work of 

different laboratories would be useful in the case of all radionuclides. 

LES C ON STA N T ES NUCLEAIRES D A N S LES PHARMACOPEES; LEUR UTILITE POUR LA NOR M ALISATION 

DES SUBSTANCES PHARMACEUTIQUES. 

Les radioéléments administrés à l'homme sont considérés par les autorités nationales et les instances 

internationales (Conseil de l’Europe, Organisation mondiale de la santé) comme des médicaments. A ce 

titre, ils sont inscrits aux pharmacopées nationales, régionales ou internationales sous la rubrique de 

«substances radiopharmaceutiques». L'élaboration des monographies par des groupes réunissant des 

physiciens, médecins, pharmaciens, a montré la nécessité de se référer à des constantes nucléaires précises 

car les textes des pharmacopées acquièrent un caractère réglementaire et législatif, susceptible d'une 

utilisation devant les tribunaux. Il est fait mention, dans les monographies, de laboratoires nationaux de 

métrologie de la radioactivité qui fourniraient les étalons auxquels se référeraient les praticiens lors de la 

normalisation des «substances radiopharmaceutiques» quant à la pureté Tadionucléidique, la te n e u T en 

radionucléide principal, la concentration radioactive. Les monographies indiquent la période radioactive, 

la nature des émissions et les rayonnements les plus caractéristiques ainsi que leur énergie. Elles signalent 

les radionucléides parasites qui accompagnent le radionucléide principal et établissent une limite > leur 

présence. Ces précisions ne se conçoivent pas sans l’établissement de tableaux de constantes nucléaires 

généralement acceptées et dont la mise â jour demande un travail de concertation entre les laboratoires 

de métrologie. Ces derniers fourniraient aux rédacteurs des monographies les données physiques qui seraient 

alors introduites dans les pharmacopées lors des révisions périodiques. Pour tous les radionucléides une 

homogénéisation des constantes nucléaires et une coordination entre les divers laboratoires paraissent utiles. 

351

352 COHEN 

L es radioélém en ts destinés à l'u sage m éd ica l sont con sid érés com m e 

des m édicam ents et à ce titre doivent présen ter des c ritè re s de qualité 

définis par le s pharm acopées. C e lle s -c i constituent des recu eils de 

m onographies dans lesqu elles sont indiquées les p rop riétés p h y sicochim 

iques et les m éthodes de vérifica tion de ce s p rop riétés. 

La pharm acopée internationale publiée par l'O rgan isation m ondiale 

de la santé, la ph arm acopée européenne rédigée par des groupes de travail 

du C on seil de l'E u rop e, les pharm acopées nationales: am éricain e, 

britannique, fra n ça ise, e tc......... décriven t p lu sieu rs substances ra d iopharm 

aceutiques. On désigne par substance radiopharm aceutique les 

m olécu les m in érales ou organiques qui contiennent un ou plu sieu rs atom es 

radioa ctifs. A in si, a lo rs que l ' iodure de sodium 131I est un exem ple de 

m olécu le m in érale relativem ent sim ple, la séru m -album in e humaine 

m arquée à l'io d e rad ioa ctif est une m olécu le organique de grande com plexité. 

L 'io d e radioactif devra p résen ter dans le s deux ca s des constantes n ucléaires 

identiques, ne pas être souillé par un autre radioisotop e ou m êm e par un 

radionucléide de nature chim ique différente. 

Nous avons réuni dans le tableau I les substances radiopharm aceutiques 

le s plus u tilisées et qui de ce fait ont été in scrites à plu sieu rs ph arm acopées. 

T e l est le ca s du chrom ate de sodium 51C r, de la cyanocobalam ine au 

cobalt-57 ou 58, du citrate de fe r 59F e , de la sérum -album ine m arquée à 

l'io d e -125 ou à l'io d e -1 3 1 , de l'iodohippurate 131I de sodium , du ro se bengale 

m arqué à l'io d e -1 3 1 , des solutions d 'io d u r e 125I o u 131I, de la ch lorm érod in e 

m arquée au m e rcu re -1 9 7 , du phosphate 32P de sodium et de l 'o r colloïd al 

198A u. 

L orsqu e l'o n relève dans les m onographies les constantes n ucléaires 

citées on en trouve en général deux: la période radioactive et l'én erg ie 

du photon gamma le plus ca ra ctéristiq u e. L es ch iffres cités dans les 

pharm acopées que nous avons exam inées (tableau II) sont en bonne con cordance 

pour le ch rom e-5 1 , le cob a lt-5 7 , le cobalt-58 et l'o r -1 9 8 . On constate une 

lé g è re d ifféren ce pour la p ériod e radioactive de l'iod e-1 3 1 qui est de 8, 0 j 

ou de 8, 08 j suivant les m on ograph ies, pour le photon gamma le plus 

ca ra ctéristiq u e de l'io d e -1 2 5 qui est de 0,028 MeV dans la pharm acopée 

européenne et la pharm acopée internationale et de 0, 0355 M eV pour la 

ph arm acopée am éricain e U. S. P. XVIII. On observ e égalem ent une légère 

d ifféren ce dans l'é n e rg ie m axim ale du rayonnem ent bêta du ph osp h ore-32 

qui est de 1, 70 M eV dans la pharm acopée fran çaise et de 1, 71 M eV dans 

la pharm acopée am éricain e ainsi qu'une d ifféren ce dans la période ra d io 

active: 14,2 j pour les pharm acopées britannique et internationale et 

14, 3 j pour le s autres. 

Il est heureux que le s d iv ers rédacteu rs de pharm acopées se soient 

a ccord é s sur le choix des données fou rn ies par la littérature scientifique, 

m ais leu rs d ifficu ltés pour réd ig er les nouvelles m onographies sont grandes. 

En effet, on trouve dans la littérature au m oins une dizaine de sou rces 

différen tes de constantes n u cléa ires qui ne sont pas toujours d 'a cco rd non 

seulem ent sur l'én erg ie des rayonnem ents ém is m ais égalem ent sur leur 

pourcentage, ce qui explique d 'a illeu rs que les m onographies soient si 

d iscrè te s à ce sujet. 

La déterm ination d'un sp ectre à p a rtir de la seule donnée de la 

m onographie est insuffisante pour iden tifier le radionucléide et a fo rtio ri, 

pour re ch erch er le s im puretés radionucléidiques qui peuvent se trou ver 

m élangées au radionucléide prin cip al, soit par suite de l'irra d ia tion

T A B L E A U I. R A D IO E L E M E N T S IN SCRITS DANS L E S P H A R M A C O P E E S 

Chrome-51 

Pharmacopée 

britannique 

(1968) 

Pharmacopée 

internationale 

(1967 et 1971) 

Pharmacopée 

européenne 

(à paraître) 

Pharmacopée 

française 

(chromate) + + + + 

Cobalt-57 

(cyanocobalamine) + + 

Cobalt-58 

(cyanocobalamine) + + + 

Fer-59 

(citrate) + 

Iode-125 (iodure) + + + 

sérum-albumine + + + 

Iode-131 (iodure) + + + + + 

iodohippurate + + + + 

sérum-albumine + + + + 

rose bengale + + 

Mercure-197 

chlormérodine + 

Or-198 (colloïde) + + + + + 

Phosphore-32 (phosphate) + + + + 

(1965) 

U .S .P . 

XVIII 

(1970) 

IAEA-SM-170/70 353

354 COHEN 

TABLEAU II. CONSTANTES NUCLEAIRES CITEES DANS LES 

MONOGRAPHIES DES PHARMACOPEES 

Chrome-51 

britannique européenne 

Pharmacopées 

internationale française U .S .P . XVIII 

Période (i) 27, 8 27,8 27,8 - 27, 8 

Energie (MeV) y : 0,32 0,32 0,32 - 0,320 

Cobalt-57 

Période (j) 270 270 270 - 270 

Energie (MeV) y ; 0, 122 0, 122 0,122 - 0. 122 

Cobalt-58 

Période (j) 71 71 71 - - 

Energie (MeV) y : 0,51 0,51 0, 51 - - 

Iode-125 

0,81 0, 81 0, 81 - - 

Période (j) 60 60 - 60 

Energie (MeV) y : 0, 028 0, 028 - 0, 0355 

Iode-131 

Période (j) 8, 0 8 ,0 8,08 8 ,0 8,08 

Energie (MeV) y : 0, 36 0,36 0,36 0,364 0, 364 

Phosphore-32 

Or-198 

Période (j) 14,2 14,3 14.2 14,3 14,3 

Energie (MeV) - e : l t 70 1,710 

Période (j) 2 ,7 2,7 2 ,7 2 ,7 2,7 0 

Energie (MeV) y : 0,41 0,41 0,41 0,41 0,412 

neutronique de la cib le par réaction nucléaire supplém entaire com m e dans 

le ca s de l-'or-198 a ssocié à l'o r -1 9 9 , soit p ar insuffisance d 'e n rich is s e 

m ent de la cible com m e dans le cas du fe r -5 9 a sso cié au fe r-5 5 . 

L es données rela tiv es à certain s radion u cléides tel le sélénium -75 

m ettent le s réd acteu rs de m onographies dans l'e m b a rra s. A titre d'exem ple 

nous avons réuni dans le tableau III le s constantes n u cléaires du m ercu re-1 9 7 

et du sélén ium -75, re le v é e s dans «R a d ion u clid es in P harm acology» [1] et 

dans «N u cle a r Data» [2]. On rem arque une grande d ifféren ce: l'une des 

sou rces bibliographiques ne donne pas l'abondance en électron s de con version 

interne; l'é n e rg y y et l'abondance en rayonnem ent gamma ne concordent 

pas pour le sélén ium -75.

T A B L E A U III. CO N STAN TE S N U C LEAIR E S DU M E R C U R E -1 9 7 E T DU S E L E N IU M -75 

Mercure 

Période Mode de décroissance 

Abondance 

Cfr) 

Energie y 

(MeV) 

Abondance y 

Référence [ 1] 65 h C . E. 100 0, 077 19,3 

(*) 

0, 069 74,5 

Abondance en électrons 

de conversion interne 

Référence [ 2] 64 h C . E. 100 0, 077 19,3 80, 7 

0, 069 74,5 

Sélénium-75 0, 19 0,5 1, 2 

Référence [ 1] 120 j C . E. 100 0, 096 3 

0,12 15 

0 ,1 4 54 

0,20 1.5 

0,27 56 

0,28 23 

0,31 1 ,4 

0,40 12, 5 

Référence [ 2] 120 j C . E. 100 0, 024 0, 03 5 ,6 

0, 066 1, 0 0 ,3 

o 0, 097 3, 1 2,7 

0,121 16,4 0 ,7 

0,136 5 5 ,5 1,6 

0,197 1,3 0,03 

0, 265 5 8 ,6 0 ,4 

0. 280 25, 2 0 ,2 

0, 304 1.3 0, 1 

0,401 12,9 


356 COHEN 

On peut pen ser que les travaux de com pilation ont été dans le s deux 

ca s m enés très sérieu sem ent et cependant ce s d ivergen ces sont e m b a rra ssantes, 

ca r les m onographies nationales ont, le plus souvent, une valeur 

juridique contraignante et les données qui y sont in scrites ne devraient pas 

p rê te r à discu ssion. 

L es pharm acopées font ré féren ce aux la boratoires nationaux de 

m étrologie de la radioactivité qui doivent fou rn ir des étalons pour lesqu els 

sont p r é c is é e s la pureté radionucléidique et la concentration radioactive. 

C es étalons servent à établir la con form ité aux norm es de pharm acopée 

des productions co m m e rcia le s de radioélém en ts. 

Il serait utile que les m éthodes de m esu re soient m inutieusem ent 

d écrites pour quelques radioélém en ts d élicats à d oser et que les lim ites 

d 'e r r e u r soient u n iform isées grâce à un com p rom is entre la p récisio n 

scientifique et l'u tilisa tion pratique. A ce titre un p rem ier effort pourrait 

con sister dans la rédaction d'un ouvrage réunissant les schém as de 

d é cro issa n ce , le s sp ectres gamma et les constantes n ucléaires des ra d io 

élém ents in scrits dans les pharm acopées et ceux dont l'u tilisation m édicale 

est m oins fréquente. L 'a ction qui a été en trep rise pour l'a sp e ct chim ique 

de la production des radioélém en ts et a conduit à la publication par l'A IE A 

de «R a d ioisotop e production and quality con tro l» [3] devrait être étendu 

aux constantes n u cléaires. L es ca ra ctéristiq u es ainsi d écrites autoriseraient 

un ca lcu l plus p ré cis des d oses d 'irra d ia tion reçu es par les tissu s 

biologiqu es lo r s de l'adm inistration des substances radiopharm aceutiques 

en vue d'une thérapeutique ou d'un diagnostic. 

REFERENCES 

[ 1] GLENN, H. J. , LAMB, J. F . , Radionuclides in Pharmacology, Section 78 of the International Encyclopedia 

of Pharmacology and Therapeutics (Cohen, Y . , Ed.), Pergamon Press (1971) 949, 

[2] Nuclear Data 131, 5 (1966); Nuclear Data В 1, 6 (1966). 

[3] IAEA, Radioisotope Production and Quality Control, TRS No. 128, IAEA, Vienna (1971). 

DISCUSSION 

D.J. HOREN: I would like to make a com m ent and then ask a question 

o f D r. Cohen. T his m ight be the appropriate se ssio n in which to point out 

that many isotop es used in m edicin e are contained in the com pilation entitled 

"R adioactive atom s, A uger ele ctro n s, alpha, beta, gam m a and X -r a y data" 

by M.J. M artin and P.H. B lich e rt-T o ft (N uclear Data, P art A , J 1 (1970)). 

In addition, we have som e other isotopes evaluated in the sam e m anner, 

which are not contained in that publication. I can say that we would w elcom e 

any inquiries from m ed ica l people on other isotop es which are not so covered , 

as w ell as com m ent on the quality and usefulness o f the tabulations in 

question. 

My question to D r. Cohen is as follow s: Is there a p roblem in the use 

o f these ra d ioisotop es as far as ensuring hom ogeneity o f the actual injected 

dosage o f the isotope is con cern ed, i.e. once you have it in the solution? 

Y . COHEN: The a ccu ra cy o f the volum e withdrawn from the via l is, 

I would say, ±10.


D.J. HOREN: But does the radioactivity rem ain hom ogeneously 

distributed throughout the volu m e? D oes it ever plate on to the w alls o f 

the container? 

Y . COHEN: With c a r r ie r -fr e e radionuclides you do have a quantity 

o f the radion u clides which stick to the w alls o f the con tain er. H ow ever, 

a radiopharm aceu tical is fo r the m ost part a com pound to which a c a r r ie r 

has been added, so you do not have to cope with this question. A ccord in gly, 

the solution is hom ogeneous throughout its volu m e. The p roblem s are, 

first, that from one country to another the cu rie does not always r e fe r to 

the sam e quantity o f radioactivity. Second, there are a num ber o f ra d io- 

nuclidic im purities that can accom pany radioph arm aceu ticals. Third, 

the literatu re gives differen t values fo r variou s data. So I think it would 

be n ecessa ry fo r the A gen cy to issue a com pilation o f the m ost w idely 

accepted data in this field , fo r the use not o f p h y sicists but o f m ed ical 

p eop le. 

D.J. HOREN: I would agree with this. Such a com pilation would 

be a v e ry useful thing. 

M . LEDERER: W here data have im portant leg a l im p lication s, or 

w here th eir a ccu ra cy is extrem ely im portant, it m ight be useful to devote 

a con feren ce (or part o f a con feren ce) to establishing "au th oritative" best 

valu es. E xam ples o f ca se s fo r which this has been done are the h a lf-life 

o f 14C and the isotop ic abundances o f the elem ents. 

Y . COHEN: An exam ple o f the legal im plication s o f scien tific accu ra cy 

is the situation which a rise s when som eone applies to the United States F ood 

and D rug A dm in istration fo r authorization to use a new radiopharm aceu tical. 

The FDA req u ires a ra d iotoxicolog ica l assay, which m eans that he has to 

calcu late the d ose d eliv ered to the body. A s P r o fe s s o r K ellersh oh n m entioned 

in the presentation o f his paper (IA E A -S M -170/97), this calcu lation is related 

exactly to the percen tage and energy o f the g a m m a -rays and electron s being 

adm inistered. H ow ever, when the applicant m akes his calcu lation on the 

b a sis o f d ifferen t tables, he ends up with differen t resu lts and different 

a n sw e rs. 

The a ccu ra cy o f data on radiopharm aceu ticals depends on the ra d ionuclide 

involved. One p er cent a ccu ra cy, which is quite easy to attain, 

is gen erally su fficien t when you have an im purity. But it might happen 

that one p er m ille is requ ired (i.e. 0.1% ). This would be the ca se, for 

exam ple, with technetium from m olybdenum made from fissio n products. 

H ere the need fo r a ccu ra cy is m uch g reater than with technetium made 

from irra d iated m olybdenum and not from fissio n prod u cts. The question 

is v e ry intricate and there are no sim ple answ ers.

I A£ A-SM-170/92 

APPLICATION OF NUCLEAR DATA 

IN THE PREPARATION OF RADIONUCLIDES 

FOR USE IN MEDICINE AND BIOLOGY 

R. B. R. PERSSON 

Radiation Physics Department, 

Lasarettet, Lund, 

Sweden 

Abstract 

APPLICATION OF NUCLEAR D A T A IN THE PREPARATION OF RADIONUCLIDES FOR USE IN MEDICINE 

A N D BIOLOGY. 

At he IAEA Consultants' Meeting held December 11, 1972, at Studsvik, Sweden, nine experts in various 

fields of experience gathered in order to exchange information on the application of nuclear data in the 

preparation of radionuclides for use in medicine and biology. For reactor-produced radionuclides, it was 

concluded that the averaged thermal neutron cross-sections for the production of all useful ràdionuclides are 

required with an accuracy within a few per cent. Accurate decay-scheme data are also needed. Furthermore, 

cross-section data for the resonance region 5 eV - 1 M e V are not well known for many materials and better 

information is required. For radionuclide generators, the main problem is to evaluate the best production- 

techniques for the parent radionuclide and to obtain a daughter nuclide with high radionuclidè purity. The 

data needs to meet these requirements were discussed. Similar data needs for the production of radionuclides 

by accelerators were discussed. Furthermore, it was suggested to use the number of transformations per 

particle (R) or its inverse as a standard to express the production yield of radionuclides by charged-particle 

reactions. Radionuclide production with fast neutrons and photons was also discussed as well as some general 

problems concerning production-parameters, toxicology etc. 


In preparation fo r the IAEA Sym posium on A pplications o f N uclear Data 

in S cien ce and T echnology to be held in P a ris 12 - 16 M arch, 1973, a p re 

paratory m eeting was held on the 11th of D ecem ber, 1972, at Studsvik, 

Sweden. 

The o b je ct o f this m eeting was to enable the exchange o f inform ation 

on the applications of nuclear data in the preparation of radionuclides fo r 

use in m edicin e and biology. 

Nine experts in variou s field s of experien ce participated in the m eeting1. 

The follow ing su bjects w ere d iscu ssed : 

R ea ctor-p rod u ced radion u clides, 

G en era tor-p rod u ced radion u clides, 

1 Participants: 

R. Bergman, Gustaf Werners Institute, Uppsala, Sweden 

R. Bodh, AB Atomenergi, Studsvik, Sweden 

Y . Cohen, Dept of Radioelements, Saclay, France 

H . Condé, Research Institute of National Defence, Stockholm, Sweden (INDC representative) 

B. Jung, Radiation Physics Department, Akademiska SjukhuSet, Uppsala, Sweden 

B. Persson, Radiation Physics Department, Lasarettet, Lund, Sweden (Scientific Secretary of the meeting) 

P. Schmeling, AB Atomenergi, Studsvik, Sweden 

K . Svoboda, Nuclear Research Institute, Rez, Prague, Czechoslovak Socialist Republic 

T . Wiedling, Institute of Neutron Physics, Studsvik, Sweden 

359

360 PERSSON 

A cce le ra to r-p ro d u ce d radion u clides, 

R a dion u clid e-p rod u ction with fast neutrons, 

U se o f m ed ical betatrons fo r photon-activation, 

Other data im portant fo r the preparation and use o f radionuclides in 

m edicin e and biology, 

Sum m ary, con clu sion and re q u e sts. 

2. R EA CTO R -PRO D U CE D RADIONUCLIDES 

The m ost com m only used re a cto r-p ro d u ce d radion u clides fo r m ed ical 

and b io lo g ica l re se a rch are 14C, 3H, 32P , 125I, 35S, 131I, 51C r, 59F e, 203Hg, 

45Ca and, fo r clin ica l applications, 131I, 125I, 14C, 51C r, 198Au, 133X e, 32P, 

3H, 99T cm(99M o), 59F e, 75Se, 58C o, 85Sr, 197Hg, 113Inm, 47Ca. 

The follow in g param eters m ust be con sid ered when producing ra d ionuclides 

in a rea ctor: 

2.1. T arget 

It is im portant to know the isotop ic abundance of the different nuclides 

in the target. It can som etim es be advantageous to irradia te enriched m aterial. 

F o r exam ple n orm al iron has abundances o f 5. 8% 54F e, 91. 7% 56F e, 

2.2% 57F e and 0. 3% 58F e. If the F e -ta rg e t is enriched to 98% 54F e , alm ost 

pure 55F e can be produced. On the other hand if the target is enriched to 

85% 58F e, the 55F e-con tam ination of the 59F e produ ced is only about 5% [1 ] . 

2.2. P roduction c r o s s -s e c tio n s and rea ctor-n eu tron sp ectra 

The m ost im portant o f the neutron reactions com m only used fo r activation 

involve the capture o f a therm al neutron with the coin ciden t em ission 

of a gam m a ray. The c r o s s -s e c tio n s at therm al energy o f the (n, 7 ) reactions 

are fa irly w ell-know n. The rea ctor-n eu tron spectrum also contains epith 

erm al and fast neutrons which often induce nuclear reaction s giving secon d 

ary p a rticle s other than photons, e.g. 32S (n ,p )32P , 14N(n, p)14C , 40С а(п,й )31А г, 

6L i(n ,o )3H fo r which the c r o s s -s e c tio n s are not w ell known. 

Thus, fo r radion u clide-p rodu ction in a re a cto r, we need neutron- 

reaction c r o s s -s e c tio n s as a function of energy fo r the naturally occu rrin g 

isotop es and elem ents, and, in som e ca ses, also fo r radion u clides. A verage 

c r o s s -s e c tio n s and yield s fo r rea ctor-n eu tron sp ectra would be helpful as 

w ell as inform ation on reson an ce integrals and yields with and without 

cadm ium c o v e r s . Inform ation on flu x-d en sity d ep ression co rre ctio n s is 

also needed [ 2] . H ow ever, the accu ra cy in the calcu lation o f the production 

rate is lim ited by uncertainties in the shape o f the rea ctor neutron spectrum 

and in the c r o s s -s e c tio n s fo r epitherm al and fast neutrons. 

2.3. Side products 

T h ere are v ery often reson an ces in the neutron-capture c r o s s -s e c tio n 

and inform ation on reson a n ce-stru ctu re is extrem ely im portant from the 

standpoint of radionuclide production. F o r exam ple, the 197Au(n, 7 ) 198Au- 

reaction has a reson an ce at 5 eV and one can prevent the contam ination 

fro m the secon d ary therm al neutron-induced reaction 198Au(n, 7 ) 199Au by 

wrapping the target with a cadm ium fo il which absorbs therm al neutrons [ 1 ] .

IAE A-SM-170/92 361 

The p roblem s o f secon dary neutron-capture are v ery im portant in the 

production of radion u clides. F o r exam ple, in the production o f 125I(60d) 

through 124X e(n, 7 )125X e -> 125I, the c r o s s -s e c tio n fo r the reaction 

125I(n, 7)126I(14d) is fa irly high 900 b and 126I is an undesirable contam ination 

which should be m inim ized. It was rep orted that the production o f 1261 

som etim es is unexpectably high which m ay indicate a higher c r o s s -s e c tio n 

fo r epitherm al neutrons. Secondary capture reaction s seriou sly lim it the 

quality o f many radionuclide products. 

3. GENERATOR-PRODU CED RADIONUCLIDES 

A ra d ion u clid e-g en era tor is understood to be a system which p eriod ica lly 

m akes available a p a rticu lar radionuclide from a parent radionuclide o f 

lon g er h a lf-life . About 10-15 such radionuclide gen erators have been 

designed and con stru cted fo r use in m edicin e and biology [ 3-6]. 

The m ost im portant nuclear data fo r production and use o f these 

radionuclide gen era tors are: 

H a lf-liv es of parent and daughter radion u clides; 

D ecay sch em es o f parent and daughter radion u clides; 

P roduction c r o s s -s e c tio n fo r parent and in terferin g radion u clides. 

N uclear data defining the usefulness of the daughter radionuclide in 

question fo r m ed ica l scintigraphy and nuclear m edicin e in gen eral are: 

The photon spectru m o f the daughter radionuclide, including both 

7 -e n e rg y and em ission ra tes, m ust be suitable fo r good detection with 

fixed a n d /o r m ob ile system s. The h a lf-life o f the parent m ust be long 

enough in com p a rison with the h a lf-life o f the daughter to p erm it a notably 

lon ger use o f the daughter nuclide. 

The electron spectrum o f the daughter nuclide m ust be known and it 

m ust enable d elivery o f a low absorbed dose to the patient p er unit of 

activity. 

The follow in g gen erator system s are m ost used at presen t in m ed ical 

scintigraphy (daughter parent): 

9 9 T c m ( 99M o ) < 1 1 3 I n m ( 113S n )< 8 7 g r m (8 7 Y ) j 68G a ( 68G e ) j 81K r m (81R b ) , 

137B am( 131C s), 132I ( 132T e), 188R e (188W ). 

A s an exam ple, 99T c m has the follow ing v e ry favourable nuclear 

ch a ra cte ristics fo r u se'in m ed ical scinitgraphy: 

The h a lf-life of 6 h is suitable fo r m ost scin tigraphic exam inations 

and allow s a daily elution of the gen erator. The gam m a-ray en ergies are 

alm ost exclu sively 0.14 M eV (0.1405 (94%) and 0.1426 (6%) which make 

99T c m v ery usable) both fo r scanning d evices and gam m a ca m era s. The 

decay o f 99T c m through internal transition does not cau se the em ission of 

any corp u scu la r radiation except con v ersion and A uger electron s and the 

internal con v ersion co efficien t is low : e K = 0. 10. The radiation -absorbed 

d ose p er activity unit is th erefore low . 

Other exam ples can also be given to point out differen t aspects of the 

use o f gen era tor-p rod u ced radion u clides. F o r departm ents o f nuclear

362 PERSSON 

m edicin e fa r rem oved from production and distribution cen tres, the half- 

life o f 67 h fo r the parent " M o is an im portant disadvantage. 

113Inm(Sn) gen erators are m uch m ore suited fo r use in distant areas 

becau se the parent 113Sn has a h a lf-life o f 115 days. The n uclear data for 

113Inm are not so favourable fo r scintigraphy as fo r 99T c m because o f the 

sh orter h a lf-life 99. 8 min and the higher gam m a-energy 0.393 M eV . The 

gam m a energy is , how ever, v e ry clo s e to that o f 131I — 0. 364 M eV — so that 

the sam e collim a tor and detection equipment can be used fo r both 

radion u clides. 

The other radioisotop e gen erators are still at developm ent stage and 

not w idely used in clin ica l p ra ctice . T heir use is, how ever, in creasin g. 

F o r the near future the follow ing gen erator system s w ere suggested: 

72A s(72Se), 82R b(82S r), ^ g Y Cd), 191Irm(191O s). 

The developm ent and use o f radionuclide gen erators can be based on 

standard nuclear tables such as the Table of Isotopes [ 7 ]. The production 

para m eters o f m ost of the parent radionuclides are, how ever, not w ell 

known. D etailed c r o s s -s e c tio n data and excitation functions fo r different 

alternative nuclear reactions fo r production of the parent radionuclides 

and eventual contaminants are th erefore greatly needed. 

4. CYCLOTRON-PRODU CED RADIONUCLIDES FOR BIOLOGICAL AND 

MEDICAL USE 

During the past few y ea rs a num ber of cy clotron s have been installed 

m ore o r le ss exclu sively fo r b iolog ica l and m ed ica l p u rp oses. S everal 

m ed ical, b io lo g ica l and biop h ysical institutions are engaged in p rojects 

in which cy clotron s are used fo r radion u clide-produ ction , activation 

analysis and ra d iob iologica l re sea rch . The num ber of cyclotron s fo r this 

purpose w ill be about 30 by 1975 (Table I) [ 8, 9 ]. 

The ch a ra cte ristics o f cu rren tly available m ed ical cyclotron s are shown 

in T able II [ 9 ]. As can be seen in this table m ost of these cyclotron s a ccelera 

te proton s, deuterons and helium ions up to en ergies of 15 - 30 MeV 

and se v e ra l have capabilities over 50 M eV . Future con stru ctions w ill 

probably also a ccelera te 7L i, 12C, 160 and other heavy ions to useful en ergies 

and flu x-d en sities [2]. 

A sum m ary of cy clotron -p rod u ced radionuclides in cu rren t use are given 

in T able III. 

T o this lis t can be added a num ber o f radion u clides, which are parents 

o f potential ra d ion u clid e-g en e ra to rs. 

The use o f heavy ions like 12C and 160 w ill open a quite new and 

interesting field fo r both radion u clide-produ ction and activation -an alysis. 

A particu la r radionuclide m ay be produced by sev era l differen t reactions 

involving p, d, 3He, a, etc. A s an exam ple, 18F can be produced by any 

of the follow ing rea ction s: 

1. 19F (p ,p n )18F 

19F (p, 2n)18Ne ß+ -*■ 18F 

2. lsO (p ,n )18F 

3. 22N e(p ,on )18F

4. 20N e(p ,tf)18F 

5. 160 (a , 2n)18Ne ß+ - 18F 

160(

T A B L E I. C Y C L O T R O N S USED IN ISO T O P E P R O D U C T IO N F O R M E D IC A L PU R POSES 

U S A 

Location Type of machine Manufacturer 

1. Washington University Fixed energy 7 .5 M e V D Allis Chalmers 1965 

Medical School, St. Louis, M o. 

2. Massachusetts General Variable energy D Allis Chalmers 1967 

Hospital, Boston, Mass. 

3. Sloan-Kettering Institute Fixed energy Cyclotron Corp. 1967 

for Cancer Research, New York, N .Y . CS-15 

4. Argonne Cancer Hospital, Fixed energy Cyclotron Corp. 1969 

Chicago, 111. CS-15 

5. New England Nuclear Corp., Fixed energy Cyclotron Corp. 1969 

Billerica, Mass. CS-22 

6. M t. Sinai Hospital, Fixed energy Cyclotron Corp. 1970 

M iam i Beach, Florida CS-22 

7. University of California Fixed energy Cyclotron Corp. 1971 

at Los Angeles, Los Angeles, Calif. CS-22 

8. Mediphysics, Fixed energy Cyclotron Corp. 1971 

Emeryville, Calif. CS-22 

9. University of Southern Califomia-County Fixed energy Cyclotron Corp. 1971 

of Los Angeles, Los Angeles, California CS-22 

10. Brookhaven National Laboratory, Variable energy Research machine 

Upton, N .Y . 60" 

11. Donner Laboratory, UCRL, Variable energy Research machine 

Berkeley, California 88” 

12. N A S A Lewis Research Center, Variable energy Research machine 

Cleveland, Ohio 88" 

364 PERSSON

T A B L E I. (continu ed) 

13. Oak Ridge National Laboratory, 

EUROPE 

Oak Ridge, Tenn. 

14. Hammersmith Hospital, 

15. 

16. 

17. 

18. 

19 

London, Great Britain 


German Cancer Research Center, 

Heidelberg, Fed. Rep. of Germany 

Nuclear Research Center, 

Jülich, Fed. Rep. of Germany 

CEA, Department of Biology, 

Orsay, France 

IK O , Amsterdam and University of Groningen, 

Groningen, Netherlands 

Medizinische Hochschule Hannover, 

Fed. Rep. of Germany 

20. Univeristy of Liège, Belgium 

21. Nuclear Research Institute 

Prague, Czechoslovakia 

Variable energy 

8 6 " 

Fixed energy 

Fixed energy 

Variable energy 

MC-20 

Production machine 

A . E .G . 1972 

A . E .G . 1972 

(1955) 

Thompson-CSF 1971 

(Philips) 

Scanditronix 1973 


CO 

UI

TABLE I. (continued) 

ASIA 


22. IPCR, Saitama, Japan Variable energy 

23. University of Tokyo, Japan 

24. Institute of Radiological Science 

Chiba, Japan 

S O U TH AMERICA 

25. Instituto de Engenharia Nuclear 

Rio de Janeiro, Brazil 

63" 

IPCR-NAIG and TOSHIBA 

CS-30 Cyclotron Corporation 


CV-28 Cyclotron Corporation 

366 PERSSON

T A B L E II. SP E C IF IC A T IO N S O F C U R R E N T L Y A V A IL A B L E M E D IC A L C Y C L O T R O N S [9 ] 

CS-22* Cs-30* CV-28* Actitron** Th-CSF (70)** MC-20*** 

Beam Energy P 22 26 2 - 24 6 - 19 8 - 70 2 .5 - 20 

(MeV) d 12 15 2 - 14 3 - 11 11 - 35 1 .5 - 1 0 

3 He 31 39 5 - 36 3 - 2 8 18 - 93 3 .0 - 2 7 

a 24 30 6 - 2 8 6 - 2 2 22 - 70 2 .5 - 20 

External P 50 60 70 70 20 100 

Beam d 50 100 100 70 40 100 

Current 3 He 50 70 70 50 - 50 

( M ) a 50 50 50 50 - 50 

Internal P 100 500 500 - - - 

Beam d 100 500 500 - - - 

Current 3 He 100 150 150 - - - 

(ЦА) a 100 100 100 - - - 

* The Cyclotron Corporation ** Thompson-CSF *** Scanditronix . 


368 PERSSON 

TABLE III. CYCLOTRON-PRODU CED RADIONUCLIDES IN CURRENT 

USE [9]. The m ost im portant nuclides in this re sp e ct are underlined. 

Radionuclide Half-life 

Principal radiation 

(keV) 

Chemical form of the 

radiopharmaceutical 

11 с 2 0 ,4 min 511 C O , C 0 2 , Haemoglobin 

13 N 10,0 min 511 n 2 , n h J" 

150 2 .1 min 511 O g , Со, C O 2 , H2O 

i ï 

110 min 511 Complex, Amino Acids 

43K 2 2 .4 h 373, 619 KC1 

a Fe 8 ,2 h 165, 511 Ferric citrate 

CTGa 78 h 93, 184, 296 Gallium citrate 

11 Br 57 h 242, 522 NaBr 

81 Rb 4 .7 h 450, 511 RbCl 

81Krm 13 s 190 Kr 

84 Rb 33 d 511, 880 RbCl 

e,Srm 2 .8 h 388 Strontium citrate 

111 In 67.2 h 173, 247 InCl3, Transferrin, Globulin 

123 j 

13.3 h 159 Nal, Hippuran, Albumin 

129 Cs 3 2 .4 h 375 CsCl 

131 Cs 9 .7 d 29 CsCl 

157 Dy 8 ,1 h 326 HEDTA-complex 

201 

7 3 .5 h 170, 140 T1C1 

203Pb 52.1 h 280, 400 Pb-citrate 

5. RADIONUCLIDE-PRODUCTION WITH FAST NEUTRONS 

C yclotron s can be used as neutron-generators through the reaction 

7B e(p, n )7L i. 

Another and le ss expensive method fo r fast-n eutron production utilizes 

the 3H(d, n)4He reaction . 

Deuterons are a ccelera ted by an electrosta tic a cce le ra to r o f 150 - 400 kV 

and focu sed on a cooled tritium target w here the 3H(d, n )-rea ctio n takes p la ce. 

The neutrons are alm ost m on oen ergetic with an energy in the range of 

14 - 15 M eV, depending on the deuteron energy and the neutron d irection . 

The neutron-production rates obtained in these m achines are about 

IO10 - 1012 neutrons p er secon d . T hese m achines are m ostly used for 

therapy and ra d io -b io lo g ica l experim en ts, and fo r activation -an alysis of 

m acroelem en ts in b iolog ica l tissu es. They are not v e ry useful fo r ra d ionuclide 

production o f high sp e cific activity.


Neutrons produced by high-energy proton a cce le ra to rs could be used 

fo r production of labelled b iop olym ers. 

Neutrons with en ergies higher than 20 M eV can be used fo r production 

of 11C , 13N, 150 , 30P and 53F e (with T i of 20, 10, 2, 2 .5 and 8 .5 m inutes, 

Z 

resp ectiv ely ). 

T h ere is a need fo r calculations of an optim um production rate in which 

the ra d ioly sis of the irradiated substances would also be con sid ered . 

6 . USE OF M EDICAL BETATRONS FOR PHOTON-ACTIVATION 

B etatrons are available at many hospitals fo r radiotherapy. T hese 

a cce le ra to rs produ ce electron beam s of typical 40 M eV energy with a 

cu rren t o f about 1 ßA. The electron s strike a platinum target and produce 

"brem sstrah lu n g" photons distributed in energy up to the m axim um electron 

energy. 

The flu e n ce -rate of photons with en ergies grea ter than 10 M eV is in 

the ord e r o f 1 0 14 photons m ' 2 s "1 at a point about 0. 2 - 0. 3 m from the 

target in the forw ard beam d irection . 

In the energy region 10 - 35 M eV, the dominant feature o f ph oto-n u clear 

absorption is e le c tr ic dipole absorption ob served as the giant resonance 

in the absorption c r o s s -s e c tio n sp ectru m . The reson an ce has its m axim um 

value at about 22 M eV fo r light nuclei and at about 13 M eV fo r heavy nuclei. 

The width of the reson an ce is about 4 MeV fo r sp h erica l nuclei and about 

8 M eV fo r stron gly deform ed ones [ 12]. 

The p rod u ction -yield is given by the ex p ression 

Y (t¡) = kj n j l - exp (- Xtj)j J a(E)

370 PERSSON 

T here is a great lack o f dependable and system atically presented in form 

ation about the ra d ioly sis o f the target m aterial daring irradiation with both 

neutrons and charged p a rticle s. Gas production can take p lace and other 

unwanted ch em ica l sp ecies can be form ed which influence the radioch em ical 

treatm ent which is to follow [ 14-16]. 

The requ est fo r both the volu m ic radioactivity C i/litr e and the con cen tration 

of the ch em ical elem ent in question in g /lit r e o r a to m /litre o r m o l/litr e 

(M) was stre sse d . The sp e cific activity is then ea sily obtained by taking 

the quotient o f volu m ic radioactivity and ch em ica l concentration. 

It was also prop osed by SVOBODA [ 17] that it m ight be even m ore 

useful to introduce a term defining "the degree of deviation fro m c a r r ie r - 

fre e state": this is Dcp, the negative logarithm o f the s p e cific activity, 

w here 

D 

CF 

10 

log 

w here NA = num ber of radioactive atom s, 

Ns = num ber of stable atom s o f the sam e elem ent, 

NT = total num ber of atoms of the sam e elem ent. 

F o r total c a r r ie r -fr e e solution: 

Na 

Ns = 0 and, thus, DCF = 0 

It was stre sse d that further inform ation is needed about the tox icology 

of many of the elem ents used as radioactive tra ce rs in m edicin e and biology. 

8. CONCLUSIONS 

8.1. R ea ctor production 

The demand made on nuclear data fo r rea ctor-p rod u ced radionuclides 

are the follow ing: 

A veraged therm al-neutron c r o s s -s e c tio n s relevant fo r the production 

o f useful radionuclides (See section 2) are requ ired with an accu ra cy within 

a few p er cen t. A ccurate d eca y -sch em e data are also needed. 

The neutron c r o s s -s e c tio n in the reson a n ce-reg ion 5 eV - 1 M eV is 

not w ell known fo r many m aterials and better inform ation is required. 

Inform ation is needed on reson an ce integrals and yield s with and without 

cadm ium c o v e r s . Inform ation on n eutron-fluence d ep ression correction s 

is also needed [ 2 ]. H ow ever, the a ccu racy in the calcu lation of the production 

rate is lim ited by uncertainties in the shape o f the rea ctor neutron spectrum , 

the irradiation geom etry and position . 

8.2. G en erator production 

The m ain p rob lem is to evaluate the optim um production téchniques 

fo r p resen t and potentially useful parent nuclei. 

The contam ination of the daughter nuclide with undesirable radionuclides 

is a p roblem which also m ust be con sid ered seriou sly .

8.3. A c c e le r a t o r p ro d u ctio n 


F o r the calcu lation o f R fo r ch a rg ed -p a rticle a cce le ra to rs used fo r 

production of radion u clides there is a need to know c r o s s -s e c tio n s as a 

function of energy, 0 (E), fo r all nuclear reaction s leading to useful ra d io 

nuclides (See Table III) and fo r all com m only accelera ted p a rticle s, e.g. 

1H, 2H, 3H, 3He, 4He and, p ossibly, also 7L i, 12C and 160 . 

The m ass-stop p in g pow er S /p and the range of ch arged p a rticles in 

variou s m aterials are also needed, but are already w ell known and quite 

rea d ily available [18]. 

It was concluded that there is an urgent need fo r experim en tal d eterm inations 

and tabulations of R . The m easurem ent o f R m ight at p resen t be 

an e a sie r task than detailed studies o f o(E) and th eoretical calcu lation s. 

8. 4. R adionuclide production with fast neutrons 

Neutrons gf en ergies above 20 MeV can be used fo r production of 1:LC, 

13N , I 5 0 j 30p a n d 53F e _ 

T h ere is a need fo r calculations of an optim um production rate in which 

the ra d ioly sis o f the irradiated substances would also be con sid ered . 

8. 5. R adionuclide production with betatrons 

It was concluded that p ositron em itters such as 11С , 13N, 30 P and 31S 

in activities o f the o rd e r of 10 - 100 /uCi p er g and 150 1 - 40 m C i p er g 

could be produ ced in b iologica l m aterials with betatrons. The production 

y ield s are known with su fficien t a ccu ra cy. It was suggested that the p o s 

sibility o f producing labelled biop olym ers with sh ort-liv ed ra d ioisotop es 

should be con sid ered . 

8.6. G en eral rem arks 

It would be v ery useful fo r the p rod u cers and u sers to have an annually 

rev ised manual fo r production data, nuclear data and gam m a sp ectra fo r 

a ll radion u clides which are in cu rren t use in m edicin e and biology. IAEA 

m ight be the organization which would best be able to m eet this need. 

ACKNOWLEDGEMENT 

Many thanks are due to AB A tom en ergi in Studsvik, who acted as host 

fo r the m eeting. 

REFERENCES 

[1] BAKER, P .S ., "Radioactive Pharmaceutical", Ch. 8, Reactor-produced Radionuclides (ANDREWS, G . A . , 

KNISELEY, R. M . , W AGNER, H . N . , Jr., Eds), US Atomic Energy Commission CONF-651111, Oak Ridge 

(1966). 

[2] TILBURY, R. S . , private communication, Sloan-Kettering Institute, N .Y . (1972). 

[3] RICHARDS, P ., "Radioactive Pharmaceuticals", Ch. 10, Nuclide Generators, (ANDREWS, G. A . , 

KNISELEY, R .M ., W A G NER , H . N . , Jr., Eds), US Atomic Energy Commission CONF-651111. Oak Ridge 

(1966).

372 PERSSON 

[4] BERNHARD, H ., LIESER, K . H . , Isotopengeneratoren” ein Überblick über den Stand der Entwicklung, 

Euro-Spectra 9 Nr 1 (1970) 20. 

[5] HENRY, R ., Isotope generators, J. Nucl. Biol. M ed. 15 (1971) 105. 

[ 6] T O U Y A , J .J ., New applications of radiopharmaceuticals labelled with generator-produced radionuclides, 

in Medical Radioisotope Scintigraphy 1972 2 (Proc. Symp. Monte Carlo, 1972) in press. 

[7] LEDERER, C . M . , HOLLANDER, J .M ., PERLMAN, I ., Table of Isotopes (6th Edn), John W iley ( 19 68). 

[8] LAMBRECHT, R . M . , W O LF, A .P ., "Accelerator-Produced Nuclides and Radiopharmaceutical Production", 

presented at an IAEA panel meeting, Amsterdam (1971). 

[9] GLASS, H .I ., New applications of radiopharmaceuticals labelled with cyclotron-produced radionuclides, 

in Medical Radioisotope Scintigraphy 1972 £(Proc. Symp. Monte Carlo, 1972) in press. 

[10] SV O BODA, K ., "The Uses of Cyclotrons in Chemistry and Biology” , Buttwerworths London (1970) 383. 

[11] SV O BODA, K ., SILVESTER, D .J ., Quantities and units used in the production of radionuclides by charged 

particle bombardment, Int. J. Appl. Radiât. Isot. 2£(1971) 269. 

[12] BÜLOW, B ., F O R K M A N , B ., Photonuclear cross-sections, Nuclear Physics Report, Lund 7208, University 

of Lund, Sweden. 

[13] BRUNE, D ., M A T T S S O N , S ., L1DEN, K ., Application of a betatron in photonuclear activation analysis. 

Anal. Chim. Acta 44(1969) 9. 

[ 14] LINARCRE, J. K . , A list of materials which may be accepted for irradiation in BEPO by the shift manager, 

without reference to the reactor manager AERE-M 1535 (1965). 

[ 15] TRUSWELL, A . E . , Irradiation of small samples in the reactor D IDO and PLUTO, AERE-M1563 (1965). 

[16] Sicherheitsbetrachtungen für einfache Bestrahlungen in FR 2. Internbericht RB 3/65, Kernforschungs 

zentrum Karlsruhe, Germany (1965). 

[ 17] SVOBODA, K . , On terms defining the specific activity of accelerator-produced radioisotopic preparations, 

Report Ú .J .V . 2712-Ch Rez, Czechoslovakia (1971). 

[18] BARKAS, W . H . , BERGER, M .J ., Tables of Energy Losses and Ranges of Heavy Charged Particles, 

Report N A S A SP-3013, National Aeronautic and Space Administration, Washington D .C . (1964). 

DISCUSSION 

M. LEDERER: This is not the first tim e that the need fo r m ore "data" 

on production has been m entioned. P erhaps a gen eral re feren ce on the 

su bject would be d esira b le. Such a re feren ce would be a com bination of 

useful m easu red data (e.g. neutron c r o s s -s e c tio n s ), system atics fo r other 

quantities which can be calculated (e.g. c r o s s -s e c tio n s fo r ch arg ed -p a rticle 

rea ction s), and "co o k -b o o k "-ty p e knowledge, often essen tial fo r dealing 

with the many p roblem s that a rise from the p resen ce o f im p u rities. 

R.B.R. PERSSON: The m eeting concluded that there is a great need 

fo r a gen eral re fe re n ce w ork o r "co o k book " o f the type you m ention. This 

would, how ever, not only cov er production data (such as c r o s s -s e c tio n s , 

target m a teria ls, im purities etc.) and decay sch em es o f the radion u clides, 

but also include tables o f 7 -r a y en ergies and em ission rates as w ell as 

figures o f 7 -s p e ctra re co rd e d by a standardized technique. 

G.A. KOLSTAD: T his question pertains to you r last recom m endation. 

The range o f p a rticle a cce le ra to rs you have d iscu ssed is rather lim ited. 

Have you con sid ered the use o f h eavy-ion bom bardm ents (i. e. M > 4) o r 

h igh er-en ergy bom bardm ents (i.e. 200-800 M eV) fo r the production of 

p ro to n -rich nuclides with differen t nuclear p rop erties? F or exam ple 123I 

can be produced at the 200 M eV B rookhaven Linac fo r Isotope P roduction 

(BLIP) o r at the 800 MeV Clinton P . A nderson M eson P h y sics F acility at 

L os A lam os (LA M PF) at rather low co s t. It is not always n ecessa ry for 

the a cce le ra to rs to be located at the hospitals — only near enough for 

shipment o f the p rod u cts.


R.В.R. PERSSON: Our d iscu ssion s con cern in g the s o -c a lle d m ed ica l 

cy clotron s w ere m ainly lim ited to sm a ll m achines operated by a sm a ll 

organ ization. W e did not devote m uch attention to la rge m achines like 

those at B rookhaven and the L aw ren ce R adiation L aboratory in B erk eley, 

which we con sid ered to be som ething v ery sp ecia l. O f cou rse, there are 

extensive uses fo r such m achines in producing radionuclides o f in terest. 

G . A . KOLSTAD: I should point out that both the B LIP and the L A M P F 

have fa cilities associa ted with them fo r the production o f radioisotop es 

and ch em ica l fabrication o f the d esired p rod u cts.

Section V 

RADIOISOTOPES IN CHEMISTRY

Chairman 

K.H. LIESER (Federal Republic of Germany) 

%

IAEA-SM -170/96 

RADIOISOTOPE APPLICATIONS IN CHEMISTRY - 

A REVIEW 

L. GORSKI 

IAEA, Laboratory Seibersdorf, 

Vienna, Austria 

Abstract 

R A D IO ISO TO PE A P P L IC A T IO N S IN C H E M IS T R Y - A REVIEW. 

V a riou s m e th o d s o f a p p lic a t io n o f ra d io is o to p e s in c h e m is try — th e m o s t im p o r ta n t use o f th e la tte r 

b e in g th at as tra cers — a re c h a r a c t e r iz e d ; th e n e c e s s ity o f k n o w le d g e o f n u c le a r d a ta fo r th e in d iv id u a l 

a p p lic a tio n s is b r ie f ly d iscu ssed . 

The discovery of radioactivity, 77 years ago, by Becquerel in P aris, 

was due to an effect which should now rather be classified as a new branch 

of radiochem istry, i. e. radiation chem istry. The chem ical aspects of 

radioactivity w ere, however, later covered up by the physical face of this 

phenomenon. It is only with the discovery of induced radioactivity, that the 

use of radioisotopes for chem ical investigation could be applied in a wider 

fram ework. The next great discovery in nuclear physics — fission of 

uranium -235 — was also proved experim entally for the first time with the 

help of some radiochem ical techniques. 

It is not possible to describe all chem ical applications of radioisotopes 

in this short contribution. Some applications of great importance are 

discussed in papers on activation analysis and hot atom chem istry, in 

these Proceedings. 

The m ost important use of radioisotopes in chem istry is their application 

as tracers. The use of radiotracers can be of interest in cases in 

which we wish to investigate the transfer or movement of atom s, m olecules, 

chem ical compounds, substances or any other m a sse s. M ost of the physicochem 

ical phenomena are connected with such transfers of matter from one 

phase to another or from one place to another. Such p ro cesses as evaporation, 

dissolution, partition between two different phases, adsorption on 

the surface, chem ical reactions, analytical separations, etc. are exam ples 

of physico-chem ical occurrences related to m ass transfer on a m olecular 

or on a la rg e -sca le level. If the m olecules or m a sses in the movement 

can be labelled in som e way — which perm its them to be distinguished from 

other sim ilar m olecules or m a sses not taking part in the p rocess investigated 

— the study of this particular p rocess is easy to perform . If the 

labelling is recognized easily and quickly, then also the kinetics of the considered 

p rocess can be observed. There are many ways of tagging m olecules 

or substances: colouring, mixing with some easily recognizable substances 

(e. g. fluorescent compounds) or introducing slightly different atom s into 

the m olecules. Two ways of m olecular tagging are now in use: labelling 

with non-natural composition of stable isotopes and labelling with radioactive 

isotopes. These two labelling modes operate on a m olecular level, 

but can also be used on la r g e -m a ss level. Other labelling system s (e. g. 

colouring substances) can only be applied to la rg e -sca le experim ents with 

larger m a sse s involved. 

377

378 GÓRSKI 

Unfortunately, the labelling with non-natural composition of stable 

isotopes can only be recognized with the use of m a ss spectrom eters or 

some sim pler devices derived from the same principle. In any case, 

the recognition of the labelled substances must be made by collecting 

the sam ples from the investigated substance and analysing them in the 

detecting device. 

Labelling with radioisotopes enables one to observe the transfer 

without sampling or introducing any m easuring device directly in the 

reaction medium. This is made possible, of course, by using the 

penetrating rays emitted by m ost of the radioisotopes. In addition, the 

speed and facility of such m easurem ents makes labelling with radioisotopes 

very advantageous. There is not much the investigator must really know 

of the nuclear properties of the radioisotopes used. In m ost cases, he 

will only be interested in the exact knowledge of the decay schem e, which 

is n ecessary in planning the measuring method, and of the activity to be 

used in each experiment. 

Sometimes a method of "p ost-radioactive labelling" can be used. It 

consists of labelling with a non-radioactive elem ent, which is then detected 

and m easured by subsequent neutron activation of collected sam ples. This 

method, rather sim ple in execution, has all the inconveniences mentioned 

above in connection with labelling with non-natural composition of stable 

isotopes. But it has also som e benefits: low cost, the concentration of the 

labelling substance can be very low (a factor very important in the study 

of refining p ro cesses in the m etallurgy of very pure m etals and alloys), 

no health hazards, etc. 

The labelling also gives some other possibilities: One of them is the 

investigation of the precursor-product relationship, and of reaction pathways. 

This can be also regarded as a special case of a transfer process. 

The suspected atom s, groups or m olecules of a precursor are labelled 

with radioactive isotopes and then this radioisotope is sought in the supposed 

product. This application is of great importance in biochem istry, since the 

identification of complex m etabolism pathways in the living organism is 

not easy. 

The m ost interesting results can be obtained from the use of tracers 

in the study of p rocess kinetics. Diffusion, exchange between two (or m ore) 

pools, and the turnover rate are some of the best known exam ples of such 

tracer applications. 

The use of tracers enables also the measurem ent of some physicochem 

ical constants such as solubility of low -soluble substances, vapour 

p ressure of low -volatile substances, partition coefficient between two 

phases, surface measurem ent of powders or porous m atter, stability 

constants of complex compounds, etc. In all these ca ses, we make use 

of the fact that radioisotopic atom s can be detected and m easured even in 

a very low concentration. Other tracers do not perm it such dilution factors 

as with radioisotopic tracers. Some radioisotopes can be obtained alm ost 

c a rrie r-fre e — e. g. the radioisotopes of elem ents represented in the 

fission products; in such case s, effectively weightless amounts of radiotracer 

can be detected easily. It is easy to calculate that a ca rrie r-fre e 

radioisotope with a h alf-life of two weeks has an activity of about 3 X 105 Ci 

per gram ,i. e. if we can m easure an activity of 1 dps, which is quite easy, 

we can detect 10"16 g of the pure radiotracer.

IAEA-SM- 1 7 0 /96 379 

There are also some analytical applications of radioisotopic tracers. 

Each analytical procedure requires two principal steps: separation and 

isolation of the analysed component from the sample and the measurem ent 

of the amount of the isolated component. In the past, the analytical chem ists 

only used separation procedures of 10 0% efficiency, which means that the 

analysed component was isolated completely in a pure form for subsequent 

measurem ent of the m ass. 

But such methods are, in general, tim e-consum ing and som etim es 

difficult to apply. Now, many analytical separation procedures have an 

efficiency lower than 100%. The determination of the actual efficiency 

can be carried out by adding a sm all quantity of labelled compound to the 

analysed substance. Then the labelled compound, which should be identical 

with the analysed component, is isolated. A fter measuring the ratio of 

activities before and after the separation or between two separated substances, 

it is possible to calculate the recovery of the analysed compound in the 

separation procedure and to take it into account for the en d-resu lt. This 

method also enables discovery of those steps in the separation procedure 

where lo sse s occur. 

A sim ilar method using radioactive tracers is the method of isotope 

dilution. The aim of this method is the determination of m a sse s or of 

volumes not accessible to direct m easurem ent. The analytical use of 

this procedure is frequently demonstrated in the case of analysis of a 

mixture of amino acids. The quantitative isolation of a particular amino 

acid from such a mixture is very difficult, but it is possible to isolate 

only a part of the total content in a very pure form . If it is possible to 

know what part of the total content has been isolated and weighed, then 

the original amount of this amino acid will be known. The determination 

of the ratio of the weight of the isolated part to the total content can be 

perform ed by isotope dilution. It is only n ecessary to have this particular 

amino acid in labelled form . Then we add a known amount of tracer compound 

to the sample before starting the separation procedure. This radioactive 

reagent labels the total amount of the amino acid to be analysed. The labelled 

m olecules are isolated with the same recovery as the non-labelled ones. We 

can easily measure the ratio of the specific activity of the added amino acid 

at the beginning to the specific activity of that isolated after the separation. 

This figure is exactly the ratio of the total weight of the amino acid to the 

weight of the added labelled reagent. 

In geochem istry, the radioactive decay law is used for the determination 

of the age of rocks (geochronology). In this case, we make use of natural 

contamination of many m inerals with some radioactive tracers: uranium, 

thorium, potassium , tritium and others. From the well-known law of 

radioactive decay, we can derive the formula 

Xtt = l n ( l + Nn /N j) 

where N u /N j is the actual atomic ratio of the daughter and parent isotopes, 

e .g . 206Pb and 238U. This can be m easured by m ass spéctrom etry o r, in 

som e cases, by activation analysis. The successful application of this method 

requires the absence of the daughter isotope at the time of formation of the 

m ineral and no subsequent chem ical change in the composition of the m ineral. 

With such pairs of isotopes as 207 P b /235U; 206P b /238U; 208P b /232Th; 

40A r / 40K; 87S r / 87Rb it is possible to determine the age of rocks up to

380 GÓRSKI 

several billions of years. For shorter periods 14С is used (in the range 

of several thousand of years) and tritium (in the range of several tens of 

years). 14C dating is frequently used in archeology and tritium dating 

is applicable in age determination of underground waters in hydrology. 

P recise knowledge of the h alf-life of the applied radioisotope is a fundamental 

requirement in the application of this method. 

14C and tritium tracers are exam ples of many other radioisotopes 

produced by the interaction of particles from cosm ic rays with stable atom s. 

Some of them are short-lived (e. g. 37A r, 35 days), some are long-lived 

(e. g. 39A r: 270 years). The amount of these radioisotopes and the ratio 

of their respective activities can give information on the age of m eteorites 

and the intensity of cosm ic radiation in the interplanetary space. 

The exam ples given above and some other facts demonstrate that 

there are many naturally occurring radioisotopes among the so-called 

"stab le elem ents" (atomic number s 82), e .g . rubidium, which is regarded 

as a stable elem ent, consists to 28% of 87Rb, which has a h alf-life of the 

order of 1010 years, about ten tim es longer than 238U. 115In is another 

noticeable example. Its abundancy in the natural element is 96%, and the 

h alf-life is of the order of 1014 years. About 30 natural isotopes with 

Z á 82 are suspected or have been proved to be radioactive, m ostly with 

very long h alf-lives. Some other elem ents, as, e. g. krypton, are now 

"n atu rally" occurring radioactive isotopes as the result of continuous 

environmental pollution with fission products of uranium, one of which is 85Kr. 

Radioactive isotopes are also used for studying the structure of m olecules 

or crystal lattices. One method consists of observing the rate of 

isotopic exchange between the radioactive and non-radioactive isotopes 

in the m olecule. The kinetics of isotopic exchange depends on the strength 

of the chem ical bond between this particular atom and the rest of the m olecule. 

A lso the position of the atom in the molecule has a certain influence. 

The central atom in complex compounds is well protected from isotopic 

exchange by the peripheral groups. When there is m ore than one atom of 

the same element in a m olecule, there can be equivalence independent of 

the position of the atoms in the m olecule, but som etim es such equivalence 

does not exist. In this last case, the rate of isotopic exchange will depend 

on the position of the radioactive tracer in the structure of the m olecule. 

If the positions in the structure investigated are equivalent, then the rates 

of isotopic exchange will be equal and not dependent on the position of the 

radioisotopic tracer. 

Another use of radioisotopes for structural studies is the Mossbauer 

effect. This effect is frequently applied for the investigation of bonds and 

fields in the crystal lattice. 

From our short description of current applications of radioisotopes 

in chemistry we see that in most of the non-sophisticated applications only 

data on half-lives and disintegration schemes are needed,knowledge of which 

is necessary for successful use of radioisotopes in chemical research. 

Only for some analytical applications of radioactivity, especially activation 

analysis, which directly exploit some nuclear reactions, knowledge of c r o s s - 

sections and exact information on the spectra of the emitted radiations 

are n ecessary.

IAEA-SM -170/96 381 

DISCUSSION 

J. A . CZU BEK: Although I am not involved personally in problem s 

of chem istry, I would like to make two comments on nuclear data r e 

quirements in geochem istry which are of importance to those of us working 

in nuclear geophysics. We need a good knowledge of two constants which 

are also of interest for geochem istry. The first is the radioactive decay 

constant for 40K (for gamma em ission). The existing data range from 

2. 8 to 3. 6 g am m a/s per gram of natural potassium , which is of course 

quite unsatisfactory for us. The second is the fission decay constant for 

uranium, which is needed in geochem istry for age determination by trace 

detection in m icas. The use for this purpose of the uranium glasses produced in 

Czechoslovakia duringthe 19th century is not quite satisfactory, owingtothe short 

time elapsing from this period. The purpose of m y comment is to encourage 

the m easurem ent of these values, which are really needed by users. 

L. HJÄRNE: When mentioning, for exam ple, in d iu m -115, Dr. Górski 

touched upon a matter which is of some importance to many of us. I am 

referring here to the natural abundances of isotopes. We often rely on one 

of the nuclide charts for information of this kind, but, when we need better 

accuracies, we have some difficulties finding good data. 

I have been informed that in the next edition of the GE nuclide chart the 

revision of this kind of data will include a substantial reduction of the number 

of significant figures quoted. The reason is twofold: 

(1) The natural variation of the abundances is greater than previously 

assum ed; and 

(2) The accuracies of m easurem ents are not as good as previously 

believed. 

Can anyone comment on whether this matter should be considered 

within the scope of nuclear data and on how unsatisfactory the situation 

really is? 

M. LEDERER: The situation really is serious and the problem has 

been considered by the International Com m ission on Atom ic W eights. It 

appears that m ost abundance m easurem ents are accurate to no better 

than >*» 1% relative, with the exception of a few calibrated m easurem ents, 

which may be accurate to * 0. 1 % relative. I believe the ICÁW plans to 

review the abundances about every two years because of their importance 

to atomic weights. The m ost recent values are (apparently) those quoted 

on the latest GE chart. I have found no recent compilation on natural 

variations in the abundances. The ICAW notes certain elem ents for which 

natural variations lim it the accuracy of atomic weight determinations. 

D. BERÉNYI: The role of nuclear data on radioisotopes in X -r a y 

fluorescence analysis was not mentioned in the review. This method is 

very important in widely different fields where the rapid analysis of 

sam ples is a requirem ent. What is your opinion on this subject? 

L . GÓRSKI: The paper was devoted to applications in chem istry, 

to the exclusion of all analytical methods, which w ill be discussed in the 

various special session s of this symposium. I agree that the knowledge 

of the cro ss-se ctio n s for production of X -r a y s in different isotopic sources 

of X -r a y s is very important for this application, but this is to some extent 

an extra-nuclear phenomenon.

NUCLEAR DATA REQUIRED 

FOR THE INTERPRETATION 

OF HOT-ATOM CHEMISTRY 

A.H .W . ATEN 

Euratom, Central Bureau for Nuclear Measurements, 

Geel, Belgium 

Abstract 

N U CLEAR D A T A REQUIRED FOR THE IN TERPRETATIO N OF H O T -A T O M C H E M IS T R Y . 


In h o t - a t o m c h e m is tr y r a d io a c t iv e a to m s a re r e le a s e d b y tw o p r o ce ss e s fr o m th e b on d s jo in in g th e m to 

th e m o le c u le , in w h ic h th ey w e r e o r ig in a lly c o n t a in e d . E ither e m is s io n o f a p a r t ic le or a p h o to n g iv e s a 

r e c o il t o th e r a d io a c t iv e a to m or a p o s it iv e c h a r g e is g iv e n to th e a to m in q u e stio n d u rin g th e r a d io a c t iv e 

tr a n sfo rm a tio n and th is c h a r g e , i f s u ffic ie n t ly h ig h , r e le a s e s th e a t o m . T o understand w h at h a p p en s in h o t - 

a to m c h e m is tr y k n o w le d g e o f th ese tw o p h e n o m e n a is e s s e n tia l. In th e c a s e o f n eu tron c a p tu r e , th e g a m m a 

p r o ce ss e s d e t e r m in e th e v a lu e o f th e r e c o il e n e r g y . T h e s itu a tio n is e v e n m o r e d iffic u lt in th o se c a s e s w h ere 

b on d s a re b ro k e n b y a p o s it iv e c h a r g e . T h is m a y e ith e r b e ca u se d b y th e a b s e n c e o f e le c t r o n p a irs re s p o n s ib le 

for th e c h e m i c a l b on d от by e le c t r o s t a t ic r e p u ls io n b e tw e e n d iffe r e n t parts o f th e ch a rg e d m o le c u le . In this 

c a s e , th e e s s e n tia l in fo r m a tio n is th e v a lu e o f th e p o s it iv e c h a r g e (o r rath er th e fr a c t io n o f c a s e s in w h ic h e a c h 

c h a r g e o c c u r s ). P o s itiv e c h a r g e s n o r m a lly a rise fr o m e le c t r o n ca p tu r e or fr o m c o n v e r s io n o f g a m m a ra y s. In 

th e la tte r c a s e , it is a lso e s s e n tia l to k n ow th e d e la y b e tw e e n th e r a d io a c t iv ity p r o ce s s and th e p r o d u c tio n 

o f th e c o n v e r te d g a m m a rays. 

INTRODUCTION 

The field of hot-atom chem istry covers the chem ical reactions of those 

atoms in which the nucleus has just been form ed by a nuclear reaction or 

by a radioactive p ro cess. 

A s such cases norm ally involve only a relatively sm all number of 

atom s, the usual technique is to study only those p rocesses which produce 

radioactive nuclides and allow accurate m easurem ents to be perform ed 

on very sm all amounts of m aterial. 

To understand the results of such reactions, information is required 

on the kinetic energy and the electrical charge of the atom and on the time 

scale of the separate p rocesses involved. 

F or the various nuclear p rocesses used in hot-atom studies the 

essential data are of a widely different nature, and we shall therefore 

consider separately the following possibilities: 

1. Nuclear reactions induced by charged particles or by high-energy 

neutrons or photons. Nuclear fission also com es into this category, 

as does a-d ecay. 

2. Neutron capture. 

3. Electron capture. 

4. Isom eric transitions. 

5. ß”-decay. 

6 . ß+-decay. 

It will be seen that the situations are rather different depending on the 

way in which the nucleus has been form ed. 

383

384 ATEN 

1. NUCLEAR REACTIONS INDUCED B Y CHARGED PARTICLES OR BY 

H IGH-ENERGY NEUTRONS OR PHOTONS. NUCLEAR FISSION, 

» -D E C A Y . 

If a nucleus is produced by the action of a charged particle or a high- 

energy neutron or photon or by alpha-decay, it receives a recoil energy 

of the order of 104 to 105 eV . In the case of nuclear fission, the kinetic 

energy of the fission fragments is even higher, of the order of 108 eV. 

Such energies greatly exceed norm al ionization energies or chemical 

bond energies and therefore the radioactive nucleus will not be able to 

form a chem ical compound until it has lost by far the larger part of its 

energy. 

Under these circum stances, energy lo sse s are caused mainly by 

ionization in the surrounding medium, and the radioactive particle itself 

will also lose a number of its electrons. Below about 103 eV various 

scattering p ro cesses are important in relieving the particle of its energy. 

A large amount of radiation damage has now been done and the particle 

leaves behind it a track of radicals, and, if it is form ed in a solid matrix, 

also of displacem ents. It will finally come to rest at a large distance, 

which even in condensed phase amounts to hundreds of angstrôm s, away 

from the spot where it has been form ed. 

A s the particle slows down its positive charge will diminish and it is 

usually assum ed that by the time its energy has been reduced to about 102 eV 

it will have becom e electrically neutral. At this stage, it is able to react 

with m olecules of the m atrix or with radicals from its own track or from 

general radiation damage in the medium. 

Under these circum stances, the final products form ed will not be 

much influenced by the original condition or the original energy of the 

radioactive atom after its birth and no special information on the nuclear 

p rocess is needed for the explanation of the products of these hot-atom 

reactions. 

It may, however, happen that delayed 7 -r a y s are emitted at a moment 

when the energy of the particle has already been reduced to a thermal value. 

If under these conditions, i. e. after a delay of, at least, the order of 

1 0 '13 to 1 СГ12 seconds, a 7 -r a y is emitted, this will norm ally be a 7 -r a y of 

fairly low energy which will be converted to an appreciable degree. Under 

these circum stances, the atom will again be released from the molecule in 

which it is contained and will be capable of participating in one or more 

new chem ical reactions. The results of such p rocesses will be discussed 

in section 4. 

At the moment when the particles come to rest — which occurs very 

roughly a few 1 0 ' 13 s after the nuclear process — a fraction of them has 

already entered into the chem ical combination in which they will finally 

be found. In m ost cases, however, another part is still present as single 

atom s, in free radicals, or in som e other unstable form . A s such they may 

p ersist for a much longer time before they reach a stable condition. In 

liquid and gaseous system s, this final stabilization process presumably 

involves diffusion over very appreciable distances. 

2. NEUTRON CAPTURE 

If a nucleus is activated by neutron capture, the energy gain of about 

6 MeV (the binding energy of the neutron in the product nucleus) must be


dissipated by the emission of 7-rays. If the entire energy is emitted as a 

single 7 - ray the recoil energy (ER) of the nucleus is given by the equation 

_ 536 2 

R ” M E? 

if Ej, is expressed in MeV and ER in eV. It should, however, be realized 

that not all of this energy is available for breaking the chemical bond or 

bonds by which the radioactive is held in its mother molecule. 

In simple molecules, the fraction of the recoil energy available for 

bond breaking is, at most, equal to (M-m)/M, where M designates the mass 

of the molecule and m that of the radioactive atom [ 1] . 

If more than one 7-ray is emitted, the situation is much more complicated 

as the total recoil energy imparted to the nucleus is determined by the 

angle under which the 7-rays are emitted, at least, if the two gamma-rays 

are produced not more than 10"15 to 10'14 seconds apart. 

In the case of a thermal neutron capture reaction the recoil energy of 

the nucleus does not exceed normal chemical bond energies by a large 

factor. In a condensed phase, the particle will not move more than a few 

angströms from its original site and will not have to undergo more than a 

few collisions before it can form a stable chemical bond. In principle, it 

might even happen that, because of compensation of recoil processes, the 

particle gets such a small energy that it cannot leave the molecule or ion 

in which it was originally contained. This phenomenon, "primary retention", 

is, however, very rarely observed, if at all. 

The situation is again complicated if delayed 7-rays are emitted 

by the product nucleus because in this case, as was already mentioned 

in section 1, after the radioactive particle has first formed a 

chemical combination, it will be released once more and will have to form 

a second molecule or ion in order to stabilize itself (see section 4 ). 

3 . ELECTRON CAPTURE 

In the case of electron capture, the product nucleus, first of all, suffers 

a recoil due to the emission of a neutrino. In principle, one might expect 

that a neutral atom would be formed. If electron capture is followed by 

one or more 7 - ray emissions, the latter processes give recoil energies to 

the nucleus comparable to that due to the neutrino emission, and the two 

(or more) recoil energies should be summed in the appropriate way. 

However, the hole in the К -shell (or, in the case of L-capture, in the 

L-shell, etc. ) will be filled up by an electron from one of the outer shells 

with emission of X-rays. Such a process is accompanied by the liberation 

of electrons (Auger effect) and this means that the product atom is left with 

a high positive charge (see Fig. 1). Moreover, this charge is by no means 

equal for all atoms produced but there is a certain probability distribution 

for atoms with various ionic charges [ 2 ]. If the atom in which electron 

capture takes place is part of a molecule, the electrical charge produced on 

the ion of the product nucleus will immediately spread over the entire 

molecule and the electrostatic repulsion created in this way is sufficiently 

strong to break it up. Also the deficiency in electrons of the molecule 

weakens the chemical bonds and may even in itself be sufficient to separate 

two atoms if both bonding electrons of a pair are absent at a certain moment.

386 ATEN 

F IG . 1 A . A v e r a g e p o s it iv e c h a r g e le f t o n a n a to m in w h ic h a h o le has b e e n g e n e ra te d in th e K - or L -s h e ll. 

The fact that the radioactive atom is left with a positive charge after 

the breaking-up of the m olecule may also influence its ultimate chem ical fate. 

But here, too, we have the possibility that after electron capture and 

after the product nucleus has reached a stable chem ical state, delayed 

7 -ra y s will be emitted, the conversion of which will again release the 

radioactive atom and force it to undergo a second hot-atom p rocess, as 

will be explained in section 4. 

4. ISOMERIC TRANSITIONS 

In the case of a low -energy т-ra y emitted by a nucleus such a 7 -r a y is 

converted to an appreciable degree. This means that the energy is taken 

over by one of the electrons of the atom (normally a К -electron) and that the 

hole form ed in the shell of this electron is filled up by an electron from a 

higher shell in the atom. 

Owing to this p rocess, a number of electrons finally leave the atom and, 

as in a case of K - capture, the final ion is left with a very appreciable 

charge (Fig. 2). (These charges will be roughly, but not exactly, equal to 

those produced by K -capture. ) Thus, if the atom is part of a molecule it 

will be liberated by electrostatic repulsion or by the absence of the electrons 

constituting the chem ical bond and, carrying — or having carried originally — 

a positive charge, it will react again with som e constituent of the medium. 

In som e cases, compounds of atoms with an excited nucleus can be used as 

such in hot-atom experim ents, owing to the long h alf-life of som e metastable 

nuclei, and then the results of delayed 7 -em ission can be studied by themse 

lv e s. Important exam ples are the two products of neutron capture in 

the stable bromine isotopes. The radioactive isotopes produced — 80Br and

100 

10 

IAEA-SM -17 0/28 387 

1 5 10 15 

CHARGE 

F IG . I B . R e la t iv e fr e q u e n c y o f fo r m a tio n o f io n s c a rr y in g d iffe r e n t p o s it iv e c h a r g e s for th e tra n sition 

iaXem _ iaXe_ 

82Br — both have an isom er, the first one with a h alf-life of 4 hours, the 

second of 6 minutes. Of the isom er 80B rm many compounds have been 

prepared and the hot-atom reactions following its highly .converted gam m a- 

em ission have been studied. 

Quite frequently, however, the delayed 7 -em ission follows other nuclear 

p rocesses like beta-em ission and the hot-atom reactions induced by the 

conversion process must be studied in the medium in which also the 

prim ary hot-atom reactions have taken place. 

5. ß~ -D E C A Y 

In the case of ß '-d e ca y , we have, first of all, to deal with the recoil 

p ro cess. In this case, it is m ore complicated than in that of electron 

capture because we now have two different reco ils. One is due to the 

em ission of the electron, and the other to that of the neutrino. A s the two 

energies have quite comparable values, one has to know the angular 

distribution to compute the effective recoil energy available. 

There is, however, a second effect which is not quite negligible. 

When a nucleus em its an electron, one would, in principle, expect to obtain 

a product ion which should be short of exactly one electron. However, in 

this case again secondary p rocesses take place and in some product atoms 

electrical charges larger than one are observed (electron shake-off). 

Little is known about these phenomena but som e estim ates are given in 

Table I. 

Evidently, any delayed converted 7 -r a y will cause a second hot-atom 

p rocess and, in this way, will ultimately decide the fate of the radioactive 

product. But in the case of ß-d eca y even 7 -r a y s emitted within 10"13 s or 

le ss are important if they occur since the recoil energy due to them is not 

much lower than that due to the ß-p article and the neutrino.

388 ATEN 

T A B L E I. R ELATIVE FREQUENCES OF IONIC CHARGES PRODUCED BY 

/3-D E C A Y (GAS PHASE) [ 3] 

6. J3+-D E C A Y 

V ery little is known about the chem ical effects of positron decay. The 

prim ary product should be a negative ion, but it is m ost unlikely that such 

an ion is sufficiently stable to last until the final reaction of the radioactive 

atom takes place. However, positron em ission is rarely used in hot-atom 

studies and this process will not be discussed in the present report. 

CONCLUDING REMARKS 

On the basis of the preceding discussion it is easy to recognize which 

item s in the field of nuclear data are of interest to students of hot-atom 

chem istry. It will, of course, be realized that part of the data do not really 

refer to the nucleus in question, but rather to the atom as a whole. 

In all cases it is of the highest importance to know whether there are 

any gam m a-rays delayed by m ore than 1 0 '13 s what their intensity per 

decay is, their conversion coefficient and the average ionic charge of the 

product atom, or — even better — the frequency distribution of the various 

ionic charges. (This problem is complicated by the fact that the charge

IAE A -S M -17 0/28 389 

m ay not be independent of the composition of the m atrix. ) If the converted 

gamma ray is followed by one or more other gamma rays, details 

concerning the latter should also be known, as they determine the kinetic 

energy of the radio-atom at the stage where its final fate is decided. 

F o r all reactions producing low -energy (< 50 eV) recoils (all categories 

except that under section 1), one should know the number of 7 -photons 

emitted per decay (if any), their energies, and either their angular 

correlation or their delays, depending on whether the delay exceeds about 

10'15 s or not. 

In the case of electron capture, we also need more accurate information 

on the positive charges carried by the product atom, together with the m ass 

difference between the parent and the daughter atom, whence we can derive 

the recoil energy given to the atom by the escape of the neutrino. 

F o r ß ' - decay, one should have the same information as for electrón- 

capture, but, in addition, the shape of the beta-spectrum should be known. 

It will be evident that, at present, we are very far away from having 

the entire information asked for in the preceding paragraphs, and it is 

quite possible that we shall never be able to obtain all of it. Some of the 

m ore important aspects are, however, well within our reach. Concerning 

the de-excitation schem es of product nuclei of nuclear reactions and daughter 

nuclei of radioactive transitions, a good deal is already known and there do 

not seem to be any fundamental obstacles which could keep us from extending 

this knowledge to all nuclides which are of sufficient interest to hot-atom 

chem ists to warrant the effort. 

REFERENCES 

[ 1 ] S T Ö C K L IN , G . , C h e m ie h eisser A t o m e , V e r la g C h e m ie , W e in h e im /B e r g s tr . (1 9 6 9 ) 1 8. 

[ 2 ] C A R LSO N , T . A . , H U N T , W . E . , KRAUSE, M . O . , Phys. R e v . 1 5 1 (1 9 6 6 ) 4 1 ; CARLSO N , T . A . , 

W H IT E , R . M . , C h e m ic a l E ffe cts o f N u cle a r T ra n sfo r m a tio n s, (P r o c . S y m p . V ie n n a , 1 96 4) 1, IA E A , 4 

V ie n n a (1 9 6 5 ) 2 3 . 

[ 3 ] C A R LSO N , T . A . , Phys. R e v . 131 (1 9 6 3 ) 6 7 6 ; SNELL, A . H . , P L E A SA N TO N , F . , Phys. R ev . 107 

(1 9 5 7 ) 7 4 0 ; 111 (1 9 5 8 ) 1 3 3 8 . 

DISCUSSION 

K. H. LIESER (Chairman): I would like to stress the point that nuclear 

data give only an explanation of the very first step in hot-atom reactions. 

H ot-atom chem istry involves recoil effects, excitation of the hot atoms 

and secondary reactions as well as radiation effects. While the prim ary 

reco il effects depend on nuclear properties, the other effects, such as 

excitation, formation of radicals and secondary reactions, depend essen 

tially on the properties of the atom s and of the surroundings. Thus, in 

hot-atom chem istry the situation is very complex. 

A . H. W . A T E N : I would say that the second chapter is chem istry 

and the fact that the properties of the electrons already enter into what 

one calls the nuclear data is really a sign of the indiscrete behaviour on 

the part of the nuclear p hysicists, who have taken into the field of their 

activity part of the properties of the electrons of the atom s instead of 

restricting them selves to the nuclei.

Section VI 

FISSION-PRODUCT NUCLEAR DATA

Chairman 

G. В. YANKOV (USSR)

IAEA-SM -17 0/94 

FISSION-PRODUCT CHAIN YIELDS 

FROM EXPERIMENTS IN THERMAL REACTORS* 

E.A.C. CROUCH 

Chemistry Division, 

UKAEA Research Group, 

AERE, Harwell, Berks, 


Abstract 

FISSIO N -PR O D U C T C H A IN YIELDS FROM EXPERIM ENTS IN T H E R M A L REA C TOR S. 

P u blish ed v a lu e s o f th e y ie ld s o f fissio n p r o d u c ts fr o m th e th e r m a l n eu tron in d u c e d fis s io n o f 227T h , 

229 T h , 233U , 235 U , 239Pu, 241Pu, 242m A m , 245C m , 249C f , and fr o m th e " p ile " - n e u t r o n - in d u c e d fis s io n o f 227A c , 

231 p 3i г э г 232 u i 237 H p and !41A m h a v e b e e n assessed and r e c o m m e n d e d v a lu e s fo r th e ch a in y ie ld s lis te d . 

1. Introduction 

Fission Product yields were last collected and assessed by a member 

of AERE in 1965 (Ref. 1). Since that time other collections, assessments, 

reviews and predictions have been made (Refs. 2, 3, 4, 5), but because of 

the continuous flow of new experimental results it becomes necessary to 

make the next assessment at approximately yearly intervals. Because the 

number of experimental results is getting too large to be conveniently 

handled in a card index file, and the simple arithmetic of adjustment and 

correction is increasing with each new assessment, a less onerous method 

of assessing the experimental results must be found. To this end there 

has been established at AERE a computer file library of fission product 

yields (Ref. 6 ), and an interrogation program (Ref. 7), to extract information 

from the library. 

235 

There are still lacunae in the experimental results even for U 

thermal neutron fission (e.g. the yields at mass numbers 107, 108, 110, 

113 and 116 among others, are undetermined experimentally), and there is a 

need both for academic and technological reasons, to have a sound means of 

estimating missing yields. It is intended that a mathmatical model of the 

fission process will be fitted to the available experimental results (e.g. 

Ref. 8 sets out some preliminary ideas), so that missing values in general 

shall be estimated with some confidence. Such a process is suited to fast 

and frequent computer processing and the methods of Refs. 6 , 7 and 8 can 

be made automatic. 

However, it seems prudent (and it may very well turn out to be necessary), 

to make preliminary assessment of the available results by the 

usual subjective methods so that starting estimates of the parameters of 

the fitted model shall be reasonable, and this paper is meant to provide 

part of such a necessary basis. Further papers dealing with fast fission 

and spontaneous fission will appear later as the work is completed. 

Independent yields will also be dealt with separately. In order that 

these assessments shall be the more easily applied to the objective methods 

* T h e co n te n ts o f th is p a p e r h a v e b e e n e x a m in e d and r e c o m m e n d e d b y th e U K C h e m ic a l N u cle a r 

D a ta C o m m itt e e . 

393

394 CROUCH 

it was thought proper to make some estimates of the errors to be associated 

with each recommended chain yield. It is believed to be the first time 

that this has been done and the method used is described in detail. In 

such a compilation as this there are bound to be errors, and readers are 

asked to let the author know of any that they detect. 

2. Basis of the Assessment 

i) It would seem proper to define certain terms used by those engaged 

in the determination or use of Fission Product yields. There are 

three kinds of Fission Product yields as defined below and they are 

usually expressed as a number of fission product atoms formed per one 

hundred fissions i.e. in the form of a percentage. 

a) Independent Yield 

An independent yield is the probability of formation of a 

given nuclide in fission, after prompt neutron emission but 

before any radioactive decay of itself or it's precursors occurs. 

Sometimes independent yields are expressed as 'fractional independent 

yields' i.e. as a fraction of the chain yield. 

b) Cumulative Yields 

A cumulative yield is the probability of formation in fission 

of a nuclide after prompt and delayed neutron emission and before 

it decays, but including the independent yields of its precursors. 

A 'fractional' cumulative yield is a cumulative yield expressed 

as a fraction of the chain yield. Effectively a cumulative yield 

is the sum of all the independent yields in a decay chain up to 

and including the atomic number of the nuclide concerned. 

c) Chain Yield 

A Chain Yield is the probability of formation in fission of a 

given stable nuclide after prompt and delayed neutron emission 

and after the decay of all its precursors. It is effectively the 

sum of all the independent yields contributing to a given mass 

decay chain. Usually it is the cumulative yield of the last 

(stable) member of a decay chain of given mass number. 

ii) Treatment of published results; yield adjustments 

The published data for this assessment were stored in a computer 

file library (Ref. 6 ), and for each fissile isotope an interrogation 

program (Ref. 7), caused all cumulative and chain yields to be 

printed out. It was assumed that the printed list contained no 

duplicate values because during compilation of the library experimental 

results but not assessed values from compilations were included. 

All entries were checked to ensure that values previously reported 

by the same author(s) were omitted if the new entry were a recalculation 

of the previous work and not a new determination. Corresponding 

to the print-out, punched cards were produced for the thermal fission 

products of the nuclides 233U, ^ U, ^^Pu and 241-Pu, and the adjustments 

to be described below were applied to the reported results by 

means of computer routines which will be used in future computerised 

assessments using objective methods (see Ref. 8 for preliminary description). 

The results on the fission products of other fissile


isotopes, and those produced in fission induced by other neutron 

energies, were adjusted by hand calculations on the figures contained 

in the printed output of the interrogation routine. 

As previously explained (Refs. 5, 7), there are three ways of 

classifying fission product yields depending on what corrections or 

adjustments have to be made to them before they can be combined with 

other similar results to give an average value. 'One-nuclide' yields 

are those yields relative to the yield of say ■'•^Ba or ^%o. Then if 

the reference yield is known the others can be adjusted relative to 

it. 

'Other' yields (i.e. other than 'one-nuclide' or 'R-value'), are 

yields which have been determined absolutely or effectively absolutely, 

and which do not require or are not amenable to adjustment. This 

kind of yield is determined by simultaneously measuring the absolute 

number of fissions and the number of atoms of the resulting fission 

products. Sometimes the fissile isotope and the fission products are 

measured in the same piece of fissile material, sometimes the fissions 

are measured in a small quantity of the fissile material which is 

irradiated in close propinquity to the fissile material in which the 

fission products are measured. 

In some cases yields are effectively absolute because after measuring 

the relative yields of a sufficient number of fission products, 

a smooth curve against mass-number is drawn and all the yields are 

multiples by a common factor which forces the area under the curve to 

sum to 200%. Usually no adjustment can be applied to the resultant 

yields. 

'R-value' yields are calculated as follows: 

x 

У, = У, 

л х л R - 

A 1 2 

* XA R 

LA2 A1 ^ 

Where у is a yield and A an activity, 

X is the nuclide of interest, gg 

R is the reference nuclide, usually Mo, 

1 refers to the nuclear reaction of interest, 

2 refers to the standard reaction, Thermal neutron fission 

usually of 235ц, less frequently, of ^^Pu. 

The term in brackets in the above equation is called 'R-value' and is 

made up of measured radioactivities derived from the reaction of 

interest and from a simultaneous standard reaction irradiation. The 

other components of the right hand side must be absolutely determined 

or assumed. 

2 2 5 The assessment process started with the thermal fission yields of 

U. First all 'other' type yields were assembled i.e. those which 

required no adjustments. Mean values for such reference nuclides as 

14 0Ba, 99Mo and 97zr were calculated and used to adjust the 'one- 

nuclide' type yields. If 'other' type yields were not available to 

establish a good absolute value for a reference nuclide of a 'one- 

nuclide' result then the adjustment was made by reference to the 

recommended value given in Ref. 2, which failingjRef. 3. Finally 

all the results for a given mass number were used to find a mean and

396 CROUCH 

its uncertainty; the chain yield recommended being composed of results 

determined as chain yields and cumulative yields eligible (see later), 

for inclusion as chain yields. 

239 

Attention was then turned to the Pu fission yields. First all 

'other' type results were assembled and absolute values for reference 

yields were obtained. The 'one-nuclide* yields were then adjusted 

in the same way as those of U. 'R-value* yields were adjusted 

using the 235u yields already established, along with the ^39pu reference 

yield derived from 'other* and 'one-nuclide1 yields. Finally 

the mean value and its uncertainty were found using all the results 

available. For a given mass-number the recommended chain yield 

contains those cumulative yields eligible for inclusion as chain 

yields. 

239 

The assessment process described above for Pu, was applied to 

all the other fissile isotope fission yields. However, for some 

fissile nuclides not many experimental results are available so their 

values for reference nuclide yields cannot be established. In such 

cases authors commonly assume a reference nuclide yield and when this 

is so the assumed yield is indicated in the tables of results (below). 

iii) Treatment of Published results: Error estimates 

The uncertainties to be associated with a given measurement are 

reported by the authors in a variety of ways, and frequently not at 

all. Usually a mean value is given together with limits expressed 

as yield X + x, where x may be a standard deviation corresponding to 

the precision of the measurement only, not to the absolute accuracy 

of the measurement. 

In this work two methods of expressing the experimental uncertainty 

or 'error* (the word being used in no pejorative sense), were 

used. In the first method the error (considered as a standard error), 

used in this paper (as opposed to the figure reported by the author), 

has been adjusted if necessary to what seemed to be a reasonable 

estimate of the absolute accuracy. Thus a yield given in an original 

paper as being subject to an error of + 0 .1% of the mean value, has 

been attributed a much larger error even if the yield were determined 

by mass-spectrometry. For this purpose no reported yield has been 

attributed a standard error of less than + 3% of the mean value unless 

very good reason was shown in the paper. Likewise a yield reported 

without an estimate of its accuracy was attributed a standard error 

of + 157c if the yield was determined radiochemically and + 10% if by 

mass-spectrometry. There were occasions when better accuracy was 

attributed because there seemed good cause. Of course in those cases 

where reasonable errors were attributed to their results by the 

authors themselves, they were used unchanged. 

The weighted mean of all the reported yields (after adjustment), 

for a given mass number in a given fission reaction was then calculated 

using the reciprocal of the square of the attributed standard 

error as weight for each result, together with the standard error of 

the weighted mean as follows: 

Weighted mean yield = where is the nth 

yield and is its attributed standard error.

Standard error of the weighted mean yield = 

IA E A -SM -nO /94 397 

The weighted sum of squares of the deviations of each included 

yield from the weighted mean (which should be distributed asX was 

then calculated, 

where Y is the weighted mean 

w ... 

yield. 

If in fact it was significantly different from % then either the 

fission yields were inconsistent or the attributed errors were unreal- 

istically small. 

The second method of expressing the experimental uncertainty was 

simply to use the reported yields for a given mass number after adjustment, 

to calculate a simple mean and standard deviation directly. 

These two figures should agree with the weighted values found as 

described above. If they agreed then the attributed errors were 

realistic and the yields consistent, but if they differed then either 

the yields were inconsistent or the attributed errors were smaller 

than the errors indicated by the variations about the simple mean. 

It was also possible to find the attributed error larger than that 

calculated from the simple mean in cases whose only two or three 

reported results fortuitously agreed closely, although it was known 

that the experimental method was subject to larger error. 

Finally the weighted mean yield was taken as the required assessed 

yield and the uncertainty (expressed as a standard error), was taken 

as the greater of the standard error of the weighted mean yield (see 

above), or the simple standard error calculated as 

S№- Y)2 

(n-l) 

3. The assessed yields 

where Y is the simple mean yield. 

The assessed ______ fission j _____ yields ____»ivenîn are 

Tables I-XV. The yields for 

227дс> 231pa> ^ 237jjp an(j ¿41дт are those obtained by "Pile" 

irradiations; they are not properly "thermal" yields and those who use 

them are urged to refer back to the orginal papers if considerations of 

the neutron energy/distribution are at issue. Nevertheless they are 

listed here with the "thermal" yield as they will probably be used in 

conjunction. It must be noted in passing that the "thermal" yields here 

tabulated are not often obtained under conditions which eliminate the 

effects of fast neutrons present in the reactor. Reliance is placed upon 

the fact that thermal neutron fission reaction rates are in general far 

greater than the fission reaction rates due to fast neutrons. 

1 A l l ta b le s a te to b e fo u n d at th e en d o f th is p a p e r .

398 CROUCH 

It should also be mentioned that the Tables show yields which were 

determined as chain-yields, and also cumulative yields which can be taken 

as chain-yields since the independent yields of nuclides of the same mass 

number, but greater atomic number, are negligible. An indication of the 

admissibility of cumulative yields for this purpose may be gleaned from 

Ref. 9 which tabultes independent yields. In general no cumulative yields 

have been used unless they account for 99.007» of the chain yield as calculated 

in Ref. 9. 

4. References 

LÜ CROALL, I.F., "Yields from neutron induced fission", AERE-R 5086, 

(November 1965). 

_ 235 

[2j MEEK, M.E., RIDER, B.F., "Summary of fission product yields for U , 

U , Pu239 and pu24-l at thermal, fis sion spectrum and 14 MeV neutron 

energies", APED-5398-A (Revised October 1968). 

[3] FLYNN, K.F., GLENDENIN, L.E., "Yields of fission products for several 

fissionable nuclides at various incident neutron energies", ANL-7749, 

(December 1970). 

[4| SIDEBOTHAM, E.W., "F ission product yield data extrapolated for some 

actinides", TRG Report 2134(R), (1972). 

[5] VON GUNTEN, H.R., "Distribution of mass in spontaneous and neutron 

induced fission", Actinide Reviews, 1(1969), p 275. 

[6] CROUCH, E.A.C., "A library of neutron induced fission product yields 

maintained and interrogated by computer methods. Part 1. Establishment 

of the library", AERE-R 6642 (December 1970). 

[7] CROUCH, E.A.C., "A library of neutron induced fission product yields 

maintained and interrogated by computer methods. Part 2. Interrogation 

of the library", AERE-E 7207. 

[8 ] CROUCH, E.A.C., "The Assessment of Fission Yields", Chemical Nuclear 

Data - measurements and applications. Proceeding of the International 

Conference, Canterbury (September 1971). 

[9] CROUCH, E.A.C., "Calculated Independent yields in thermal neutrons 

fission of 233u, 235u, 239pUj 24lpu ancj fission of ^^Th, ^38]j and 

2 4 0Pu, AERE-R 6056 (March 1969). 

[10] HOLDEN, N.E., WALKER, F.W., "Chart of the nuclides", General Electric 

Company, Knolls Atomic Power Laboratory, Tenth Edition, (December 

1968). 

5. Explanation of the Tables 

Mass Number (Col. 1) 

This entry gives the mass-number of the fission product decay chain. 

Element (Col. 2) 

The symbol of the element used to estimate the chain yield. Several 

entries in this column does not imply that all were used in the calcula-


tion of the chain yield. Chain yields determined as "chain yields" are 

entered as such. A figure in brackets alongside an element symbol 

indicates that the nuclide is isomeric and the isomeric yield is given, 

the number is the order of the isomer in the 'Chart of the Nuclides'. 

Literature Reference (Col. 3) 

The number given in Column 3 gives the literature reference as set 

out in Table XVI. 

Corrected value and error (Col. 4) 

Column 4 gives the adjusted yield as a percentage followed by the 

error as a standard deviation expressed as a percentage of the yield. 

Thus the first entry for Br in Table 1 is to be read "7.00 + 0.77o". The 

author's estimates of error are stated when they are given, otherwise an 

arbitrary default value is inserted (see para. 2 (iii) above). 

Means: Weighted and simple (Col. 5) 

The two figures entered on one line in column 5 are the mean as a 

percentage yield, the error as a percentage of the mean yield. The types 

of mean are differentiated by (w) for weighted and (s) for simple. Each 

mean is based on the values given in Column 4 as segregated by the horizontal 

lines. In some cases, usually when only two results are given in 

Column 4, the weighted mean only or the simple mean only appears in 

Column 5. This is because in the former case the weights are not equal 

and there would be no point in calculating a simple mean, or in the latter 

case there would be no point in calculating a weighted mean when the 

weights are equal or nearly so. 

Note however, that the actual weights used in deriving the content of 

Column 5 from those of Column 4 are not necessarily those given in 

Column 4 which are the author's estimates or the default values (see paragraph 

2 (iii) above). 

Recommended Chain Yields (Col. 6 ) 

Column 6 lists the recommended chain yield on the same line as the 

mass-number of the first column. The figures given in brackets are the 

indicators of yields still undetermined experimentally and they are interpolated 

values found by curve drawing through the neighbouring points. No 

attempt has been made to interpolate values when insufficient results are 

available to draw a smooth curve, or in regions where fine structure is 

likely to exist.

400 CROUCH 

Table I 

I 

Ac Pile Neutron induced fission 

1 2 3________4 5______ 6 

83 Br 229 7.00 10 7.00 10 

89 Sr 229 7.89 10 7.89 10 

91 Sr 229 5.82 10 5.82 10 

97 Zr 229 0.31 10 0.31 10 

99 Mo 229 0 . 1 1 10 0 . 1 1 10 

105 Ru 229 0 .8 8 10 0 .8 8 10 

109 Pd 229 0.24 10 0.24 10 

1 1 1 Ag 229 0.16 10 0.16 10 

1 1 2 Ag 229 0.14 10 0.14 10 

1 2 1 Sn(2) 229 0.092 10 - - 

132 Te 229 4.59 10 4.59 10 

140 Ba 229 8.23 10 8.23 10 

143 Ce 229 6.17 10 6.17 10 

227 Th Thermal 

Table II 

Neutron induced fission 

1 2 3_______ 4 5 6 

77 As 2 1 1 1.4 15 1.4 15 

83 Br 2 1 1 1 . 1 32 1 . 1 32 

89 Sr 2 1 1 8 .0 6 8 .0 6 

90 Sr 2 1 1 8.72 10 8.72 10 

91 Sr 2 1 1 6 . 2 1 16 6 . 2 1 16 

95 Zr 2 1 1 3.4 9 3.4 9 

97 Zr 2 1 1 2.41 24 2.41 24 

99 Mo 2 1 1 1.44 10 1.44 10 

103 Ru 2 1 1 0.58 16 0.58 16 

105 Ru 2 1 1 0.28 14 0.28 14 

106 Ru 2 1 1 0.19 32 0.19 32 

109 Pd 2 1 1 0.33 4 0.33 4 

1 1 1 Ag 2 1 1 0.051 20 0.051 20 

1 1 2 Pd 2 1 1 0.029 2 1 0.029 2 1 

113 Ag 2 1 1 0.034 2 1 0.034 2 1 

115 Chain 2 1 1 0.177 15 0.177 15 

1 2 1 Sn(2) 2 1 1 0 . 1 1 36 - - 

125 Sn(2) 2 1 1 0.43 23 - - 

127 Sb 2 1 1 0 .6 8 24 0.63 29 0.63 29 

Te(2) 2 1 1 0.53 47 

129 Te 2 1 1 1.36 2 1 1.36 2 1 

131 I 2 1 1 2.61 18 2.61 18 

132 Te 2 1 1 3.30 18 3.30 18 

133 I 2 1 1 4.80 2 1 4.80 2 1 

137 Cs 2 1 1 6.93 18 6.93 18 

140 Ba 2 1 1 7.71 15 7.71 15 

141 Ce 2 1 1 7.62 7 7.62 7 

143 Ce 2 1 1 6.97 7 6.97 7 

144 Ce 2 1 1 5.95 7 5.95 7 

147 Nd 2 1 1 0.18 28 0.18 28

1 2 

229„, Th 


Table III 

Thermal neutrons induced fission 

3 . 4 5 6 

77 As 304 .106 15 .106 15 

Ge(l) 648 . 0 1 1 15 

78 Ge 649 0.052 15 0.052 15 

83 Br 304 8 . 1 1 15 (W) 6.48 7 6.48 9 

649 6.40 4 (S) 6 .8 8 9 

226 6.14 0.5 

84 Br 649 1 0 .8 8 4 (S) 1 0 .8 8 2 1 0 .8 8 10 

Chain 226 1 0 .8 8 4 

85 Chain 226 10.79 1 10.79 10 

87 Chain 226 8.75 1 8.75 10 

88 Rb 649 7.66 6 (S) 8.65 7.5 8.65 7.5 

Chain 226 9.64 .5 

89 Sr 304 7.3 15 (W) 8.46 9 8.46 12 

649 9.3 3 (S) 8.30 12 

90 Sr 226 2.7 20 (W) 7.72 9 7.72 9 

304 6.79 14 

649 8.44 4 

91 Sr 304 5.78 17 (W) 6.81 9 6.81 9 

Y 649 7.40 5 

92 Y 649 6.40 9 6.40 10 

93 Y 649 4.40 6 4.40 10 

95 Zr 304 2.64 15 (W) 2.64 10 2.64 10 

649 2.60 15 

97 Zr 649 0.61 15 0.61 15 

99 Mo 304 0.162 15 (W) 0.153 9 0.153 9 

649 0.15 4 

103 Ru 304 0.044 15 (S) 0.025 76 0.025 76 

649 0.006 10 

105 Ru 304 0.025 15 (S) 0 .0 1 2 52 0 .0 1 2 52 

649 0.008 3 

106 Ru 304 0.0203 15 (s) 0.016 27 0.016 27 

649 0.0117 8 

109 Pd 304 0.0132 15 (S) 0.0102 30 0.0102 30 

649 0.0071 10

402 CROUCH 

Table III (cont) 

Th thennal neutrons induced fission 

1 2 3 4 5 6 

1 1 1 Ag 304 0.0203 15 (S) 0.0207 7 0.0207 7 

649 0 .0 2 1 4 

1 1 2 Pd 304 .0182 15 (S) 0.0196 7 0.0196 7 

649 .0 2 1 3 

113 Ag 304 .0167 15 (S) 0.0153 6 0.0153 1 1 

649 .0144 12 

115 Cd 304 .0213 15 (S) 0.0199 1 1 0.0199 1 1 

649 .0184 6 

117 Cd 649 .0163 12 (w) 0.0165 6 0.0165 6 

In 649 .0166 7 

118 Cd 649 .0174 5 0.0174 10 

1 2 1 Sn(2) 649 .074 2 

125 Sn(2) 304 .040 15 0.042 1 1 

Sn(l) 649 .0 0 2 2 14 

127 Sb 304 .04 15 0.042 1 1 

649 .0084 4 

Te 304 .0405 15 

129 Te 304 .125 15 (w) 0.124 1 1 0.124 1 1 

Sb 649 .1 2 2 7 

131 Chain 227 .64 5 (W) .595 5 .595 20 

I 304 .882 15 (s) .651 20 

649 .43 1 1 

132 Te 227 1.218 5 (W) 1.124 5 1 . 1 2 1 1 

304 1.125 15 (S) 1.113 1 1 

649 0.87 6 

133 Chain 227 3.02 5 (W) 3.04 5 3.04 5 

I 649 4.00 24 

134 Chain 227 6.03 5 (w) 5.90 5 5.90 5 

I 649 5.30 13 

135 I 649 4.96 5 (w) 5.46 4 5.46 1 1 

Chain 227 6 . 1 0 5 (S) 5.53 1 1 

136 Chain 227 6.03 5 6.03 10


Table III (cont) 

i 

Th thermal neutrons Induced fission 

J_____ 2_____ 2________ä______________ 5______________ 6 

137 Cs 304 5.98 15 (W) 6.94 5 6.94 9 

649 6 . 1 0 12 (S) 6.53 9 

Chain 227 7.60 5 

138 Cs 649 8 .0 0 3 8 .0 0 5 

139 Ba 649 8.96 1 8.96 5 

140 Ba 304 7.30 15 (W) 9.74 5 9.74 17 

649 8.30 15 (S) 9.28 17 

Chain 227 12.25 50 

141 La 649 8.35 0.5 (W) 8.03 6 8.03 6 

Ce 304 7.91 15 

649 7.83 5 

142 La 649 8.50 9 (W) 5.66 5 5.66 23 

Chain 227 5.38 5 (S) 6.94 23 

143 Ce 649 8.87 3 (W) 5.48 5 5.48 27 

Chain 227 5.14 5 (s) 7.03 27 

144 Ce 304 8.72 15 (w) 6.15 5 6.15 16 

649 9.57 3 (S) 7.96 16 

Chain 227 5.60 5 

145 Pr 649 5.40 15 (w) 3.30 5 3.30 27 

Chain 227 3.13 5 (S) 4.26 27 

146 Chain 227 2.14 5 2.17 10 

147 Pr 649 1.83 15 1.83 15 

148 Chain 227 1.07 5 1.07 10 

149 Pm 649 0.71 15 0.71 15 

150 Chain 227 0.18 5 0.18 10 

151 Pm 649 0.046 15 0.046 15

404 CROUCH 

Table IV 

Pa Pile neutron induced fission 

1 2 3 4 5 6 

83 

85 

Br 

Kr( 1 ) 

661 

587 

89 Sr 230 

661 

91 Sr 

Y 

661 

230 

587 

2.27 

4.46 

6.62 

7.26 

7.34 

6.80 

6.40 

0 . 2 

3 

2.27 15 

10 

0 .2 

15 

10 

0 .5 

(S) 6.99 4 6.99 1 1 

(S) 6.85 4 6.85 9 

95 Nb 587 6.40 0 .5 6.40 15 

97 Zr 

Nb 

230 

661 

587 

99 Mo 230 

661 

587 

103 Ru 230 

661 

587 

105 Ru 230 

661 

106 Ru 230 

661 

109 Pd 230 

661 

1 1 1 Ag 230 

661 

1 1 2 Pd 230 

661 

113 Ag 230 

661 

115 Cd(2) 

Cd 

230 

661 

4.11 

4.50 

4.36 

3.40 

2.59 

2.51 

0.30 

0.33 

0.41 

0.14 

0.154 

0 . 1 0 1 

0.108 

0.076 

0.083 

0.081 

0.099 

0.047 

0.061 

0.060 

0.077 

0.072 

0.080 

10 

15 

2 

10 

15 

1 

(S) 4.32 3 4.32 9 

(S) 2.50 2.5 2.50 9 

10 

15 

1 .,3 

(S) 0.346 10 0.346 10 

10 

15 

10 

15 

10 

15 

10 

15 

10 

15 

10 

15 

10 

15 

(S) 0.147 3 0.147 1 1 

(S) .105 3.5 0.105 1 1 

(S) 

(W) 

0.080 

0.08 

1 1 

4.5 

0.080 11 

(S) 0.90 10 0.90 10 

(S) 0.054 13 0.054 13 

(S) 0.067 12.5 0.069 13 

0.080 15 

121 Sn(2) 230 0.068 10 (S) 0.074 6 0.072 11 

661 0.076 15

127 Sb 230 

661 

129 Te(2) 230 

661 

IAEA-SM -ПО/94 405 

Table IV (cont) 

Pa Pile neutron induced fission 

1.90 

0.080 

1 . 6 6 

1.18 

10 

15 

10 

15 

0.08 15 

(S) 1.42 17 1.42 17 

131 I 587 2.63 1.3 2.63 15 

132 Te 230 

587 

661 

133 

135 

Xe 

Xe 

140 Ba 

La 

587 

587 

230 

661 

587 

2.83 

3.46 

3.42 

5.21 

6.69 

6.25 

6.96 

7.18 

10 

1 

15 

1 

34 

10 

15 

1 

(S) 3.24 9 3.24 9 

5.21 

6.69 

15 

34 

(S) 6.80 5 6.80 8 

141 Ce 587 6 .8 8 1 6 .8 8 15 

143 Ce 230 

587 

661 

5.58 

5.12 

6 . 1 2 

10 

1 

15 

(S) 5.61 6 5.61 8 

144 Ce 587 4.79 3 4.79 15 

147 Nd . 587 

661 

1.89 

2.45 

2 

15 

149 Pm 587 0.95 3 

153 Sm 661 0.079 15 

(S) 2.17 13 2.17 13 

0.95 15 

0.079 15

406 CROUCH 

Table V 

I 

'Th Pile neutron induced fission 

1 2 3__________4___________________5________________ 6 

72 

73 

Zn 

Ga 

348 

326 

.000136 

.00035 

15 

50 

.000136 

.00035 

77 Ge( 2) 326 .009 22 .071 24 

As 228 .0106 0.5 (W) . 0 1 1 14 

326 .0172 35 (S) .014 24 

83 Br 228 1.98 7 (W) 1.98 7 1.98 9 

326 1.97 24 (S) 2.13 9 

348 2.51 15 

89 Sr 15 7.20 6 (W) 6.96 5 6.96 5 

326 6.70 10 (S) 6.73 4 

348 6.30 15 

90 Sr 15 7.55 6 (w) 7.24 3 7.24 4 

288 7.46 4 (S) 7.09 4 

326 7.24 20 

336 7.01 1 

348 6.18 15 

91 Sr 228 6.81 8 (w) 5.18 5 5.18 1 1 

326 7.34 1 1 (S) 6.14 1 1 

348 5.97 15 

Y 15 4.44 6 

93 Y 367 7.86 15 7.86 15 

95 Zr 228 5.30 6 5.30 6 

97 Zr 228 4.15 14 (W) 4.65 9 4.65 9 

326 5.03 15 (S) 4.77 7 

348 5.13 15 

99 Mo 2.78* 

103 Ru 228 0.149 5 (w) 0.149 4 0.15 6 

326 0.158 33 (S) 0.160 6 

348 0.188 15 

336 0.147 6 

105 Rh 228 0.031 5 (w) 0.072 14 0.072 14 

326 0.072 29 

348 0.073 15 

106 Ru 228 .0405 5 (w) .0425 5 .043 10 

326 .0435 10 (S) .0498 10 

336 .0612 15 

348 .054 15 

* Taken as reference point in all papers. 

15 

50


Table V (cont) 

232 

Th Pile neutron Induced fission 

1 2 3 4 5 6 

109 Pd 228 0.05 8 (W) 0.050 7 0.050 7 

326 0.051 20 (S) 0.051 4 

348 0.0492 15 

1 1 1 Ag 228 0.059 9 (W) 0.054 6 0.054 14 

326 0.047 20 (S) 0.058 14 

336 0 .0 8 1 15 

348 0.046 15 

1 1 2 Pd 228 0.055 9 (W) 0.057 7 0.057 14 

326 0.049 15 (S) 0.063 14 

348 0.061 15 

336 0.089 15 

113 Ag 228 0.045 7 0.045 7 

115 Cd( 1) 228 .00052 15 (w) 0.05 13 0.050 13 

Cd(2) 228 .0465 15 

348 0.055 15 

326 

(cfiain) 

0.0575 20 

117 In 228 0.048 1 1 0.048 1 1 

1 2 1 Sn 228 0.046 5 0.046 15 

123 Sn 228 0.0267 4 0.027 15 

125 Sn 228 0.037 8 0.037 15 

127 Sb 228 0.172 5 0.17 15 

131 I 228 1.57 4 (W) 1.27 5 1.27 22 

326 1.18 50 (s) 1.39 22 

336 2.14 15 

348 0 .6 8 15 

132 Te 326 2.24 29 (w) 1.76 14 1.76 15 

348 1 .6 8 15 

137 Cs 228 4.5 1 (w) 4.76 5 4.76 9 

326 6.44 15 (S) 5.90 9 

348 6.07 15 

336 6.59 15 

139 Ba 228 7.60 0.5 7.60 10

408 CROUCH 

Table V (cont) 

'Th Pile neutron induced fission 

1 2 3 4 5 6 

140 Ba 228 8.38 3 (W) 7.59 4 7.59 7 

326 6.14 32 (S ) 7.27 7 

348 5.76 15 

336 7.73 15 

15 6.94 8 

La 367 8.67 15 

141 Ce 15 6.59 5 (W) 7.60 3 7.60 6 

228 7.38 5 (S ) 7.24 6 

326 8.69 33 

336 7.26 15 

348 6.28 15 

143 Ce 367 7.12 15 (W) 6.81 4 6.81 4 

Pr 15 6.59 5 (S ) 6.91 3 

288 7.03 3 

144 Pr 228 6.98 0. 5 (W) 7.10 4 7.10 4 

Ce 15 7.15 5 (S ) 7.28 4 

326 6.93 14 

336 7.98 15 

348 6.49 15 

367 8 .14 15 

147 Nd 15 2.71 8 (W) 2.96 5 2.96 6 

228 3.08 5 (s) 3.01 6 

367 3.25 15 

149 Nd 367 1.57 15 (s) 1.22 30 1.22 30 

Pm 228 0.861 15 

151 Pm 367 0.46 15 0.46 15 

153 Sm 367 0.22 15 0.22 15 

156 Eu 228 0.0029 11 .0029 15

232u P ile 


Table 

Neutron 

VI 

induced f is s io n 

1 2 

3 4 5 

6 

85 K r( 1) 605 2.43 2 _ 

91 Y 605 7.43 2 7.43 15 

95 Z r 605 6.30 1 (W) 6.32 1 6.32 11 

Nb 605 6.36 2 (S ) 6.33 1 

97 Z r 605 4.98 1 (W) 4.99 1 4.99 11 

Nb 605 5.07 2 

99 Mo 605 4.22 2 (W) 4 .10 1 4.10 11 

Tc 605 4.08 1 

103 Ru 605 1.09 1 1.09 15 

131 I 605 4.13 1 4.13 15 

132 Te 605 4.77 1 (W) 4.80 1 4.80 11 

I 605 4 .84 1 

133 I 605 5.76 4 (W) 5.64 1 5.64 11 

Xe 605 5.63 0.5 

135 Xe 605 6.40 11 6.40 15 

137 Cs 605 8 .14 1 8 .14 15 

140 Ba 605 7.26 1 (W) 7.17 1 7.17 11 

La 605 7.04 1 

141 Ce 605 6.61 1 6.61 15 

143 Ce 605 4.68 1 4.68 15 

144 Ce 605 4.32 4 4.32 15 

147 Nd 605 1.15 2 1.15 15

410 CROUCH 

77 Ge 

As 

347 

347 

Table VII 

Thermal neutron induced fission 

0.00879 

0.0198 

15 

15 

78 (0 .0 4 ) 

79 (0 .0 8 ) 

80 (0 .1 7 ) 

0.02 15 

81 S e ( l) 85 0.0141 14 0.33 12 

Se(2) 85 0.325 12 

82 (0 .6 1 ) 

83 Se(2) 85 0.404 8 1.09 4 

Br 347 0.769 15 (W) 1.09 4 

Kr 74 1.18 4 (S ) 1.03 4 

209 1.16 1 

Chain 250 1.028 1 

84 K r 74 1.97 4 (W) 1.81 3 1.81 4 

209 1.93 5 (S ) 1.88 4 

Chain 250 1.73 1 

85 K r (2 ) 209 0.574 4 2.32 7 

590 0.512 2 

K r ( l ) 609 2.33 3 

Rb 74 2 ,54 4 (w) 2 32 3 

Chain 250 2.22 0.5 (S ) 2.38 7 

86 K r 74 3.30 4 (w) 3.06 3 3.06 4 

209 3.25 1 (S ) 3.15 4 

Chain 250 2.90 1 

87 Rb 74 4.61 4 (w) 4.18 3 4.18 7 

Chain 250 4.06 1 (S ) 4 .34 7 

88 Sr 17 5.30 6 (w) 5.47 2 5.47 2 

18 5 .30 6 (S ) 5.42 2 

74 5.54 4 

210 3.78 15 

220 5.38 3 

Chain 250 5.57 1 

89 Sr 32 6.91 2 (W) 6.12 3 6.12 5 

74 6.15 4 (S ) 6.06 5 

210 5.00 15 

309 5.56 3 

347 6.15 15 

Y 220 6.61 4


Tab le V I I (c o n t ) 

U Therm al neutron induced f is s io n 

1 2 3 4 5 6 

90 Sr 17 5.80 7 (W) 6.33 3 6.33 4 

18 5.80 7 (S ) 6.22 4 

28 4.56 2 

28 4.46 3 

74 6.75 4 

309 6.19 0 .5 

Zr 220 5.80 4 

Chain 250 6.96 1 

91 Sr 32 6.59 2 (w ) 6.56 2 6.56 2 

309 • 4.82 6 (S ) 6.56 1.5 

609 6.36 3 

Y 76 6.90 10 

309 3.55 2 

347 4.50 15 

Zr 74 6,45 4 

210 6.31 15 

220 6.74 3 

Chain 250 6.60 1 

92 Zr 74 6.72 4 (W) 6.66 3 6.66 3 

210 6.37 15 (S ) 6.58 2 

220 6.53 4 

Chain 250 6.69 1 

93 Zr 74 7.01 4 (W) 7.06 3 7.06 3 

210 6.88 15 (S ) 6.99 1 

Chain 250 7.09 1 

94 Zr 74 6.68 4 (W) 6.80 3 6.80 3 

210 6.92 15 ( s ) 6.80 1 

220 6.69 4 

Chain 250 6.91 1 

95 Zr 74 6.23 4 (W) 6.27 3 6.27 5 

309 5.01 12 (S ) 6.02 5 

347 6.26 15 

609 6.17 2 

Nb 309 5.16 12 

Mo 210 6.92 15 

Chain 250 6 .40 1 

96 Zr 94 5.67 4 (w) 5.78 3 5.78 3 

210 6.78 15 (S ) 6.00 2 

220 5.69 5 

Chain 250 5.84 1

412 CROUCH 

Table VII (cont) 

233 U Thermal neutron induced fission 

1 2 3 4 5 6 

97 Zr 609 5.73 2 (W) 5.57 3 5.57 5 

Nb 609 5.75 2 (S) 5.87 5 

Mo 74 5.51 4 

310 6.69 15 

Chain 250 5.82 1 

98 Mo 74 5.22 4 (W) 5.24 3 5.24 7 

2 1 0 6.27 15 (S) 5.57 7 

Chain 250 5.22 1 

99 Mo 76 4.80 10 (W) 5.08 3 5.08 3 

197 4.96 3 (S) 4.98 2 

347 5.16 15 

609 4.80 15 

Chain 250 5.16 1 

10 0 Mo 74 4.49 4 (W) 4.50 3 4.50 16 

2 1 0 6.96 15 (S) 5.30 16 

Chain 250 4.46 1 

10 1 Ru 74 2.87 4 (s) 3.10 3 3.10 3 

Chain 250 3.27 1 

102 Ru 74 2 . 1 0 4 (W) 2.31 3 2.31 3 

Chain 250 2.48 1 

103 Ru 43 1.71 6 (w) 1.61 4 1.61 15 

309 2 .0 2 4 (s) 1.35 15 

347 0.933 15 

609 1.52 2 

104 Ru 74 0.94 4 (W) 1 .0 0 3 1.00 3 

Chain 250 1.04 1 

105 (0.52) 

106 Ru 43 0.19 6 (w) 0.262 3 0.262 3 

309 0.26 12 

347 0.263 15 

Chain 250 0.262 1 

107 (0.105) 

108 (0.087) 

109 Pd 347 0.052 15 

110 

0.052 15 

(0.032)



U Thermal neutron Induced fission 

1 2 3 4 5 6 

1 1 1 Pd 25 0 .0 2 1 10 (W) 0.0203 7 0 .0 2 7 

Ag 309 0.0187 1 

347 0.0242 15 

1 1 2 Pd 309 0.0125 3 (W) .013 9 0.013 9 

347 0.0154 15 

113 (0.014) 

114 (0.015) 

115 Cd(l) 347 0 . 0 0 1 1 15 .019 15 

Cd(2) 347 0.0176 15 

( 1 1 0 (0.0154) 

117 Sn 246 0.0146 7 0.015 7 

118 Sn 246 0.0151 7 0.015 7 

119 Sn 246 0.0153 7 0.015 7 

120 Sn 246 0.017 7 0.017 7 

1 2 1 Sn(2) 347 0.0198 15 0 .0 2 15 

12 2 Sn 246 0.0189 6 0.019 6 

123 (0.024) 

124 Sn 246 0.0313 5 0.031 5 

125 Sn( 2) 347 0.0593 15 0.116 1 1 

Chain 250 0.116 1 1 

126 (0.262) 

127 Sb 309 0.59 14 0.59 15 

347 0 . 1 0 1 15 

Te 347 0.0736 15 

128 (1.04) 

129 (1.61) 

130 (2.40) 

131 I 309 2.84 7 3.51 2 

347 2.96 15 

Xe 74 3.52 4 (W) 3.51 2 

209 3.45 1 (S) 3.51 1 

Chain 250 3.51 1 

609 3.57 2

414 CROUCH 


U Thermal neutron Induced fission 

1 2 3 4 5 6 

132 Te 309 4.32 6 (W) 4.41 6 4.81 6 

347 5.38 15 

Xe 74 4.82 4 (W) 4.81 3 

Chain 250 4.88 1 (S) 4.41 6 

609 4.70 6 

133 I 309 3.37 9 (W) 5.85 2 5.88 2 

Xe 609 5.94 6 (S) 5.77 2 

Cs 16 5.20 6 

16 5.50 2 

72 5.60 3 

74 5.77 4 

209 5.74 15 

Chain 250 6.06 1 

381 5.85 15 

381 6 . 1 1 15 

381 5.85 15 

609 5.86 2 

134 Xe 74 6.18 4 (W) 6.14 3 6.14 3 

209 6.08 1 (S) 6.13 1 

Chain 250 6.13 1 

135 I 273 4.59 1 5.81 3 

Xe 72 6 .0 0 3 (W) 5.81 3 

74 6 .0 2 4 

609 5.40 1 

136 I 347 1.87 15 6.89 5 

Xe 74 6.89 4 

137 Cs 16 5.80 5 (W) 6 . 1 2 2 6.12 3 

16 5.16 3 (S) 6.25 3 

19 6.16 2 

43 8.32 6 

74 6.58 4 

209 6.58 2 

220 6.41 2 

309 5.39 2 

383 6.13 2 

Chain 250 6.93 3 

381 6.63 15 

381 6.58 15 

381 6.60 15



233 

U Thermal neutron induced fission 

1 2 3 4 5 6 

138 Chain 250 5.97 1 (W) 5.96 3 5.96 3 

381 5.74 15 

139 Ba 32 6.59 2 (S) 6 . 2 0 3 6 . 2 0 3 

609 6.13 2 

La 19 5.91 4 

220 6.15 4 

140 Ba 32 6.59 2 (W) 6.32 2 6.32 3 

276 6.59 1 (S) 6.16 3 

309 5.21 5 

609 6.07 2 

347 6.59 15 

La 609 6 .0 2 1 

Ce 16 5.45 9 

16 6.16 4 

74 6.72 4 

220 6.41 4 

290 5.60 3 

Chain 250 6.53 1 

141 La 32 7.24 2 (W) 6.16 3 6.16 6 

Ce 76 7.11 10 (S) 6.28 6 

309 5.30 2 

609 6.69 2 

Pr 19 5.57 3 

220 5.79 3 

142 Ce 16 5.50 9 (W) 6.61 2 6.61 4 

16 6.06 4 (S) 6.29 4 

74 7.00 4 

220 6.30 4 

290 5.60 3 

Chain 250 6.71 1 

381 6.83 15 

143 Ce 309 6.99 5 (w) 5.83 2 5.83 3 

609 5.67 2 (s) 5.81 3 

Pr 76 5.71 10 

Nd 16 5.00 6 

16 5.19 3 

72 6.45 3 

74 6 . 2 2 4 

220 5.40 3 

259 5.86 15 

290 5.15 6 

Chain 250 5.85 1 

381 5.98 15 

381 5.90 15 

381 5.90 15

416 CROUCH 



1 . 2 3 4 5 6 

144 Ce 76 4.48 10 (W) 4.52 2 4.52 4 

309 3.69 5 (S) 4.26 4 

347 3.75 15 

609 4.54 1 

Nd 16 3.80 10 

16 3.84 4 

74 4.87 4 

259 4.56 15 

290 3.37 9 

Chain 250 4.67 1 

381 4.62 15 

381 4.72 15 

381 4.51 15 

145 Nd 16 2.82 9 (W) 3.29 2 3.39 3 

16 2 .8 8 3 (S) 3.26 3 

74 3.66 4 

259 3.44 15 

290 3.00 7 

Chain 250 3.37 1 

381 3.40 15 

381 3.39 15 

381 3.39 15 

146 Nd 16 2 .2 0 7 (W) 2.46 2 2.46 3 

16 2.24 3 (s) 2.46 3 

74 2.74 4 

259 2.58 15 

290 2.34 6 

Chain 250 2.53 1 

381 2.52 15 

381 2.52 15 

381 2.51 15 

147 Nd 76 1.73 10 (W) 1.82 3 1.82 6 

609 1.75 2 (s) 1.84 6 

Pm 19 1.53 4 

72 2 . 1 0 3 

Sm 261 2.16 15 

Chain 250 1.78 2




1 2 3 4 5 6 

148 Nd 16 1.03 10 (W) 1.24 2 1.24 4 

16 1.07 4 (S) 1.23 4 

74 1.40 4 

259 1.31 15 

290 1.15 4 

Chain 250 1.30 1 

381 1.30 15 

381 1.27 15 

381 1.27 15 

149 Pm 76 0.74 10 (W) 0.773 3 0.773 3 

Sm 16 0 .6 6 20 (S) 0.748 3 

16 0.70 4 

72 0.30 3 

74 0.79 4 

261 0.77 15 

Chain 250 0.773 1 

150 Nd 16 0.51 16 (W) 0.503 2 0.503 2 

16 0.49 4 (S) 0.507 2 

74 0.57 4 

259 0.521 15 

290 0.51 8 

Chain 250 0.50 1 

381 .484 15 

381 .491 15 

381 .491 15 

151 Pm 76 0.36 10 (w) 0.338 3 0.338 3 

Sm 16 0.54 6 (s) 0.335 3 

19 0.33 9 

72 0.30 3 

74 0.33 4 

261 0.325 15 

Chain 250 0.365 3 

152 Sm 19 0 . 2 1 10 (w) 0.198 3 0.198 4 

74 0 .2 2 2 4 (s) 0.208 4 

261 0.214 15 

Chain 250 0.186 2 

153 Sm 76 0.099 10 (w) 0.0988 8 0.099 . 13 

347 0.0857 15 (s) 0.105 13 

Eu 19 0.13 15

418 CROUCH 



1 2 3 4 5 6 

154 Sm 74 0.048 4 (W) 0.046 3 0.046 3 

261 0.047 15 (s) 0.0469 2 

Chain 250 0.0458 1 

155 (0.0231) 

156 Eu 76 0.0114 10 0.0114 10 

157 Eu 76 0.00674 10 0.0067 10 

158 (.00235) 

159 Gd '76 .000908 10 .00091 10 

160 .00031 

161 Tb 76 .000115 10 .0 0 0 12 10


Table VIII 

235 


1 2 3 4 5 6 

72 Zn 345 .041539 15 _ •0415 15 

73 Ga 345 ,031026 15 - .0 , 1 0 15 

74 Ga 262 •033408 15 - .0334 15 

77 Ge 307 .0,2361 15 _ .0081 1 1 

345 .0,3799 15 - 

ÀS 307 .0,6882 15 (s) .0081 1 1 

345 .029348 15 

78 Ge 307 .01847 15 _ .0 2 0 1 1 

Ge 345 .02053 15 - 

As 307 .02053 15 *(s) .0 2 0 1 1 

As 345 .02053 15 

79 As 158 .05506 10 (S) .055 10 .055 10 

80 (0 .1 1 ) 

81 Se(l) 83 •027586 12 0 . 2 1 10 

Se(2) 83 .2094 10 

Se(l) 345 ,028218 15 - 

Se(2) 345 .1364 15 - 

82 (0.333) 

83 Se 83 .2174 10 (W) 0 .2 2 9 0.515 4 

345 .2165 15 

Se(m) 83 .3392 6 0.34 6 

Br 345 0.49 15 0.49 15 

Kr 29 0.5529 2 (W) 0.515 1 . 2 

344 0.5088 15 (S) 0.553 4 

Chain 251 0.4967 1 .,5 

84 Br 83 0.9283 6 0.931 4 0.959 7 

308 0.9349 7 

Br(ra) 308 0.1929 16 - 

Kr 29 1 . 0 1 1 2 (W) 0.9592 2 

344 1.130 15 (S) 1.024 7 

Chain 251 0.9297 2 

85 Kr 29 0.2977 2 (W) 0.286 1 1.30 3 

243 0.2727 3 (S) 0.296 5 

344 0.3292 15 

592 0.2843 1 .2 

Chain 251 1.297 1 1.297 1

420 CROUCH 

Table VIII (cont) 


1 2 3 4 5 6 

86 Kr 29 2.053 2 (W) 1.894 1 1.89 7 

344 2.17 15 (S) 2 . 0 1 7 

Chain 251 1.807 2 

87 Sr 569 1.167 2 1 2.64 5 

Br 306 . 3.217 5 

Chain 251 2.537 0.4 (S) 2.64 5 

Chain 404 2.75 15 

88 Sr 2 1 0 3.617 15 3.69 5 

Chain 251 3.607 0 .6 (W) 3.69 0 .6 

Chain 405 3.962 15 

* 

(S) 3.78 5 

89 Sr 34 4.752 5 (W) 4.774 1.4 4.77 1.4 

289 4.777 1.5 

210 4.779 15 

345 4.724 15 

90 Sr 4 5.607 4 (W) 5.888 1 5.89 1 1 

288 4.001 3 (S) 5.17 1 1 

Chain 251 5.897 0.7 

91 Sr 34 5.726 5 5.68 4 5.90 2 

289 5.097 2 

313 5.792 1 1 

345 5.136 15 

Y 75 6.208 10 (W) 5.887 0.5 

288 5.325 4 (S) 5.904 2 . 2 

345 6.060 15 

Zr 2 10 6.032 15 

Chain 251 '5.897 0.5 

92 Sr 345 5.136 15 (W) 5.95 0.5 5.95 1 

Zr 2 10 6.093 15 (S) 6 .0 2 1 

Chain 251 5.947 0.5 

93 Y 240 6.107 10 (W) 6.34 0 .6 6.34 3 

366 6.941 10 (S) 6.49 3 

Zr 2 10 6.578 15 

Chain 251 6.337 0 .6 

94 Y 345 5.136 15 6.41 2 

Zr 2 10 6.618 15 (w) 6.41 0 .6 

Chain 251 6.407 0 .6 (s) 6.51 1 . 6



2 3 5 


1 2 3 4 5 6 

95 Zr 345 6.164 15 (W) 6.45 0.5 6.45 2 

Mo 2 1 0 6.618 15 (S) 6.41 2 

Chain 251 6.447 0.5 

96 Zr 2 1 0 6.447 15 (W) 6.23 0 .6 6.23 2 

Chain 251 6.227 0 .6 (S) 6.35 2 

97 Zr 39 6 .2 0 8 3.5 (W) 5.87 0.5 5.87 2 .: 

40 6.084 2.7 (s) 6.07 2.5 

289 5.50 3.5 

313 4.775 1 . 1 

345 6.368 15 

Mo 2 10 6.396 15 

Chain 251 5.857 0.5 

98 Hb(m) 393 0.064 19 5.77 2 

Mo 2 10 5.992 15 (w) 5.77 0.5 

Chain 251 5.767 0.5 (s) 5.88 2 

99 Mo 198 6.25 3 (w) 6.14 0.85 6.14 0 .Í 

216 6.157 1.3 (S) 6.15 0 .8 0 

289 5.977 3.5 

316 6.137 2 . 6 

331 6.031 3.4 

345 6.368 15 

Chain 251 6.137 1 . 6 

100 Mo 2 10 6.648 15 (w) 6.24 0.5 6.24 3 

Chain 251 6.237 0.5 (S) 6.44 3.2 

1 0 1 Mo 331 5.519 4 (w) 5.05 0 .8 5.05 5 

Chain 251 5.027 0 .8 (s) 5.27 5 

102 Mo 331 4.19 1 (s) 4.19 1 4.19 1 

Chain 251 4.187 5 

103 Ru 41 2.963 6 (w) 3.03 3 3.03 6 

223 2.912 6 (S) 3.21 6 

331 1.429 15 

345 3.779 15 

363 3.149 4 

104 Mo 315 2.032 15 

Chain 251 1.817 0.6 

1.82 3

422 CROUCH 



1 2 3 4 5 6 

105 Ru 331 0.8485 36 (W) 0.96 4 0.96 4 

345 0.9245 15 

363 0.9654 4 

106 Ru 222 0.3828 8 (W) 0.39 1 0.39 12 

345 0.5341 15 (S) 0.44 12 

Chain 251 0.3887 1 

107 (0.166) 

108 (0.070) 

109 Pd 39 .02938 2 (W) 0.03 1.3 0.03 3 

40 .02998 2 (S) 0.029 3 

178 .02573 15 

345 0.2875 

11 0 (0.0195) 

1 1 1 Pd 24 0.01822 10 (W) 0.017 1 0.017 1.6 

Ag 39 0.01689 1 (S) 0.0177 1 . 6 

40 0.01746 2 

178 0.01781 15 

345 0.01847 15 

1 1 2 Pd 39 .008497 1 (W) .008527 0.5 0.008537 1 

40 .008597 1 (S) .008405 0.7 

178 .008319 15 

345 .008526 15 

363 0.01217 5 

113 (.0 0 8 6) 

114 (.0090) 

115 Cd 39 .008733 3 (W) .0,877 1.5 0.00952 14 

40 .008629 2 (s) .01123 14 

178 .0 18 8 0 15 

335 .009797 10 

345 .01128 15 

363 0.1015 6 

Cd(m) 335 . 0007097 10 (W) •03736 9 

345 . 0008218 15 

116 (.0097)

IAEA-SM -17 0/94 4 2 3 


2 3 5 


1 2 3 4 5 6 

117 Cd 345 0.01026 15 (w) 0 . 0 1 2 0 . 0 1 2 

Chain 361 0.009997 2 

118 Chain 361 0.00999 2 0 . 0 1 2 

119 Chain 361 0.011 2 0 . 0 1 1 2 

120 Chain 361 0.011 2 0 . 0 1 1 2 

1 2 1 Cd 337 .006397 8 .0111 4 

In(l) 337 .003197 15 

Sn(2) 175 .01225 2 (W) . 0 1 1 1 2 

345 .01436 15 (S) .01228 4 

363 .01217 8 

337 .01097 9 

Chain 391 .01197 8 

361 .01197 2 

12 2 Chain 361 .01297 2 .0130 2 

123 Sn( 1) 176 .01971 9 .0140 2 

Sn(2) 175 .001910 1.6 

345 .001231 15 

Chain 361 .01397 2 

124 Chain 361 .01697 2 .0170 2 

125 Sn( 1) 176 .0135 10 .0296 9 

Sn(2) 175 .01165 1 (W) .01156 1 

345 .01231 15 (s) .01204 2 

363 .01217 8 

Sb 27 .02258 5 (W) .02965 1 

175 .02926 2 (s) .02814 9 

345 .02361 15 

Chain 251 .02907 1 

361 .03597 2 

126 Sb(2) 27 .000890 6 0 . 1 0 2 

Chain 361 .09997 2 

127 Sn(2) 175 .0674 1.5 (w) .0675 1.5 0.25 2 

176 .0869 15 (s) .0771 13 

Sb 175 .1035 1 (w) .104 1 

178 .0921 15 (S) .108 10 

224 .1395 6 

345 .0966 15 

417 .394 10 

Te(l) 345 .00339 15 

Chain 361 .25 2

424 CROUCH 


235 

U Thermal Neutron induced fission 

1 2 3 4 5 6 

128 Sn(2) 175 .316 1.5 (S) 0.368 14 0.50 2 

176 .420 15 

Chain 361 0.50 2 

129 Sn(2) 31 .173 6 1 . 0 2 

Sb 31 .396 8 (S) .767 2 1 

175 .626 5 (w) .565 4 

224 1 . 1 2 15 

417 .926 7 

Te(l) 345 .195 15 

Chain 361 1.00 2 

130 Sb 283 2.58 1 2 2 .0 0 2 

Chain 361 2 .0 0 2 

131 Xe 29 2.91 2 (w) 2.85 1 2.85 1 

344 2.91 15 (s) 2 .8 8 1 . 1 

251 2.79 1.5 

361 2.93 2 .,0 

132 Xe 29 4.35 2 (W) 4.26 1 4.26 1 

344 4.33 15 (s) 4.31 1 

406 4.35 15 

Chain 251 4.16 1.,4 

361 4.38 2 .0 

133 Xe 233 6.62 33 (w) 6.72 0.5 6.72 0. 

255 6.63 0.,16(S) 6.64 0.5 

345 6.46 15 

Cs 70 6.59 3 

Chain 251 6.73 0 .,6 

361 6.62 2 

379 6.75 15 

379 6.75 15 

134 Xe 29 8 .0 0 2 (w) 7.76 1 7.76 1 

344 7.70 15 (s) 7.85 1.3 

406 7.96 15 

Chain 251 7.51 1.,5 

361 8.06 2 

135 Xe 70 6.41 3 (w) 6.39 3 

345 6.06 16 (S) 6.23 3 

Cs 279 6.51 10 (w) 6.45 2 6.45 2 

Chain 361 6.45 2 (s) 6.47 0.3 

Chain 403 6.46 10

1 2 

IAEA-SM -П О/94 425 



3 4 5 

136 Xe 29 6.41 2 (W) 6.54 1.4 6.54 2 

344 6.38 15 (S) 6.39 0 .6 

406 6.28 10 

Chain 361 6.47 2 

137 Cs 47 6.24 3 (W) 6.27 0.5 6.27 1 

279 6.24 10 (S) 6 . 2 1 0.4 

Chain 251 6.28 0 .5 

Chain 361 6.17 2 

379 6.19 10 

403 '6.13 10 

138 Cs 45 7.24 4 (W) 6.80 0.4 6.80 2 

Chain 251 6 .8 0 0 .4 (S) 6.91 2.5 

361 6 .6 8 2 

139 Ba 34 6.59 5 (W) 6 .44 1 . 6 6.44 2 

289 6.40 3. 5 (S) 6.47 0.7 

345 6.47 15 

La 215 8.34 10 

Chain 361 6.42 2 

140 Ba 154 6.36 4 (W) 6.32 0.4 6.32 0 

177 6.40 10 (S) 6.36 0.5 

216 6.55 1 .,5 

289 6.30 2 

345 6.34 15 

386 6.32 4 

La 366 6.62 10 

Ce 20 6.30 5 

151 6 . 2 0 10 

215 6.41 5 

Chain 251 6.31 0 .,5 

361 6.25 2 

141 La 34 6.32 5 (W) 5.70 0.5 5.70 3 

Ce 345 5.86 15 (S) 5.60 3 

Pr 20 5.60 5 

215 5.69 5 

Chain 251 5.50 6 

361 5.73 2 

142 Ce 2C 5.80 4 (W) 5.87 0.5 5.87 1 

151 5.91 1 (S) 5.85 0.5 

Chain 251 5.88 0 .5 

361 5.80 2 

6

426 CROUCH 

1 2 


235u Thermal neutron induced fission 

3 4 5 

143 Ce 313 5.89 4 (W) 5.89 1.5 5.89 2 

345 5.55 15 (S) 5.86 2 

366 5.91 10 

Pr 75 5.98 10 

Nd 20 5.80 4 

70 5.80 3 

151 5.91 1 

215 5.90 4 

251 5.90 0.51 

258 5.91 15 

343 5.91 15 

Chain 361 5.71 2 

379 5.96 15 - 

379 6.04 15 

379 5.98 15 

144 Nd 20 5.60 5 (W) 5.42 0.5 5.42 2 

151 5.32 2 (S) 5.38 1 . 2 

215 5.69 5 

251 5.42 0.4 

258 5.49 8 

343 5.08 15 

Chain 361 5.30 2 

379 5.30 15 

379 5.31 15 

379 5.33 15 

145 Nd 20 4.00 3 (W) 3.87 0.5 3.87 1 

151 3.90 1 (S) 3.92 0 .6 

215 4.07 3 

251 3.86 0.52 

258 3.93 0 . 2 

343 3.96 15 

Chain 361 3.80 15 

379 3.94 15 

379 3.91 15 

379 3.89 15 

146 Nd 20 3.20 15 (W) 2.95 0.5 2.95 2 

151 2.95 1 (S) 3.01 1.5 

215 3.25 15 

251 2.95 0.34 

258 2.98 0.4 

343 3.07 15 

Chain 361 2.89 2 

6



235 

Ü Thermal neutron induced fission 

1 2 3 4 5 6 

147 Pm 20 2.90 14 (W) 2.17 1 . 2 2.17 4 

70 2.38 3 (S) 2.44 4 

Nd 75 2.24 10 

345 2.67 15 

366 2.52 10 

Sm 151 2.24 1 

260 2.18 2 

Chain 215 2.95 14 

251 2 . 1 2 1.9 

361 2.16 2 

148 Nd 20 1.70 6 (W) 1 .6 8 8 0 .6 1.69 1 

151 1.67 1 (S) 1.67 1 

215 1.73 6 

258 1 . 6 6 2 

343 1.79 15 

Sm 215 1.52 20 

Chain 361 1.61 2 

379 1.67 15 

379 1.67 15 

379 1.67 15 

251 1.69 0 .6 

149 Pm 75 1.06 10 (W) 1 . 0 1 1 1 . 0 1 6 

215 1.52 20 (S) 1.19 6 

345 1.33 15 

Sm 20 1.5 2 

70 1.13 3 

151 1 . 1 0 1 

260 1.04 15 

Chain 361 1 . 0 2 2 

251 1 . 0 0 1 

150 Nd 20 0.70 14 (W) 0 .6 6 5 0.637 1 

258 0.65 1 (S) 0.69 3 

343 0.72 15 

Sm 151 0.65 2 (W) 0.637 1 

Chain 215 0.712 14 (S) 0.650 2 

361 0.628 2 

379 0.650 15 

379 0.633 15 

379 0.640 15 

251 0.638 0.63

428 CROUCH 

T a b l e V I I I ( c o n t ) 

Ü Thermal neutron Induced fission 

1 2 3 4 5 6 

151 Sm 20 0.45 3 (W) .410 2 0.410 2 

151 0.414 1 (S) .420 2 

260 0.414 15 

342 0.435 15 

Chain 361 0.399 2 

251 0.408 3 

152 Sm 151 0.266 1 (W) 0.234 2 0.234 5 

260 0.261 15 (S) 0.254 5 

342 0.272 15 

Chain 361 0.260 2 

251 0 .2 1 2 

153 Sm 75 0.161 10 (W) 0.149 4 0.150 3 

282 0.129 15 (S) 0.150 6 

345 0.154 15 

366 0.150 10 

Eu 151 0.163 3 (W) 0.150 2 

178 0.158 15 

Chain 361 0.148 2 

154 Sm 151 0.0738 1 (W) 0.0652 2 0.0652 8 

260 0.0707 15 (S) 0.0736 8 

342 0.0887 15 

Chain 361 0.0724 2 

251 0.0561 1 . 6 

155 Sm 345 .0318 15 .0294 5 

Eu 151 .0321 3 (W) 0.0294 2 

Chain 361 .0291 2 (S) 0.0306 5 

156 Sm 345 0.0123 15 0.015 2 

Eu 75 0.0139 10 (W) .0129 5 

170 0.0125 8 (S) .0131 3 

178 0.0138 15 

282 0.0119 15 

345 0.0133 15 

Chain 361 0.0150 2 

157 Eu 75 .00620 10 (W) .00677 2 .00677 6 

170 .00600 2 (S) .00670 6 

345 .00760 15 

Chain 361 .00700 2

IA E A -SM -nO /94 



1 2 3 4 5 6 

158 Eu 170 .00310 20 (W) .0 0 2 0 0 2 .00200 15 

345 .00205 15 (S) .00238 15 

Chain 361 .0 0 2 0 0 2 

159 Eu 170 .0 0 1 1 0 30 .00101 3 

Gd 75 .00104 10 (W) .0 0 1 0 1 2 

183 .00113 1 1 (S) .00105 3 

282 .00104 15 

Chain 361 .0 0 10 0 2 

160 - 

161 Tb 75 .О4 8ЗЗ 10 (W) .О4 8ОЗ 7 .О4 8ОЗ 7 

183 .04824 10 (S) .04793 5 

282 .04720 15 

162 

163 

- 

164 

- 

165 

- 

166 Dy 265 .07632 50 .07632 50 

429

1 

83 

89 

91 

97 

99 

103 

105 

106 

109 

111 

112 

113 

115 

121 

125 

127 

CROUCH 

Table IX 

237 Np Pile neutrons induced fission 

2 3_________4______________5 6 

Br 662 0.265 15 (S) .317 17 0.317 17 

231 0.368 15 

Sr 662 2.04 15 (S) 2.27 11 2.27 11 

231 2.49 15 

Sr 662 4.04 15' (W) 4.0 11 4.0 11 

231 3.95 15 (S) 4.0 2 

Zr 662 6.95 15 6.95 15 

Mo 662 6.98 15 (W) 6.85 11 6.85 11 

231 6.71 15 

Ru 662 4.0 15 (W) 4.34 11 4.34 11 

231 4.68 15 (S) 4.34 8 

Ru 662 2.75 15 (W) 2.83 11 2.83 11 

Rh 231 2.90 15 (S) 2.83 3 

Ru 662 1.56 15 (W) 1.68 11 1.68 11 

231 1.79 15 

Pd(2) 662 0.30 15 (W) 0.34 11 0.34 11 

231 0.38 15 (S) 0.34 12 

Ag 662 0.085 15 (W) .092 11 0.092 11 

231 0.099 15 (S) .092 8 

Pd 662 0.072 15 (W) 0.059 11 0.059 22 

231 0.046 15 (S) 0.059 22 

Ag(2) 662 0.045 15 (W) 0.044 11 0.044 11 

231 0.042 15 

Cd 662 0.041 15 (W) 0.046 11 0.046 11 

231 0.051 15 

Su(2) 661 0.047 15 (W) 0.049 11 0.049 11 

231 0.051 15 

Su(2) 662 0.126 15 (W) 0.111 11 0.11 15 

231 0.094 15 (S) 0.11 15 

Sb 662 0.916 15 (S) 0.94 11 0.94 11 

231 0.97 15

237M Np 


Table IX (cont) 

Pile neutrons induced fission 

1 2 3 4 5 6 

129 Te 662 

231 

132 Te 662 

231 

140 Ba 662 

231 

141 Ce 662 

231 

144 Ce 662 

231 

2.60 

2.72 

6.33 

4.33 

5.30 

5.35 

4.97 

3.46 

4.31 

2.31 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

147 Nd 662 2.35 15 

156 Eu 662 0.09 15 

(W) 2 .6 6 1 1 2 .6 6 1 1 

(S) 5.33 19 5.33 19 

(S) 5.33 1 1 5.33 1 1 

(S) 4.22 18 4.22 18 

(S) 3.31 30 3.31 30 

2.35 15 

0.09 15

432 CROUCH 

Table X 

239 Pu Thennal neutron induced fission 

1 2 3 4 5 6 

72 Zn 346 .000113 15 .0 0 0 1 1 15 

73 (.00026) 

74 (.00059) 

75 (.0013) 

76 (.003) 

77 As 159 .0071 5 .0071 10 

78 As 159 .0256 5 .026 10 

79 (.036) 

80 

(.08) 

81 Se( 1) 87 0.0045 32 0.182 10 

87 0.182 8 

82 (0.24) 

83 Se(l) 87 0.149 15 0.295 3 

Se(2) 87 0.169 15 

Br 87 0.309 15 (W) .295 3 

159 0.291 8 (S) .294 2 

Kr 181 0.277 4 

196 0.290 4 

Chain 252 0.301 2 

84 Br(2) 87 0.415 10 0.478 4 

Kr 181 0.449 4 (W) .478 2 

Chain 252 0.487 2 (S) .468 4 

85 Kr( 1) 610 0.640 3 0.559 6 

Kr(2) 244 0.099 5 (w) .1 2 0 2 

592 0.128 2 (S) .114 13 

Rb 281 .512 4 (w) .559 2 

Chain 252 0.574 2 (s) .543 6 

86 Chain 252 0.77 2 0.77 10 

87 Rb 181 0.872 4 (w) 0.968 2 0.968 7 

Chain 252 1 .0 0 2 (s) 0.936 7 

88 Sr 2 1 1.39 3 (w) 1.36 2 1.36 7 

181 1.37 4 (S) 1.28 7 

237 1 .0 2 15 

Chain 252 1.35 2 

89 Sr 33 1 . 6 6 2 (w) 1.67 3 1.67 3 

181 1.63 4 (s) 1.72 3 

263 1.74 3 

346 1.85 15


Table X (cont) 

Pu Thermal neutron induced fission 

1 2 3 4 5 6 

90 Sr 2 1 2.31 2 (W) 2.09 2 2.09 5 

181 2.07 4 (s) 2.05 5 

237 1.72 15 

263 2.05 2 

Chain 252 2.09 2 

91 Sr 33 2.37 , 2 (W) 2.47 2 2.47 4 

346 2.36 15 (s) 2.43 4 

610 2.03 3 

Y 263 2.41 5 

601 2.42 1 

346 2 .8 8 15 

Zr 181 2.48 4 

Chain 252 2.52 2 

92 Zr 181 2.98 4 (w) 3.01 2 3.01 2 

Chain 252 3.02 2 

93 Zr 181 3.77 4 (w) 3.91 2 3.91 2 

Chain 282 3.95 2 (s) 3.86 2 

94 Zr 181 4.26 4 (w) 4.45 2 4.45 2 

Chain 252 4.50 2 

95 Zr 263 5.06 7 (w) 4.90 3 4.90 5 

346 5.76 15 (s) 5.11 5 

610 4.74 3 

Chain 252 4.86 2 

96 Zr 181 4.91 4 (w) 5.08 2 5.08 2 

Chain 252 5.12 2 (S) 5.02 ' 2 

97 Zr 346 5.45 15 (w) 5.54 3 5.54 3 

Mo 181 5.37 4 (S) 5.51 3 

Chain 252 5.64 3 

98 Nb(2) 396 0 .2 0 15 5.59 10 

Mo 181 5.59 4 

99 Mo 199 6 .0 2 3 (w) 6 .2 0 2 6.20 3 

263 5.61 6 (s) 6.30 3 

346 6.27 15 

688 6.17 3 

682 6.79 2 

682 6 .6 6 1 

Chain 252 6.59 3

434 CROUCH 


239 Pu Thermal neutron induced fission 

1 2 3 4 5 6 

10 0 Mo 181 6.74 4 6.74 10 

10 1 Ru 181 5.60 4 (W) 5.95 3 6.05 8 

Chain 252 6.50 4 (S) 6.05 8 

102 Ru 181 5.68 4 (W) 6 .0 0 3 6 .0 0 7 

Chain 252 6.65 4 (S) 6.09 7 

103 Ru 181 5.38 4 (W) 5.51 4 5.51 7 

346 5.63 15 (S) 5.89 7 

610 6.65 7 

104 Ru 181 5.62 4 (W) 5.99 3 5.99 9 

Chain 252 6.61 4 (S) 6 . 1 2 9 

105 Rh(2) 263 5.47 1 5.47 10 

346 3.80 15 

106 Ru 181 4.33 4 (W) 4.34 3 4.34 4 

263 4.04 5 (S) 4.43 4 

346 4.83 15 

Chain 252 4.55 4 

107 (2.70) 

108 (1.70) 

109 Pd 204 1.94 2 1 .0 8 5 

263 1.13 5 (S) 1.08 5 

346 1.03 15 

1 1 0 (0.53) 

1 1 1 Ag 204 0.265 2 (w) .267 5 0.267 5 

263 0.280 14 (S) .274 2 

. 346 0.277 15 

1 1 2 Pd 204 0.094 2 (w) 0.094 4 0.094 4 

263 0.093 3 (S) 0.097 4 

346 0.103 15 

113 Ag 159 0.065 15 

114 

0.065 15 

(0.052)




i_____ 2 . 3_________ 4________________ 5______________ L 

115 Cd( 1) 263 0.003 20 (W) .0371 4 0.0371 1 1 

346 0.00308 15 (s) .0408 1 1 

Cd(2) 204 .034 2 

263 0.033 6 

346 0.0462 15 

116 (0.038) 

117 (0.039) 

118 (0.039) 

119 (0.040) 

120 (0.042) 

1 2 1 Sn(2) 346 0.0421 15 0.0421 15 

122 (0.049) 

123 (0.058) 

124 (0.078) 

125 Sn(2) 346 0.0699 15 0.116 12 

Chain 252 0.116 12 

126 (0.24) 

127 Sb 263 0.55 6 (W) .513 5 .513 20 

346 0.38 15 (s) .415 20 

128 (0.83) 

129 (0.38) 

130 (2.30) 

131 I 263 3.80 4 (w) 3.69 2 3.69 2 

346 3.70 15 (s) 3.74 2 

610 3.96 3 

Xe 182 3.60 1 

196 3.78 2 

Chain 180 3.71 3 

252 3.60 3 

132 Te 263 5.51 5 (W) 5.35 5 5.11 3 

346 5.04 15 (S) 5.17 4 

610 4.97 2 

Xe 182 5.02 1 (w) 5.11 3 

Chain 180 5.26 3 (s) 5.12 2 

252 5.09 1

436 CROUCH 

T a b le X ( c o n t ) 

Pu T h e r m a l n e u t r o n I n d u c e d f i s s i o n 

1 2 3 4 5 6 

133 I 263 5.53 1 (W) 6.76 4 6.76 5 

346 5.14 15 (S) 6.37 5 

610 6.70 2 

Xe(2) 610 6.93 2 

Cs 2 1 5.26 3 

71 6.92 3 

Chain 180 6.90 4 

252 7.18 2 

380 6.80 15 

134 Xe 182 7.13 1 (W) 7.24 3 7.24 3 

Chain 180 7.46 3 (S) 7.26 2 

252 7.20 2 

135 I 274 6.89 2 (w) 6.71 5 7.08 4 

346 5.65 15 (S) 6.27 10 

Xe 69 7.11 44 (W) 7.08 3 

71 7.27 3 (S) 6.77 4 

610 6.67 3 

Cs 2 1 6.95 3 

236 6.95 10 

398 5.22 15 

Chain 180 7.25 3 

136 I 346 1.95 15 6.33 10 

Xe 182 6.37 1 (w) 6.33 4 

398 4.77 15 (S) 5.92 10 

Chain 180 6.62 3 

137 Cs 2 1 6.50 3 (W) 6.48 3 6.48 6 

263 5.40 7 (S) 6.14 6 

398 4.94 15 

Chain 180 6.48 3 

252 6.74 2 

380 6.72 15 

138 Ba 2 1 6.26 3 (w) 5.71 3 5.71 5 

Chain 180 6.31 3 (S) 5.99 5 

252 5.40 2 

139 Ba 33 5.89 2 (w) 5.77 5 5.77 5 

346 5.55 15 (s) 5.64 3 

610 5.47 2

IA EA - S M - 1 7 0 /9 4 437 


I 


I 2 3 4 5 6 

140 Ba 13 5.31 3 (W) 5.57 2 5.57 5 

33 5.51 2 (S) 5.60 5 

263 5 47 6 

277 4.55 2 

346 5.51 15 

610 5.29 3 

Ce 21 5.52 3 

398 7.36 15 

Chain 180 5.88 3 

252 5.61 2 

141 La 33 5.56 2 (w) 5.78 3 5.78 4 

603 4.62 3 (S) 5.37 4 

Ce 263 6.11 5 

346 5.04 15 

601 5.00 2 

610 5.27 2 

Pr 21 6.02 3 

142 La 610 5.24 4 (w) 5.05 3 5.05 6 

Ce 21 6.66 3 (s) 5.58 6 

398 6.62 15 

Chain 180 4.97 3 

252 5.04 2 

380 4.93 15 

143 Ce 263 4.28 5 (W) 4.42 2 4.42 5 

346 5.24 15 (S) 4.70 5 

603 3.94 3 

610 4.00 8 

Pr 601 4.17 2 

Nd 21 6.10 3 

71 4.49 3 

398 5.98 15 

Chain 180 4.56 3 

252 4.48 2 

380 4.51 15 

144 Ce 263 4.09 5 (W) 3.85 3 3.85 6 

341 3.11 15 (S) 4.05 6 

346 3.80 15 

610 3.61 2 

Nd 21 5.50 3 

398 5.00 15 

Chain 180 3.84 3 

252 3.78 2 

380 3.77 15

438 C R O U C H 

T a b le X ( c o n t ) 

Pu T h e r m a l n e u t r o n in d u c e d f i s s i o n 

1 2 3 4 5 6 

145 Pr 603 3.48 2 (W) 3.14 3 3.14 6 

Nd 21 4.2 3 (S) 3.49 6 

398 4.07 15 

Chain 180 3.12 3 

252 3.03 2 

380 3.04 15 

146 Nd 21 3.53 3 (W) 2.52 3 2.52 8 

398 3.36 15 (S) 2.89 8 

Chain 180 2.57 3 

252 2.49 2 

380 2.49 15 

147 Nd 263 1.46 6 (W) 2.07 2 2.07 6 

341 1.84 15 (S) 2.12 6 

601 2.10 2 

610 1.92 4 

Sm 235 1.97 3 

398 2.81 15 

Pm 21 2.58 2 

71 2.07 3 

601 2.11 4 

Chain 180 2.00 3 

252 2.15 2 

148 Nd 21 2.30 2 (W) 1.71 3 1.71 5 

398 2.27 15 (S) 1.93 5 

Chain 180 1.71. 3 

252 1.70 1 

380 1.67 15 

149 Nd 603 1.13 4 (w) 1.24 2 1.24 7 

Pm 341 1.11 15 (S) 1.36 7 

603 1.28 2 

Sm 21 1.67 1 

71 1.32 3 

398 1.81 15 

Chain 180 1.30 3 

252 1.24 3 

150 Nd 21 1.35 2 (W) 0.97 3 0.97 3 

398 1.31 15 (s) 0.98 2 

Chain 180 1.02 3 

252 0.965 2 

380 0.96 15

IAEA-SM -170/94 4 3 9 


239 


1 2 3 4 5 6 

151 Pm 603 0.724 3 (W) .791 2 .791 6 

Sm 21 1.01 2 (S) .867 6 

71 0.79 3 

235 0.821 2 

398 1.10 15 

Chain 180 0.802 3 

252 0.821 6 

152 Sm 21 0.75 2 (W) .575 3 .575 10 

235 0.538 3 (S) .673 10 

Chain 180 

252 

153 Sm 341 

346 

603 

398 0.88 15 

0.616 

0.581 

0.368 

0.401 

0.167 

3 

5 

15 

15 

4 

(W) 0.385 10 0.385 10 

154 Sm 21 0.36 3 (W) 0.255 3 0.26 12 

235 0.208 2 (S) .306 1 

Chain 180 

252 

398 0.40 15 

0.293 

0.27 

3 

2 

155 Sm 346 0.216 15 0.216 15 

156 Sm 603 0.094 3 (W) 0.086 3 .086 12 

Eu 263 .062 7 (S) .101 12 

341 .102 15 

346 .124 15 

601 .122 2 

157 Eu 603 .075 3 .075 15 

158 (0.04) 

159 Gd 341 

603 

.02 

.0213 

15 

1 

(W) .021 10 .021 10 

160 (0.01) 

161 Tb 341 .00406 15 (W) .00466 9 .0047 12 

603 .00507 2 ( s ) .00457 12 

162 

163 

164 

165 

166 D y 341 .000068 15 

(.0022) 

(.00106) 

(.00042) 

(.00017) 

.000068 V.

440 C R O U C H 

Table XI 


1 2 3 4 5 6 

77 As 104 .000445 7 .00045 15 

78 As 104 .00858 6 .0086 15 

79 (.018) 

80 (.034) 

81 (.063) 

82 (.105) 

83 Br 104 0.204 5 (W) .201 3 .201 3 

Chain 253 0.20 3 (S) .202 1 

84 Br(2) 104 .343 4 (W) .353 3 .353 5 

Chain 253 .353 3 (S) .348 5 

85 Kr(2) 593 .086 4 .387 10 

Chain 253 .387 3 

86 Chain 253 .601 3 .601 10 

87 Chain 253 0.741 3 .741 10 

88 Chain 253 .954 3 .954 10 

89 (1.19) 

90 Chain 253 1.53 3 1.53 10 

91 Y 602 1.66 2 (W) 1.76 3 1.76 5 

Chain 253 1.82 3 (S) 1.74 5 

92 Chain 253 2.23 3 2.23 10 

93 Chain 253 2.90 3 2.90 10 

94 Chain 253 3.33 3 3.33 10 

95 Zr 104 4.19 4 (W) 3.99 3 4.00 4 

Chain 253 3.92 3 (S) 4.06 

96 Chain 253 4.33 3 4.33 10 

97 Zr 104 4.72 5 (W) 4.75 3 4.75 3 

Chain 253 4.76 3 (S) 4.74 1 

98 (5.5) 

99 Mo 104 6.04 4 (W) 6.14 3 6.14 3 

688 6.15 3 (S) 6.12 1 

Chain 253 6.17 3

1 

100 

101 

102 

103 

104 

105 

106 

107 

108 

109 

110 

111 

112 

113 

114 

115 

116 

117 

118 

119 

120 

121 

122 

123 

124 

125 

126 

127 

128 

129 

130 

131 

132 

133 

134 

I A E A - S M -1 7 0 /9 4 441 

Table XI (cont) 

241 Pu Thermal neutron induced fission 

Chain 253 5.94 

Chain 253 6.32 

Chain 253 6.80 5 

Chain 253 6.08 4 

A g 

A g 

104 0.485 

104 0.147 

Chain 253 0.0416 12 

Chain 212 3.00 15 

253 3.15 3 

Chain 212 4.47 15 

253 4.64 3 

(W) 3.14 3 

(S) 3.08 3 

(W) 4.59 

(S) 4.55 

Chain 212 6.56 15 (W) 6.64 3 

253 6.71 3 (S) 6.59 1 

382 6.52 15 

Chain 212 7.80 

253 8.06 

15 

3 

(W) 7.99 

(S) 7.93 

(6 .0 ) 

5.94 

6.32 

(6 .60) 

6.80 

(6.60) 

6.08 

(5.15) 

(4.15) 

(2.9) 

(1.4) 

0.49 

(0.32) 

0.147 

(0.065) 

(0.037) 

(0.033) 

(0.031) 

(0.030) 

(0.029) 

(0.029 

(0.030) 

(0.031) 

(0.032) 

(0.036) 

0.042 

(0 .1 ) 

(0 .21) 

(0.41) 

(0.82) 

(1.65) 

3.14 

4.59 

6.64 

7.99 

10 

10 

10 

10 

15 

15 

15

442 CROUCH 

T a b l e X I ( c o n t ) 

Pu Thermal neutron Induced fission 

1 2 3 4 5 6 

135 I 275 6.93 3 7.08 5 

Chain 212 7.08 • 15 

136 Chain 212 7.04 15 7.04 5 

137 Cs 104 6.62 15 (W) 6.52 3 6.52 3 

Chain 212 6.62 15 (S) 6.49 2 

253 6.60 3 

382 6.14 15 

138 Cs 104 6.82 4 (W) 6.54 3 6.54 3 

Chain 212 6.82 15 (S) 6.67 3 

253 6.37 3 

139 (6.30) 

140 Ba 278 6.28 7 (W) 5.83 3 5.83 3 

688 5.64 2 (S) 5.89 3 

Chain 212 5.78 15 

253 5.86 3 

141 La 604 4.49 2 (w) 4.78 2 4.78 3 

Ce 104 5.14 4 (s) 4.81 3 

602 4.74 2 

688 4.81 3 

Chain 212 4.8 4 15 

142 Chain 212 4.70 15 (W) 4.77 3 4.77 3 

253 4.80 3 (S) 4.75 2 

143 Ce 104 4.68 5 ( w) 4.40 2 4.40 3 

604 3.89 2 (S) 4.36 3 

Pr 602 4.29 1 

Chain 212 4.43 15 

253 4.48 3 

382 4.38 15 

144 Ce 688 4.08 4 (W) 4.09 2 4.09 2 

Chain 212 4.07 15 (S) 4.09 1 

253 4.13 3 

382 4.08 15

I A E A - S M -1 7 0 /9 4 443 

Table XI (cont) 

241 


1 2 3 4 5 6 

145 Pr 604 3.01 3 (W) 3.14 2 3.14 2 

Chain 212 3.16 15 (S) 3.12 2 

253 3.19 3 

282 3.11 15 

146 Chain 212 2.71 15 (W) 2.65 2 2.65 2 

253 2.68 3 (s) 2.66 2 

382 2.60 15 

147 Nd 602 2.34 2 (W) 2.26 3 2.26 3 

Pm 602 2.33 4 (S) 2.30 2 

Chain 212 2.32 15 

253 2.22 3 

148 Chain 212 1.91 15 (W) 1.87 2 1.87 2 

253 1.89 3 (S) 1.88 2 

382 1.84 15 

149 Nd 604 1.47 3 (W) 1.47 3 1.47 3 

Pm 604 1.51 4 (S) 1.49 2 

Chain 212 1.55 15 

253 1.43 3 

150 Chain 212 1.23 15 (W) 1.14 2 1.16 4 

253 1.16 3 (S) 1.16 4 

382 1.10 15 

151 Pm 604 0.846 5 (S) 0.903 6 0.903 6 

Chain 212 0.959 15 

152 Chain 212 0.757 15 (S) 0.741 4 0.741 4 

253 0.725 5 

153 Chain 212 0.559 15 (W) 0.5 4 4 0.54 4 

604 0.519 3 

154 Chain 212 0.408 15 (W) 0.379 3 0.379 5 

253 0.37 3 (S) 0.389 5 

155 Eu 602 0.231 9 0.231 9 

156 Sm 604 0.158 3 

Eu 602 0.17 2 

0.17 5

4 4 4 CRO U CH 

T a b l e X I ( c o n t ) 

Pu T h e r m a l n e u t r o n i n d u c e d f i s s i o n 

157 Eu 604 0.13 3 0.13 5 

158 (0.086) 

159 Bd 604 0.0462 2 0.0462 5 

160 (0.024) 

161 Tb 604 0.00814 2 0.00814 5 

Table XII 

241л Am Pile neutron induced fission 

1 2 3 4 5 6 

89 Sr 80 0.81 6 (W) 0.89 6 0.89 20 

301 1.20 8 (S) 1.00 20 

91 Y 80 1.16 3 (W) 1.47 5 1.47 14 

Sr 301 1.90 3 (S) 1.51 14 

Sr 637 1.48 2 

92 Sr 301 2.30 5 (W) 2.20 4 2.20 5 

637 2.09 2 (S) 2.70 5 

93 Y 301 3.00 7 3.00 7 

95 Zr 80 3.90 13 (W) 3.13 4 3.13 12 

301 2.70 4 (S) 3.55 12 

637 4.04 5 

97 Zr 80 3.55 13 (w) 4.47 7 4.47 19 

637 5.16 8 (S) 4.36 19 

99 Mo 80 6.85 6 (w) 6.64 4 6.64 4 

301 6.30 3 (S) 6.68 3 

637 6.90 4 

103 Ru 301 7.70 3 (w) 7.68 4 7.68 4 

637 7.65 3 

111 Ag 80 0.89 6 (W) 0.275 4 0.28 38 

301 0.22 15 (S) 0.76 38 

637 1.19 3 

113 Ag 80 0.18 6 (S) 0.36 47 0.36 47 

638 0.49 2 

115 Cd( 2) 80 0.046 7 (W) 0.050 6 0.05 24 

638 0.075 11 (s) 0.061 24 

121 Sn(2) 80 0.045 13 

127 Sb 638 0.66 5 0.66 10 

129 Sb 638 1.32 4 1.32 10 

131 I 80 3.71 5 (S) 2.89 17 2.89 17 

301 2.1 5 

638 2.87 4

1 2 

I A E A - S M -1 7 0 /9 4 445 

Table XII (cont) 

241 Am Pile neutron induced fission 

3 4 5 

132 Te 80 4.48 7 (W) 3 .70 4 3.70 10 

638 3.37 1 (S) 3.92 10 

I 301 3.9 8 

133 I 301 4.0 0 5 (W) 4.67 4 4.67 15 

638 5.34 4 (S) 4.67 15 

135 I 301 4.5 0 6 (W) 4.63 4 4.63 4 

I 638 4.36 5 (S) 4.68 4 

Xe 638 4.87 4 

137 Cs 80 9.20 20 (W) 6.22 13 6.22 25 

301 5.60 15 (S) 7.40 25 

138 Cs 301 6.40 6 (w) 7.25 5 7.25 14 

638 8.48 6 (S) 7.44 14 

139 Cs 80 6.22 5 (w) 7.45 4 7.45 17 

638 8.68 3 (S) 7.45 17 

140 Ba 80 6.0 6 (w) 5.53 4 5.53 5 

301 5.2 2 (S) 5.61 5 

638 5.63 2 

141 Ce 80 5.04 13 (W) 4.63 4 4.67 4 

301 4 .70 2 (s) 4.75 4 

638 4.51 5 

143 Ce 301 3.40 3 (w) 2.83 4 2.83 10 

638 2.49 4 (S) 3.07 10 

Pr 80 3.32 14 

144 Ce 80 3.15 13 (W) 3.19 6 3.19 6 

301 3.20 6 

147 Nd 80 2.06 16 (W) 1.42 10 1.42 23 

638 1.30 11 (s) 1.68 23 

153 Sm 80 0.76 16 0.76 16 

6

1 

83 

84 

89 

90 

91 

92 

93 

95 

97 

99 

103 

109 

111 

112 

115 

121 

125 

131 

132 

133 

134 

135 

137 

139 

140 

141 

143 

144 

147 

149 

151 

153 

156 

157 

CROUCH 

Table X III 

Am Fission induced by thermal neutrons 

2 3 4 5 6 

Br 575 0.234 8 0.23 10 

Br(2) 575 0.364 8 0.36 10 

Sr 575 1.18 7 1.18 10 

Sr 575 1.41 7 1.41 10 

Y(2) 575 1.73 7 1.73 10 

Sr 975 2.05 8 2.05 10 

Y 575 2.56 8 2.56 10 

Zr 575 3.23 6 3.23 10 

Zr 575 4.21 7 4.21 10 

Mo 575 5.36 7 5.36 10 

Ru 575 6.95 7 6.95 10 

Pd 575 3.29 9 3.29 15 

Ag(2) 575 1.32 7 1.32 10 

Ag 575 0.-42 8 0.42 10 

Cd(1) 575 0.0047 8 0.071 10 

Cd(2) 575 0.066 8 

Chain 575 0.071 8 

Sn(2) 575 0.017 8 0.017 10 

Sn(2) 575 0.0843 10 0.11 15 

Sb 575 0.111 12 

I 575 3.12 6 3.12 10 

Te 575 4.78 6 4.78 10 

I 575 5.82 7 5.82 10 

I 575 5.95 7 5.95 10 

I 575 6.49 8 6.49 10 

Cs 575 5.84 12 5.84 15 

Ba 575 5.55 7 5.55 10 

Ba 575 5.40 7 5.40 10 

Ce 575 4.94 8 4.94 10 

Ce 575 4.23 7 4.23 10 

Ce 575 3.55 8 3.55 10 

Nd 575 2.32 8 2.32 10 

Pm 575 1.61 8 1.61 10 

Pm 575 1.13 8 1.13 10 

Sm 575 0.73 8 0.73 10 

Eu 575 0.313 7 0.31 10 

Eu 575 0.164 9 0.16 10 

Tb 575 0.0181 8 0.018 10

I A E A - S M -1 7 0 /9 4 447 

Table XXV 

Cm Thermal neutron induced fission 

1 2 3 4 5 6 

77 As 628 0.0048 24 .0048 24 

83 Br 628 0.0229 22 .023 22 

89 Sr 628 0.836 12 0.8 4 12 

90 Sr 628 1.086 14 1.09 14 

91 Y 628 1.21 24 1.21 24 

95 Zr 628 2.47 13 2.47 13 

97 Zr 628 3.05 11 3.05 11 

99 Mo 628 4.18 10 4.18 10 

103 Ru 628 6.25 14 6.25 14 

105 Ru 628 6.10 21 6.10 21 

106 Ru 628 5.83 24 5.83 24 

109 Pd 628 5.16 12 5.16 12 

111 Ag 628 3.21 19 3.21 19 

112 Pd 628 1.35 25 1.35 25 

113 Ag 628 1.72 25 1.72 25 

115 Chain 628 0 .4 0 17 0.40 17 

121 Sn(2) 628 0.036 26 0.036 26 

123 Sn 628 0.057 22 0.057 22 

125 Sn(2) 628 0.053 25 0.091 21 

Sb 628 0.091 21 

127 Sb 628 1.083 16 1.08 16 

129 Sb 628 1.76 21 1.76 21 

Te(l) 628 0.81 14 

131 I 628 2.89 13 2.89 13 

132 Te 628 3.95 18 3.95 18 

133 I 628 5.79 12 5.79 12 

137 Cs 628 7.96 8 7.96 8 

140 Ba 628 5.61 12 5.61 12 

141 Ce 628 4.58 13 4.58 13 

143 Ce 628 3.77 16 3.77 16 

144 Ce 628 2.90 21 2.90 21 

147 Nd 628 2.57 19 2.57 19 

149 Pm 628 1.95 20 1.95 20 

151 Pm 628 1.23 26 1.23 26 

153 Sm 628 1.12 25 1.12 25 

156 Eu 628 0.27 24 0.27 24

1 

89 

95 

97 

99 

103 

106 

109 

111 

112 

113 

115 

121 

125 

127 

129 

131 

132 

133 

137 

140 

141 

143 

144 

147 

2 

249 Cf Thermal 

C R O U C H 

Table XV 

neutron induced fission 

3 4 5 6 

Sr 208 1.17 25 1.17 

Zr 208 1.72 15 1.72 

Zr 208 2.35 20 2.35 

Mo 208 3.42 7 3.42 

Ru 208 5.27 12 5.27 

Ru 208 5.09 21 5.09 

Pd 208 4.92 25 4.92 

Ag 208 5.16 11 5.16 

Pd 208 3.48 16 3.48 

Ag 208 2.92 11 2.92 

Chain 208 2.46 20 2.46 

Sn(2) 208 0.34 27 0.34 

Sn(2) 208 0.2 4 25 0.24 

Sb 208 1.23 24 1.23 

Te 208 2.19 15 2.19 

I 208 3.01 15 3.01 

Te 208 3.95 7 3.95 

Te 208 5.09 10 5.09 

Cs ' 208 6.90 15 6.90 

Ba 208 4.54 27 4.54 

Ce 208 6.34 6 6.34 

Ce 208 4.90 6 4.90 

Ce 208 4.62 6 4.62 

Nd 208 2.62 15 2.62 

25 

15 

20 

10 

12 

21 

25 

11 

16 

11 

20 

27 

25 

24 

15 

15 

10 

10 

15 

27 

10 

10 

10 

15

I A E A - S M -1 7 0 / 94 449 

Table XVI 

Reference List of Fission Yield Literature 

[1 - 8] PETRZHAK, K.A., et al., AEC TR 4696. 

[4 - 12] BAYHURST, B.P., TID 5787. 

[13] CROUTHAMEL, C.E., KAFALAS, P., STUPEGIAS, D., ANL 5789. 

[14] WEISS, H.V., REICHERT, W.L., Ad 627027; TR 943. 

[15] CROOK, J.M., VOIGHT, A.F., IS 558. 

[16] IVANOV, R.N., GORSCHKOV, V.K., ANIKINA, KUKAVADZE, G.M., 

ERSCHLER, B.V., J Nucl. Energy, 9 (1959) 46. 

[ 17] ANIKINA, M.P., IVANOV, R.N., KUKAVADZE, G.M., ERSCHLER, B.V. , 

J Nucl. Energy, 9 (1959) 167. 

[ 18 - 21] ANIKINA, M.P., et al, P2040 Vol. 15 second Geneva Conf. 

[ 22 - 26] AUMANN, D.C., FLYNN, K.F., GINDLER, J.E., GLENDENIN, L.E., 

Jinc., 31 (1969) 1935. 

'27] ARAS, N.K., GORDON, G.E., Jinc., 28 (1966) 763. 

\ 28] ANIKINA, M.P., ERSCHLER, B.V., J. Nucl. Energy, 6 (1957) 169. 

: 29] BLADES, A.T., FLEMING, W.H., THODE, H.G.'1, Can. J. Chem., 34 

(1956) 233. 

[30] BUNNEY, L.R., SCADDEN, E.M., Jinc., 27 (1965) 1183. 

[31] BIRGUL, 0., LYLE, S.J., Radiochim. Acta., 8 (1967) 9. 

[ 32 - 33] BARTHOLOMEW, R.M., MARTIN, J.S., BAERG, A.P., Can. J. Chem., 

37 (1959) 660. 

[34] BAERG, A.P., BARTHOLOMEW, R.M., Can. J. Chem 35 (1957) 980. 

[ 35 - 38] BUNNEY, L.R., SCADDEN, -E.M., ABRI AM, J.O., BALLOU, N.E., 

A/Conf15/P643, second Geneva Conference Vol. 15 449. 

[ 39 - 40] BAYHURST, B.P., et al, Phys. Rev. 107 1957 325. 

[41 - 44] BALCARCZYK, L., KERATSCHEV, P., LANZEL, E., Nucleonik, 7 

1965 169. 

[ 45] BARTHOLOMEW, R.M., BAERG, A.P., Can. J. Chem., 34 1956 201. 

[46] BARTHOLOMEW, R.M., BROWN, F., HAWKINGS, R.C. , MERRITT, W.F., 

YAFFE, L., Can. J. Chem.., 31 (1953) 120. 

47] BROWN, F., Jinc., 1 (1955) 248. 

48] BROWN, F., YAFFE, L., Can. J. Chem., 31 (1953) 242. 

49] BROOM, K.M., Phys. Rev., 126 (1962), 627. 

50 - 51] BROOM, K., Phys. Rev., 133 (1964) 874. 

52 - 61] BURGUS, W.H., IDO-16797, TID-4500. 

62 - 65 BONYUSHKIN, E.K., et al., Sov. J. At. Energy, 10 (1961) 10. 

66 - бУ В АК, M.A., et al., Sov. J. Atom. Energy, 6 (1959) 429. 

68] BUNNEY, L.R., SCADDEN, E.M., Jinc., 27 (1965) 1183. 

69] BAYLY, J.G., DURET, M.F., POULSEN, N.B., TOMLINSON, R.H., 

Can. J. Phys., 39 (1961) 1391. 

[ 70 - 72] BIDINOSTI, D.R., FICKEL, H.R., TOMLINSON, R.H., A/CONT. 15/P201 

Second Geneva Conf. Vol. 15 459. 

[ 73] BORDEN, K.D., KURODA, P.K., Jinc., 31 (1969) 2623. 

[ 74] BIDINOSTI, D.R., IRISH, D.E., TOMLINSON, R.H., Can. J. Chem., 

39 (1961) 628. 

E 75 - 76] BUNNEY, L.R,, SCADDEN, E.M., Jinc., 27 (1965) 273. 

[77] BIRGUL, 0., LYLE, S.J., Radiochim. Acta., 11 (1969) 108. 

[78] GREENDALE, A.E., DELUCCHI, A.A., AD 686041.

450 C R O U C H 

T a b l e XVI ( c o n t ) 

R e f e r e n c e L i s t o f F i s s i o n Y i e l d L i t e r a t u r e 

[79] CUNINGHAME, J.G., Jinc., 6 (1958) 181. 

[ 80] CUNINGHAME, J.G., Jinc., 4 (1957) 1. 



[83 - 86] CROALL, I.F., WILLIS, H.H., Jinc., 24 (1962) 221. 

[87] CROALL, I.F., WILLIS, H.H., Jinc., 25 (1963) 1213. 

[88 - 94] CUNINGHAME, J.G., KITT, G.P., RAE, E.R., Nucl. Phy., 27 

(1961) 154. 

[ 95 - 103] CUNINGHAME, J.G., FRITZE, K., LYNN, J.E., WEBSTER, C.B., 

Nucl. Phy., 84 (1966) 49. 

104] CROALL, I.F., WILLIS, H.H., AERE/R/6154. 

Í05 - HO] PRIVATE COMMUNICATION. 

Ill - 146] COWAN, G.A., BAYHURST, B.P., PRESTWOOD, R.J., PNE-114F 

147 - 153] YUNG YEE CHU, UCRL-8926. 

Î54 - 157] СIUFFOLOTTI, L., Energia Nucleare, 15 (1968) 272. 

Î58 CUNINGHAME, J.G., Phil. Mag., 44 (1953) 900. 

j 59 - 161] CROALL, I.F., WILLIS, H.H., AERE-R4723. 

162] DELUCCHI, A.A., GREENDALE, A.E., STROM, P.O., Phys. Rev., 

173 (1968) 1159. 

[163] DENSCHLAG, H.O., Jinc., 31 (1969) 1873. 

[164 - 167] BONYUSHKIN, E.K., AEC TR 4682. 

[168 - 171] DANIELS, W.R., HOFFMAN, D.C., Phys. Rev., 145 (1966) 145. 

[172] BIRGUL, 0., LYLE, S.J., SELLARS, J., Radiochimica Acta, 

12 (1969) 66. 

[173 - 174] DAVIES, W., Radiochimica Acta, 12 (1969) 173 

[175] ERDAL, B.R., WILLIAMS, J.C., WAHL, A.C., Jinc., 31 (1969) 

2993. 

[176] ERDAL, B.R., WAHL, A.C., DROPESKY, B.J., Jinc., 31 (1969) 

3005. 

[177 - 179] ENGELKEMEIR, D., FREEDMAN, M.S., STEINBERG, E.P., SEILER, 

J.A., WINSBERG, L., ANL-4927. 

180] FICKEL, H.R., TOMLINSON, R.H., Can. J. Phys., 37 (1959) 926. 

Д81] FICKEL, H.R., TOMLINSON, R.H., Can. J. Phys., 37 (1959) 916. 

I82I FLEMING, W.H., THODE, H.G., Can J. Chem., 34 (1956) 193. 

183] FREILING, E.C., BUNNEY, L.R., BALLOU, N.E., Phy. Rev., 96 

(1954) 102. 

[184] FORD, G.P., AECD-3597, LADC-1200. 

[185 - 195] FALER, K.T., TROMP, R.L., Phys. Rev., 131 (1963) 1746. 

[196] FRITZE, K., MCMULLEN, C.C., THODE, H.G., A/CONF.15/P187, 

Second Geneva Conference. 

[197]- 207] FORD, G.P., GILMORE, J.S., LA-1997. 

[208] FLYNN, K.F., VON GUNTEN, H.R., Helv. Chim. Acta., 52 (1969) 

2216. 

[ 209] FLEMING, W., TOMLINSON, R.H., THODE, H.G., Can. J. Phys., 

32 (1954) 522. 

[ 210] FARRAR, H., FICKEL, H.R., TOMLINSON, R.H., Can. J. Phys., 

40 (1962) 1017

I A E A - S M -1 7 0 /9 4 451 

Table XVI (cont) 


[211] FLYNN, K.F., VON GUNTEN, H.R., SM-122/1 Symposium on the 

Physics and Chemistry of fission. 

[212] FARRAR, H., CLARKE, W.B., THODE, H.G., TOMLINSON, R.H., 

Can. J. Phys., 42 (1964) 2063. 

[213 - 214] GRUMMITT, W.E., MILTON, G.W., Jinc., 5 (1957) 93. 

[215] GORSHKOV, V.K., IVANOV, R.N., KORAVADZE, G.M., REFORMATSKY, I.A. 

Atomniya Energiya, 3 (1957) 11. 

[2161 VON GUNTEN, H.R., HERMANN, H., Radiochim. Acta, 8 (1967) 112. 

[217 - 219] GRUMMITT, W.E., MILTON, G.M., Jinc., 20 (1961) 6. 

[22(3 GORSHKOV, V.K., ANIKINA, M.P., Atomniya Energiya, 7 (1959) 144. 

[22^ GLENDENIN, L.E., STEINBERG, E.P., Jinc., 1 (1955) 45. 

[222 - 223] HARDWICK, W.H., Phys. Rev., 92 (1953) 1072. 

[224] HAGEBO, E., Jinc., 25 (1963) 615. 

[225] HASTINGS, J.D., TROUTNER, D.E., Radiochim. Acta., 11 (1969) 51. 

[226 - 227] HARVEY, J.W., CLARKE, W.B., THODE, H.G., TOMLINSON, R.H., 

Can. J. Phys., 44 (1966) 1011. 

[228] IYER, R.H., MATTHEWS, C.K., RAVINDRAN, N., RENGAN, K., 

SINGH, D.V., RAMANIAH, M.V., etc., Jinc., 25 (1963) 465. 

[229 - 231] IYER, R.S., JAIN, H.C., NAMBOUDIRI, M.N., RAJAGOPALAN, M.,' 

RAKISHORE, etc., Physics and Chem. of fission, Salzburg 1965. 

[232] JADHAV, A.V., RAMANIAH, M.V., RAO, C.L., SHAHANI, C.J., 

Nukleonik, 9 (1967) 43. 

[233] KATCOFF, S., RUBINSON, W., Phys. Rev., 91 (1953) 1458. 

[234] KELLER, R.N., STEINBERG, E.P., GLENDENDIN, L.E., Phys. Rev., 

94 (1954) 969. 

[235 - 236] KRIZHANSKII, L.M., MALYI, Y., MURIN, A.N., PREOBRAZHENSKII, 

В.K., J. Nucl. Energy, 6 (1957) 260. 

[237] KRIZHANSKII, L.M., MURIN, A.N., Sov. J. At. Energy 4 (1958) 95. 

[238 - 239] KAFALAS, P., CROUTHAMEL, C.E., Jinc., 4 (1957) 239. 

[240] KNIGHT, J.D., HOFFMAN, D.C., DROPESKY, B.J., FRASCO, D.L., 

Jinc., 10 (1959) 183. 

[241] KENNETT, T.J., THODE, H. G., Can. J. Phys., 35 (1957) 969. 

[242] KJELBERG, A., PAPPAS, A.C., Jinc., 11 (1959) 173. 

[243 - 244] KATCOFF, S., RUBINSON, W., Jinc., 27 (1965) 1447 

[245] LAIDLER, J.B., BROWN, F., AWRE-49/61. 

[246 - 2471 DE LAETER, J.R., THODE, H.G., Can. J. Phys., 47 (1969) 1409. 

[248 - 253] LISMAN, F.L., MAECK, W.J., et al, IN-1277. 

[254] DEL MARMOL, P., Jinc., 30 (1968) 02873. 

[255] MACNAMARA, J., COLLINS, C.B., THODE, H.G., Phys. Rev., 78 

(1950) 129. 

[256 - 257] MENON, M.P., KURODA, P.K., Jinc., 26 (1964) 401. 

[258 - 261] MELAIKA, E.A., PARKER, M.J., PETRUSKA, J.A., TOMLINSON, R.H., 

Can. J. Chem., 33 (1955) 830. 

[262] MARINSKY, J.A., EICHLER, E., Jinc., 12 (I960) 223. 

[263] MARSDEN, D.A., YAFFE, L., Can. J. Chem. 43 (1965) 249. 

[264] TIN MO, RAO, M.N., Jinc., 30 (1968) 345. 

[265'J MUNTZE, R., GROSSE-RUYKEN, H., WAGNER, G., Kernenergie,- 

12 (1969) 380.

452 c r o u c h 



£66] NERVIK, W.E., Phys. Rev., 119 (1960) 1685. 

[267 [267 - 2681 NIECE, L.H., Diss. Abstr., 27 (1966) 1249. 

[269 - 273 272) OKAZAKI, A., WALKER, W.H., BIGHAM, C.B., Can. J. Phys., 

44 (1966) 237. 

[273 - 278) 278] OKAZAKI, A., WALKER, W.H., Can. J. Phys., 43 (1965) 1036. 

I? 79] PETRUSKA, J.A., MELAIKA, E.A., TOMLINSON, R.H., Can. J. Phys., 

33 (1955) 640. 

[280 - 28 28Í) Í) PETRUSKA, J.A., THODE, H.G., TOMLINSON, R.H., Can. J. Phys., 

33 (1955) 693. 

[282] PETROW, H.G., ROCCO, G., Phys. Rev., 96 (1954) 1614. 

[283] PAPPAS, A.C., WILES, D.R., Jinc., 2 (1956) 69. 

(284 - 286] 286] PROTOPOPOV, A.N., TOLMACHEV, G.M., et al J. Nucl. Energy, A, 

10 (1959) 80. 

[287] PILLARY, K.K.S., MEYER, R.J., LARSEN, R.P., J. Radioanalyt. 

Chem., 3 (1969) 233. 

(288] REED, G.W., Phys. Rev., 98 (1955) 1327. 

(289] REED, G.W., TÜRKEVICH, A., Phys. Rev., 92 (1953) 1473. 

[290] KUKAVADZE, G.M., ANIKINA, M.P., GOLDIN, L.L., ERSCHLER, B.V., 

AEC-TR-2435. 

[291] RUNNALS, N.G., TROUTNER, FERGUSON, R.L., Phys. Rev., 179 (1969) 

1288. 

[592 - 294] REGIER, R.B., BURGUS, W.H., TROMP, R.L., Phys. Rev., 113, (1959) 

1589. 

(295 - 30Ó] REGIER, R.B., BURGUS, W.H., TROMP, R.L., SORENSEN, B.H., Phys. 

Rev., 119 (1960) 2017. 

[301] RICKARD, R.R., GOEKING, C.F., WYATT, E.I., Nucl. Sc. Eng., 

23 (1965) 115. 

[302] RAO, M.N., KURODA, P.K., Phys. Rev., 147 (1966) 884. 

[303] RAO, M.N., Radiochim. Acta., 8 (1967) 12. 

É04] RAVINDRAN, N., FLYNN, K.F., GLENDENIN, L.E., Jinc. 28 (1966) 

921. 

[305] SANTRY, D.C., YAFFE, L., Can. J. Chem., 38 (1960) 464. 

D06] STEHNEY, A.F., SUGARMAN, N., Phys. Rev., 89 (1953) 194. 

[307] SUGARMAN, N., Phys. Rev., 89 (1953) 570. 

D08] SATTIZAHN, J.E., KNIGHT, J.D., KAHN, M., Jinc., 12 (1960 206. 

(309] SANTRY, D.C., YAFFE, L., Can. J. Chem., 38 (1960) 421. 

Pio] SRINIVASAN, ALEXANDER, E.C., MANUEL, O.K., TROUTNER, D.E., 

Phys. Rev., 179 (1969) 1166. 

Dll] STROM, P.O., LOVE, D.L., GREENDALE, A.E., DELUCCHI, A.A., SAM, D. 

SAM, D., BALLOU, N.E., Phys. Rev., 144 (1966) 984. 

[312] STROM, P.O., GRANT, G.R., PAPPAS, A.C., Can. J. Chem., 43 

(1965) 2493. 

[313] OHYOSHI, E., OHYOHSI, A., SHINAGANA, M., Radiochem. Radioanal. 

Ltrs., 3 (1970) 1 

[314] STELLA, R., MORETTO, L.G., MAXIA, V., DI CASA, M., CRESPI, V., 

ROLLIER, M.A., Jinc., 31 (1969) 3779. 

P15] TERCHO, G.P., MARINSKY, J.A., Jinc., (1964) 1129. 

¡316 (316 - 325) 

325) TERRELL, J., SCOTT, W.E., GILMORE, S., MINKKINEN, C.O., Phys. 

Rev., 92 (1953) 1091.



Reference List of Fission Yie d Literature 

Г326] TURKEVITCH, A., NIDAY, J.B., Phys. Rev., 84 (1951) 52. 

[327] TONG, S.L., FRITZE, K., Radiochim. Acta., 12 (1969) 179. 

[328] TROUTNER, D.E., FERGUSON, R.L., OKELLEY, G.D., Phys. Rev., 

130 (1963) 1466. 

[329 - 330] WETHERILL, G.W., Phys. Rev., 92 (1953) 907. 

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M . L E D E R E R : A r e these data available on magnetic tapes? 

E . A . C . C R O U C H : A t present, only the input literature results are 

so available. W e do hope to have them on magnetic tape but it m a y not 

be for som e time yet. F o r this year, at least, w e are publishing the 

final results in the form of reports. 

F . F R Ö H N E R : In connection with M r . L e d e r e r 's question, I might 

mention that D r . Crouch w as kind enough to turn over his library to the 

C C D N recently. W e are now in the process of incorporating the data into 

our experimental data file and hope that we shall soon be able to answer 

requests from users in our service area or, for that matter, from other 

service areas via their respective neutron data compilation centres. 

J . B L A C H O T : W h y do you som etim es have three significant figures 

and som etim es two? 

E . A . C. C R O U C H : Sim ply because I have not trim m e d the figures to 

match the stated standard deviations; it is m y om ission entirely, and one 

m ust read the figures in conjunction with their stated standard deviations. 

W . B . L E W I S : I saw no mention in your paper of neutron capture by 

fission products. Did you a ssum e a value for this and then subtract or 

add it? 

E . A . C. C R O U C H : No corrections w ere m ad e for neutron capture; 

it w as assum ed the author would have done this. 

M . L A M M E R : Do you estimate m issin g yield values from a m athe 

matical m odel for the case of 235U , 239P u etc. therm al fission as well, 

or only for types of fission w here yields are not well known? W hat is the 

confidence level of such estimates? 

E . A . C . C R O U C H : W e have not tested m athematical m odels to date, 

as the basic evaluations are m o re important to the U K A E A , although the 

references in the paper give som e prelim inary ideas. W e have, however, 

done sufficient w ork to see that m odel fitting is possible; I would prefer 

not to say m o re at present, 

M . L A M M E R : M e a sured relative yields norm alized in such a m anner 

that the sum of yields totals 2 0 0 % are based on interpolated values and 

radiochem ical m easurem ents from the earlier literature. A t the time 

of evaluation these data w ere known far better. Such m easurem ents m ust 

in any case be considered as relative yields. W h y is an adjustment not 

possible, as indicated in section 2 (ii) of your paper? 

E . A . C. C R O U C H : I would not say that adjustment is not possible. 

H o w e v e r, the very act of drawing a smooth curve through the exponential 

points implies the setting up of a m odel, the validity of which m a y be 

doubtful. So I prefer to leave such results as the author left them: he 

obviously hoped to m ak e an estimate of absolute yields. 

M iss K . W A Y : U nder what circum stances were data omitted? In 

other w ords, w ere data very different from the m e a n included in arriving 

at that average? 

E . A . C . C R O U C H : The x2 test w as used with the weighted m e a n to 

establish if any results w ere obviously wrongly weighted. The weights 

w ere then adjusted so that no result w as omitted although its weight might 

be so low as to render its effect negligible. The exception to this is the 

case w here an error can definitely be detected in the paper; but as far as

458 C R O U C H 

m y m e m o r y goes only one paper w as ignored in the thermal yields. I ought 

to add that I do not include project progress reports in the evaluations; 

the results m ust have been m ad e public somewhere.' 

C . D E V I L L E R S : C an you say whether the deviations which you observe 

in the yields as between your compilation and that of M e e k and R ider are 

com parable with the uncertainties reported by the latter authors? 

E . A . C. C R O U C H : Most of the r eco m m ended yields agreed with 

W a lk e r 's and M e e k and R id e r's figures, within the figures taken as standard 

deviations for those works. I a m not certain what exactly M e e k and Rider 

m eant by their error indicator letters. 

W . H . W A L K E R : I should like to m ake a brief com m ent in this connec 

tion: the results of M e e k and Rider in N E D O - 1 2 1 5 4 ('7 2 ) have been replaced 

by a n e w version currently available only as computer output. Som e yields 

have been changed substantially, and m ost of the values quoted by D r . Crouch 

have been changed.

CUMULATIVE YIELDS OF 

THERMAL NEUTRON FISSION PRODUCTS 

Some Results and Recommendations 

Based on a Recent Evaluation 

W .H. WALKER 

Chalk River Nuclear Laboratories, 

Chalk River, Ontario, Canada 

Abstract 

I A E A - S M -1 7 0 /3 4 

C U M U L A T IV E YIELDS OF TH ERM AL NEUTRON FISSION P R O D U C T S : SOM E RESULTS A N D R ECOM M EN 

D A T IO N S BASED O N A RECENT E V A L U A T IO N . 

A c a r e fu l a n a ly sis o f c u m u la tiv e y ie ld s in th e th e rm a l n eu tron fissio n o f 233U , 235U , 233Pu and 241 Pu 

h as r e c e n t ly b e e n c o m p le t e d . T h e m e th o d s used and s o m e o f th e p r o b le m s e n co u n te re d are d iscu ssed . 

Errors are assign ed to a ll y ie ld s and th e e ffe c t s o f th e c o r re s p o n d in g u n c e r ta in tie s in n e u tro n a b s o rp tio n and 

r e a c t iv it y a re e s tim a te d . A p r o g ra m o f m e a su re m e n ts w h ic h c o u ld r e d u c e th e m a jo r u n c e rta in tie s req u ires 

m a s s -s p e c tr o m e t r ic m e a su re m e n ts o f r a d io a c t iv e and s ta b le isobars fo r a g iv e n fis s ile s p e c ie s plus y -r a y 

m e a su re m e n ts fo r a ll fo u r fis s ile s p e c ie s o f r e la t iv e y ie ld s fo r a la r g e n u m b e r o f r a d io a c t iv e n u c lid e s th at 

a re is o b a r ic w ith n u c lid e s fo r w h ic h th e y ie ld s h a v e b e e n m e a su re d m a s s -s p e c tr o m e t r ic a lly . T h e se m e a s u re 

m e n ts a re d iscu ssed and r e c o m m e n d a tio n s m a d e fo r p re se n ta tio n o f d a ta in a w a y th at w ill m in i m iz e u n c e r 

ta in tie s in fu tu re e v a lu a tio n s . 

T h o u g h m u c h e f f o r t h a s g o n e i n t o t h e m e a s u r e m e n t a n d 

e v a l u a t i o n o f f i s s i o n p r o d u c t c r o s s s e c t i o n s , t h e r e h a s b e e n 

l i t t l e s u p p o r t b y r e a c t o r s c i e n t i s t s o f w o r k o n f i s s i o n p r o d u c t 

y i e l d s . T h i s i s s u r p r i s i n g s i n c e t h e r a t e a t w h i c h n e u t r o n s a r e 

a b s o r b e d b y a p a r t i c u l a r f i s s i o n p r o d u c t i s p r o p o r t i o n a l t o t h e 

p r o d u c t o f i t s y i e l d , y, a n d i t s c r o s s s e c t i o n , a , i f a i s s m a l l , 

o r t o y o n l y i f ct is v e r y l a r g e . I n t h e m o s t r e c e n t w o r k o n 

y i e l d s t h e i n t e r e s t h a s b e e n p r i m a r i l y i n t h e i r u s e a s b u r n u p 

m o n i t o r s r a t h e r t h a n i n o b t a i n i n g a n i m p r o v e d k n o w l e d g e o f 

f i s s i o n p r o d u c t a b s o r p t i o n . 

A r e c e n t e v a l u a t i o n o f t h e r m a l f i s s i o n y i e l d s a t C h a l k 

R i v e r [ 1 ] p r o v i d e s a n e x c e l l e n t b a s i s f o r d e t e r m i n i n g u n c e r t a i n 

t i e s i n f i s s i o n p r o d u c t a b s o r p t i o n s i n c e i t i n c l u d e s a n e s t i m a t e 

o f t h e e r r o r i n t h e c u m u l a t i v e y i e l d s a t e a c h m a s s . 

T H E E V A L U A T I O N O F F I S S I O N P R O D U C T Y I E L D S 

T h e n e w C h a l k R i v e r e v a l u a t i o n o f f i s s i o n p r o d u c t y i e l d s i s 

a n i m p r o v e d v e r s i o n o f t h e o n e f o r 236u t h e r m a l f i s s i o n p r e s e n t e d 

a t t h e H e l s i n k i c o n f e r e n c e [ 2 ] , e x t e n d e d t o i n c l u d e d a t a f o r 2 3 3 U , 

s a 9 P u a n d 3 4 1 P u . T h i s e v a l u a t i o n i s b a s e d m a i n l y o n m a s s s p e c t r o 

m e t r i c m e a s u r e m e n t s w h i c h c o v e r f r o m 6 6 % (3 4 1 Pu) t o 9 2 % (S 3 U) 

o f t h e t o t a l y i e l d . R a d i o m e t r i c d a t a c o v e r i n g t h e s a m e m a s s e s a r e 

u s e d o n l y t o c h e c k f i n a l n o r m a l i z a t i o n s . T h e y a r e a l s o u s e d t o 

459

460 W ALKER 

o b t a i n y i e l d s a t m a s s e s w h e r e n o m a s s s p e c t r o m e t r i c d a t a a r e 

a v a i l a b l e , m a i n l y t h e y i e l d s i n t h e w i n g s o f t h e l i g h t a n d h e a v y 

m a s s p e a k s a n d i n t h e v a l l e y b e t w e e n . 

T h e e v a l u a t i o n m e t h o d is, t h e r e f o r e , q u i t e d i f f e r e n t f r o m 

t h e u s u a l o n e i n w h i c h a n e r r o r i s a s s i g n e d t o e v e r y m e a s u r e d 

y i e l d a n d t h e r e c o m m e n d e d y i e l d a t e a c h m a s s i s t h e n o b t a i n e d 

b y a l e a s t s q u a r e s a n a l y s i s . T h i s is t h e m e t h o d u s e d b y M e e k 

a n d R i d e r i n a s e r i e s o f r e p o r t s o n f i s s i o n p r o d u c t y i e l d s t h e 

l a s t o f w h i c h w a s p u b l i s h e d i n 1 9 7 2 [ 3 ] . T h e m a i n d i s a d v a n t a g e 

o f t h i s l a t t e r a p p r o a c h is t h a t i t is d i f f i c u l t t o p r o p e r l y t a k e 

a c c o u n t o f t h e h i g h a c c u r a c y w i t h w h i c h t h e m a s s s p e c t r o m e t r i s t 

c a n m e a s u r e b o t h r e l a t i v e a b u n d a n c e s o f t h e i s o t o p e s o f o n e 

e l e m e n t a n d t h e r e l a t i v e a m o u n t s o f d i f f e r e n t e l e m e n t s . T h e 

s e c o n d o f t h e s e d e t e r m i n a t i o n s i s l e s s a c c u r a t e t h a n t h e f o r m e r , 

b u t e v e n t h e n i s u s u a l l y c o m p a r a b l e i n a c c u r a c y t o t h e b e s t 

r a d i o m e t r i c m e a s u r e m e n t s . 

A l t h o u g h i t i s g i v e n i n d e t a i l i n [1] I w i l l o u t l i n e t h e 

e v a l u a t i o n m e t h o d h e r e f o r t h r e e r e a s o n s - f i r s t , t o d e m o n s t r a t e 

t h e a d v a n t a g e s r e f e r r e d t o a b o v e m o r e c l e a r l y , s e c o n d , t o p r o v i d e 

b a c k g r o u n d m a t e r i a l f o r a d i s c u s s i o n o f p o s s i b l e f u t u r e m e a s u r e 

m e n t s , a n d t h i r d , b e c a u s e t h e v e r s i o n i n [l] i s q u i t e d e t a i l e d 

a n d i s p r i m a r i l y o f i n t e r e s t t o a s m a l l g r o u p o f s p e c i a l i s t s . 

T h e m e t h o d p r o c e e d s i n t h r e e e a s i l y s e p a r a t e d s t e p s - t h e 

d e t e r m i n a t i o n o f i s o t o p i c a b u n d a n c e s , t h e d e t e r m i n a t i o n o f r e 

l a t i v e e l e m e n t y i e l d s , a n d f i n a l n o r m a l i z a t i o n . 

I s o t o p i c A b u n d a n c e s 

T a b l e I i s t a k e n f r o m [1] a n d s h o w s t h e m e a s u r e d i s o t o p i c 

a b u n d a n c e s o f t h e N d f i s s i o n p r o d u c t s , w h e r e i s o t o p i c a b u n d a n c e 

is d e f i n e d a s t h e n u m b e r o f a t o m s o f o n e i s o t o p e d i v i d e d b y t h e 

n u m b e r o f a t o m s o f t h e e l e m e n t , e x c l u d i n g r e l a t i v e l y s h o r t - l i v e d 

i s o t o p e s s u c h a s 1 1 - d a y 1 4 7 N d . T h e v a l u e s o f L i s m a n e t a l . [ 4 ] 

a r e a v e r a g e s o f r e s u l t s f r o m s e v e r a l s a m p l e s o f e a c h f i s s i l e 

m a t e r i a l a n d t h e a s s i g n e d e r r o r i s t h e s t a n d a r d d e v i a t i o n f r o m 

t h e a v e r a g e . T h e e r r o r s a s s i g n e d t o t h e f i n a l a v e r a g e s a r e a l s o 

s t a n d a r d d e v i a t i o n s . 

T h e f i r s t p o i n t t o n o t e a b o u t t h e d a t a i s t h e g e n e r a l l y 

s m a l l s c a t t e r b e t w e e n m e a s u r e m e n t s , w i t h s t a n d a r d d e v i a t i o n s o f t e n 

l e s s t h a n 1 % . T h e g r e a t e s t u n c e r t a i n t y , u p t o ^4% f r o m t h e m e a n 

f o r 3 a 3 u f i s s i o n , o c c u r s f o r 1 S 0 N d , w h i c h h a s a s m a l l i s o t o p i c 

a b u n d a n c e a n d is, t h e r e f o r e , m o r e d i f f i c u l t t o m e a s u r e a c c u r a t e l y . 

T h e f a c t t h a t t h e s t a n d a r d d e v i a t i o n o f t h e m e a n u s u a l l y e x c e e d s 

t h a t o f a s i n g l e s e t o f m e a s u r e m e n t s ( L i s m a n e t a l . [ 4 ] ) i n d i c a t e s 

t h a t t h e r e a r e p r o b a b l y s m a l l s y s t e m a t i c e r r o r s i n t h e d i f f e r e n t 

m e a s u r e m e n t s . 

T h o s e r e s u l t s o f S t e i n b e r g a n d G l e n d e n i n [5] t h a t w e r e n o t 

u s e d r e q u i r e s o m e c o m m e n t . F o r 1 4 3 N d t h e d i f f e r e n c e f r o m t h e


TABLE I. R E LATIV E YIELDS OF NEODYMIUM ISOTOPES 

335u 

Stein berg, G le n d e n in (1955) 

M e laika et a l . (1955) 

333y 

143Nd 1 44Nd 145Nd 14SNd 147Nd* 14SNd 1 6 °Nd 

.2 8 2 0 х 

.2861 

.2723* 

.2 6 7 2 1 

.1 8 4 9 х 

.1903 

.1 4 7 4 х 

.1 4 4 5 

.0 8 1 4 

.0 8 0 4 

.0 3 2 5 

.0 3 1 5 

F a rrar, Tomlinson (1958) .2 8 6 6 .2661 .1906 .1447 .1093 .0805 .0315 

Chu (1959) .2897 .2607 .1912 . 1448 .0817 .0319 

Rider et a l . (1965) .2927 .2593 .1911 .1441 .0 8 1 6 .0313 

Lisman et al. (1970) .2 8 8 4 

± 0.4 % 

Average .2885 

± 0.9% 

.2 6 4 0 

± 0.9% 

.2 6 3 5 

± 0.9% 

.1893 

± 0.6 % 

.1 9 0 5 

± 0.4% 

.1443 

± 0.3% 

.1 4 4 5 

± 0.2% 

.0827 

± 0.5 % 

.1093 .0814 

± 1.1 % 

.0312 

± 0.5 % 

.0316 

± 0.8 % 

M elaika et a l . (1955) .3201 .2 5061 .1879 .1412 .0717 .0285 

Ivanov et al- (1959) .3 2 2 4 s .2 5 6 6 3 .1821 .1412 .0663" .0324* 

B id in o s t i et al- (1961) .3197 .2503 .1881 .1 4 0 8 .0 7 2 0 .0291 

Rider et al- (1 9 6 6 ) .3253 .2533 .1862 .1381 .07 02 .0268 

Lisman et al- (1970) .3198 

± 0.2 % 

2 3 9 Pu 

Average .3 2 1 5 

± 0.7 % 

.2 5 7 4 

± 0.4 % 

.2536 

± 1.3% 

.1 8 5 0 

± 0.3% 

.1859 

± 1.4% 

.1389 

± 0.3 % 

.1 4 0 0 

± 1.0% 

.0717 

± 0.6% 

.0 7 1 4 

± 1.2% 

.0272 

± 2.4% 

.0279 

± 3.8% 

W ile s et al. (1956) .2 7 1 4 . 2 2 9 1 1 .1 8 4 9 .1523 .1029 .0594 

K r iz h a n s k ii et a l . (1957) .2743 .2 3 0 5 .1827 .1 5 2 8 .0993 .0603 

F i c k e l , Tomlinson (1959) .2703 .2 3 0 7 a .1852 .1522 .1 0 1 4 .0603 

Rider et a l . (1966) .2 7 4 4 .2 2 9 4 .1 8 5 0 .1512 .1 0 1 4 .0586 

Lisman et al. (1970) .2725 

± 0.3% 

241 Pu 

Average .2726 

± 0.7 % 

.2286 

± 0.9% 

.2297 

± 0.4 % 

.1847 

± 0.2% 

.1845 

± 0.5% 

.1 5 1 8 

± 0.2 % 

.1521 

± 0.4% 

.1 0 3 4 

± 0.7 % 

.1017 

±1. 6% 

.0 5 9 0 

± 0.4% 

.0 5 9 5 

± 1.3% 

Farrar et al. (1964) .2537 .2328 .1807 .1551 .1094 . 06834 

Rider et a l . (1967) .2 5 6 0 .2385 .1817 .1 5 2 0 .1 0 7 5 .0643 

Lisman et al. (1970) .2 5 5 6 

± 0.2 % 

Average .2551 

± 0 .5 % 

.2356 

± 0 .1 % 

.2356 

± 1.2 % 

.1 8 1 9 

± 0.1 % 

.1814 

± 0 .4 % 

.1 5 2 8 

± 0.2 % 

.1532 

± 0 .9 % 

* Y i e l d s f o r t h i s i s o t o p e n o t i n c l u d e d i n n o r m a l i z a t i o n 

.1077 

± 0.2 % 

.1082 

± 1 .0 % 

* N o t u s e d i n t a k i n g a v e r a g e . R e m a i n i n g y i e l d s n o r m a l i z e d a s s u m i n g a v e r a g e 

v a l u e a t t h i s m a s s 

1 Corrected for change in T i ( 144Ce) from 282 to 2 8 4 .4 d - 23SU , + 0 .4 % 

(see t e x t ); 233U , + 0 .5 % ; 3 3 9 Pu, + 1 .0 % . 

2 Corrected for change in a ( 143Nd) from 280 b to 325 b . See te x t . 

3 corrected for change in T i ( 144Ce) from 278 d to 2 8 4 .4 d - 339 Pu, + 1 .5 % . 

4 R esults for two samples w ire quoted w ith r e la t iv e 1B0Nd y ie ld s 

d i f f e r i n g by 4 .4 % , Only the value w ith the smaller standard deviation 

is used h e r e . 

.0 6 6 4 

± 1.0 % 

.0 6 6 3 

± 3 .0 %

462 W ALKER 

a v e r a g e i s o n l y t w i c e t h e s t a n d a r d d e v i a t i o n a n d w o u l d n o r m a l l y 

b e i n c l u d e d . W h i l e n o d e t a i l s a r e a v a i l a b l e c o n c e r n i n g t h e 

i r r a d i a t i o n , I b e l i e v e i t w a s s i m i l a r i n i n t e g r a t e d f l u x t o t h o s e 

o f L i s m a n e t al. [4] w h e r e 1 4 3 N d v a l u e s w e r e i n c r e a s e d 2 % o r m o r e 

t o t a k e a c c o u n t o f l o s s b y n e u t r o n c a p t u r e . T h e 1 4 4 N d i s o t o p i c 

a b u n d a n c e i s d e c r e a s e d a c o r r e s p o n d i n g a m o u n t . S i n c e n o m e n t i o n 

o f s u c h a c o r r e c t i o n is m a d e b y S t e i n b e r g a n d G l e n d e n i n t h i s is 

p r o b a b l y t h e s o u r c e o f t h e d i s c r e p a n c y a n d f o r t h i s r e a s o n t h e i r 

m a s s 1 4 3 a n d 1 4 4 r e s u l t s a r e o m i t t e d . F o r m a s s e s 1 4 5 a n d 1 4 6 

t h e d i f f e r e n c e s a r e s i m i l a r i n m a g n i t u d e , b u t c a n n o t b e e x p l a i n e d 

b y n e u t r o n c a p t u r e s i n c e t h e 1 4 E N d c r o s s s e c t i o n is o n l y a b o u t 1 / 6 

o f t h e 1 4 a N d c r o s s s e c t i o n . T h e s e r e s u l t s a r e o m i t t e d s i m p l y 

b e c a u s e t h e y d i f f e r f r o m t h e m e a n o f t h e o t h e r v a l u e s b y m o r e t h a n 

t e n t i m e s t h e s t a n d a r d d e v i a t i o n s o f t h e m e a n . 

P r o c e e d i n g i n t h i s m a n n e r w i t h e a c h e l e m e n t m e a s u r e d m a s s 

s p e c t r o m e t r i c a l l y g i v e s t h e s h a p e o f s e g m e n t s o f t h e y i e l d c u r v e , 

e a c h s e g m e n t c o r r e s p o n d i n g t o a n e l e m e n t , a s s h o w n i n F i g u r e 1 ( a ) 

f o r t h e h e a v y m a s s e s i n 2 3 5 u t h e r m a l f i s s i o n . 

R e l a t i v e E l e m e n t Y i e l d s 

I s o t o p e d i l u t i o n is t h e m o s t c o m m o n m e t h o d u s e d t o d e t e r 

m i n e r e l a t i v e a b u n d a n c e s o f t h e d i f f e r e n t e l e m e n t s m a s s s p e c t r o 

m e t r i c a l l y . A m e a s u r e d n u m b e r o f a t o m s o f t h e s a m e e l e m e n t a r e 

a d d e d t o t h e f i s s i o n p r o d u c t s a m p l e a n d t h e i s o t o p i c a b u n d a n c e s 

o f t h e m i x e d s a m p l e a r e d e t e r m i n e d . T h e a d d e d m a t e r i a l is 

p r e f e r a b l y a s i n g l e i s o t o p e n o t p r o d u c e d i n f i s s i o n , b u t t h e 

n a t u r a l l y o c c u r r i n g e l e m e n t h a s a l s o b e e n u s e d . T h e r a t i o o f 

f i s s i o n p r o d u c t a t o m s t o a d d e d a t o m s i s c a l c u l a t e d f r o m t h e 

i s o t o p i c a b u n d a n c e s a n d f r o m t h i s d a t a t h e n u m b e r o f f i s s i o n 

p r o d u c t a t o m s f o r e a c h e l e m e n t c a n b e d e t e r m i n e d r e l a t i v e t o a 

p a r t i c u l a r e l e m e n t . 

T h e s e c o n d m e t h o d c a n r e a d i l y b e u n d e r s t o o d f r o m 

F i g u r e 1 ( a ) . I t is n o t n e c e s s a r y t o w a i t u n t i l a l l t h e r a d i o 

a c t i v e i s o t o p e s h a v e d e c a y e d b e f o r e t h e m a s s a n a l y s i s i s m a d e , 

a n d t h e o p e n c i r c l e s s h o w w h e r e t h e s e h a v e b e e n m e a s u r e d . T h e 

f i n a l v a l u e s f o r r a d i o a c t i v e i s o t o p e s h a v e , o f c o u r s e , b e e n 

c o r r e c t e d f o r r a d i o a c t i v e d e c a y . T o u s e t h e s e c o n d m e t h o d , 

i s o b a r i c l i n k i n g , o n e s i m p l y e q u a t e s t h e i s o t o p i c a b u n d a n c e s o f 

t h e t w o i s o b a r s t o o b t a i n t h e r e l a t i v e n u m b e r s o f a t o m s o f t h e 

t w o e l e m e n t s i n v o l v e d . 

T a b l e II, t a k e n f r o m [l], s h o w s r e l a t i v e e l e m e n t y i e l d s f o r 

a 3 S U f i s s i o n . T h e v a l u e s l i s t e d a r e i n a t o m s p e r a t o m o f Z r f o r 

t h e l i g h t m a s s e s o r N d f o r t h e h e a v y m a s s e s . T h o s e o b t a i n e d b y 

i s o b a r i c c o u p l i n g a r e i n d i c a t e d b y t h e s u p e r s c r i p t i. N o t e t h a t 

t h e s t a n d a r d d e v i a t i o n s a r e m o r e v a r i a b l e t h a n t h o s e i n T a b l e I, 

w i t h a m a x i m u m o f 6 . 3 % f o r Sm. ,

I A E A - S M -1 7 0 /3 4 463 

MASS 

F IG . 1 . H e a v y -m a s s d a ta fo r th e th e rm a l n eu tron fis s io n o f 235U : 

a ) R e la tiv e a b u n d a n ce s o f X e , C s , B a, C e , N d , S m and Eu is o t o p e s ; b ) P e rce n t y ie ld s . 

F i g u r e 1 ( b ) s h o w s h o w t h e i n d i v i d u a l e l e m e n t r e s u l t s o f 

F i g u r e 1 ( a ) a r e f i t t e d t o g e t h e r i n t h i s w a y t o g i v e t h e s h a p e 

o f t h e b u l k o f t h e h e a v y m a s s p e a k i n 2 3 5 u f i s s i o n . H e r e t h e 

y i e l d s h a v e b e e n n o r m a l i z e d s o t h a t t h e N d e l e m e n t y i e l d i s 2 0 . 4 0 % 

a s d e t e r m i n e d b y m a s s s p e c t r o m e t r i c m e a s u r e m e n t s o f t h e n u m b e r o f 

f i s s i o n s . T h i s v a l u e m a y b e e x p e c t e d t o h a v e a 2 - 3 % u n c e r t a i n t y . 

N o t e t h a t t h e r a d i o a c t i v e i s o b a r y i e l d s a g r e e w i t h t h e s t a b l e 

i s o b a r y i e l d s w i t h i n t h e i r e r r o r s , e v e n t h o u g h t h e y m a d e o n l y a 

m i n o r c o n t r i b u t i o n t o d e t e r m i n i n g r e l a t i v e y i e l d s .

464 W ALKER 

TABLE II. RELATIV E ELEM ENT YIELDS IN 235U THERMAL 

NEUTRON FISSION 

Element Kr Rb Sr Y Zr Mo Ru 

Iso to p ic masses 

included in 

element y ie ld 

8 3 ,8 4 

86 

8 5 ,8 7 8 8 ,9 0 8 9 ,9 1 9 1 ,9 2 , 

9 3 ,9 4 , 

96 

E l e m e n t Y i e l d s R e l a t i v e t o Z r 

9 7 ,9 8 , 

100 

1 0 1 ,1 0 2 

1 0 4 ,1 0 6 

Lisman et al. 

(1970) .1 1 2 4 .1 2 5 2 .3 0 8 4 1 .0 0 0 . 5796 .3707 

Farrar et al. 

(1962) .2992 .3422 1 .0 0 0 

± 0.7% 

S tein b erg, 

Glendenin 

(1955) .3031 1 .0 0 0 . 5852 .3 6 3 3 1 

Petruska et al. 

(1955) .1 2 3 8 ® (.3 0 3 6 ) 

Average .1 1 2 4 .1 2 4 5 .3 0 3 6 .3422 1 .0 0 0 .5 8 2 4 .3682 

± 0.6 % ± 1.5 % ± 0.5% ± 0.7 % 

Element Xe Cs Ba Ce Nd Sm 

Iso to p ic masses 1 3 1 ,1 3 2 1 3 3 ,1 3 7 138 1 4 0 ,1 4 2 143-146 1 4 7 ,1 4 9 

included in 134 14.4 1 4 8 ,1 5 0 1 5 1 ,1 5 2 

element y ie ld 154 

Element Y ie ld s R elative to Nd 

Lisman et al. 

(1970) .7 0 6 8 .6 3 5 9 .3323 .8 6 0 1 .0 0 0 . 18383 

R ider et al. 

(1 9 6 5 ,1 9 6 7 ) .6 2 8 4 .3 1 9 4 1 .0 0 0 

F a r r a r , Tomlin 

s o n , (1962) .7 6 5 0 1 ' 4 .6 3 4 6 1,B .3 3 1 9 .8 6 2 1 1 1 .0 0 0 .1 9 7 9 1 

Chu (1959) .8546 1 .0 0 0 .2009 

Petruska et a l . 

(1955) 

S tein b e r g , Glen - 

d enin (1955) 

Average .7 0 6 8 .6 3 3 0 .3279 

± 0.6 % + 2 .3 % 

.5 6 6 2 х . 2627* .8178®'* 1 .0 0 0 

.8592 

■ ± 0.5% 

From average r e la tiv e .8 6 4 2 1 

y ie ld s (Tables 8 ,9 ) ± 1.6 % 

1 .0 0 0 .2147 

1 .0 0 0 .1993 

± 6.3% 

1 U s in g is o b a r ic links 

x Not used in taking average 

1 Based on absolute y ie l d of loeRu determined by ß-counting. 

A ssigned h a l f w eight in tak in g average 

2 Based on an isotope d ilu t io n measurement g iv in g Rb atoms/ 

Sr atoms = 2 .4 5 1 and assuming a Sr y ie ld of 0 .3 0 3 6 

3 W ith 1 4 7 Sm reduced 2 .5 % {Table 10) 

4 Not used because i t is based on an unpublished value of the 

133Xe y ie ld for which no data on decay corrections is 

av a ilable 

6 From Cs y ie ld s of Petruska et al (1955b ) using mass 137 

isobars 

s Based on mass 140 and 142 only , u sin g average re la t iv e 

abundances of Table 8

F i n a l N o r m a l i z a t i o n 


F i n a l l y , a s s h o w n i n F i g u r e 1 ( b ) , t h e r a d i o m e t r i c y i e l d s 

a r e i n t r o d u c e d . T h e i r p r o p e r r o l e c a n n o w b e m u c h m o r e c l e a r l y 

u n d e r s t o o d - n a m e l y t o d e f i n e t h e y i e l d s i n t h e v a l l e y b e t w e e n 

t h e l i g h t a n d h e a v y m a s s p e a k s , a n d i n t h e i r w i n g s , a n d t o 

c o n t r i b u t e t o t h e f i n a l n o r m a l i z a t i o n o f t h e m a s s s p e c t r o m e t r i c 

y i e l d s . 

I n t h e c a s e o f t h e 3 3 5 u h e a v y m a s s e s i n F i g u r e 1(b) t h e 

m a s s s p e c t r o m e t r i c y i e l d s a s i n i t i a l l y n o r m a l i z e d s u m t o 9 5 . 6 % , 

w h i l e t h e r a d i o m e t r i c a n d i n t e r p o l a t e d y i e l d s a d d t o 3 . 3 % . T h e 

s u m is t h u s s h o r t o f t h e r e q u i s i t e 1 0 0 % b y 1 . 1 % a n d t h i s c o u l d b e 

m a d e u p b y i n c r e a s i n g a l l r a d i o m e t r i c y i e l d s b y 1 / 3 o f t h e i r 

v a l u e ; h o w e v e r , e v e n i f o n e w i s h e d t o a r g u e t h a t s u c h a c h a n g e 

i s w i t h i n t h e i r e r r o r r a n g e , t h i s d a t a i s t a k e n f r o m s o m a n y 

d i f f e r e n t s o u r c e s t h a t o n e c e r t a i n l y c o u l d n o t c l a i m t h a t t h e y 

w o u l d h a v e a c o m m o n s y s t e m a t i c e r r o r o f t h i s m a g n i t u d e . S i n c e 

t h e r e q u i r e d c h a n g e t o t h e s e t o f m a s s s p e c t r o m e t r i c y i e l d s is 

l e s s t h a n t h e e r r o r a s s u m e d f o r t h e o r i g i n a l n o r m a l i z a t i o n , it 

i s m u c h m o r e r e a s o n a b l e t o i n c r e a s e t h e m a s s s p e c t r o m e t r i c d a t a 

o n l y , a n d t h i s is t h e c o u r s e f o l l o w e d . 

I n t h e p r e s e n t c a s e t h e m o r e a c c u r a t e r a d i o m e t r i c m e a s u r e 

m e n t s , t h o s e a t m a s s e s 1 3 7 , 1 3 9 a n d 1 4 0 , s u p p o r t t h e ~ 1 % i n c r e a s e 

i n t h e m a s s s p e c t r o m e t r i c y i e l d s . 

I n [1] t h e y i e l d s a r e r e q u i r e d t o s a t i s f y a s e c o n d 

c o n d i t i o n , i n a d d i t i o n t o 2 y. = 1 . 0 0 0 , i n o r d è r t o s a t i s f y a n 

a d d i t i o n a l r e q u i r e m e n t , n a m e l y t h a t t h e m e a n n u m b e r o f n u c l e o n s 

o f t h e f i n a l d i s t r i b u t i o n s h o u l d e q u a l t h e n u m b e r o f f i s s i o n i n g 

n u c l e o n s l e s s t h e a v e r a g e n u m b e r o f n e u t r o n s p e r f i s s i o n , 

i . e . Z y . A. = A , + 1 -v 

i i x f 

T o s a t i s f y t h i s r e s t r i c t i o n a f e w a d j u s t m e n t s w e r e r e q u i r e d , 

e i t h e r i n i n d i v i d u a l r a d i o m e t r i c v a l u e s , o r b y u s i n g d i f f e r e n t 

n o r m a l i z a t i o n f a c t o r s f o r m a s s s p e c t r o m e t r i c y i e l d s a b o v e a n d 

b e l o w t h e p e a k , i . e . s l i g h t l y s k e w i n g t h e o r i g i n a l m a s s s p e c t r o 

m e t r i c s h a p e o f e i t h e r t h e l i g h t o r h e a v y m a s s p e a k . T h e c h a n g e s 

w e r e w i t h i n t h e r a n g e a l l o w e d b y t h e a s s i g n e d e r r o r s . 

A S S I G N M E N T O F E R R O R S A N D T H E I R E F F E C T O N F I S S I O N P R O D U C T A B S O R P T I O N 

B e c a u s e o f t h e s e p a r a t i o n i n t o t h r e e d i s t i n c t s t e p s u s e d i n 

t h i s a n a l y s i s t h e e s t i m a t i o n o f y i e l d e r r o r s i s r e l a t i v e l y 

s t r a i g h t f o r w a r d , c o n s i s t i n g o f t h a t d u e t o t h e i r i s o t o p i c a b u n 

d a n c e , t h e r e l a t i v e e l e m e n t y i e l d , a n d f i n a l n o r m a l i z a t i o n . T h e 

e r r o r s f o r i n d i v i d u a l y i e l d s a r e c o r r e l a t e d b y b o t h t h e i r d e p e n 

d e n c e o n r e l a t i v e e l e m e n t s y i e l d s a n d t h e n o r m a l i z a t i o n r e q u i r e 

m e n t t h a t 2 y. = 1 . 0 0 0 . T h u s a c h a n g e w i t h i n t h e r a n g e a l l o w e d 

b y t h e e r r o r s f o r o n e y i e l d , s a y a n i n c r e a s e f o r o n e n u c l i d e i n

Fission 

Product 

А Л 

a ± Да 

- barns - 

TABLE III. FISSION-PRODUCT ABSORPTION IN THERM AL REACTOR FUELS 

33Bu 333v 

к; 

1+ 

Ду (%) 

b a r n s /fis s io n (total no. of absorptions in nuclide ? (total 

fis s io n s x irradiatio n)3 

339pu 341Pu 336Ub 

азбуЬ 

э 

339 Pu Nat 

he азбцЬ 

a3 9pub a41Pub Nat U + P U ^ Th+333b 

13БХе (345+14) 104 6 .6 0 + .1 6 6 .2 1 + .1 5 7 .6 9 + .2 4 7 .0 6 + .2 4 82 .4 + 2 . 0 1 3 .0 6 40. 5 2 2 .7 + .4 7 .7 1 17.7 2 1 6 .3 2 1 6 .6 6 + .5 0 1 2 .8 4 + .3 2 

143Nd 329+10 5 .9 5 + . 08 5 .8 5 * .1 0 4 .5 3 + .0 6 4 .5 2 + .0 6 7 .7 2 + .2 2 7 .5 4 5.97 6 .4 7 + .1 9 6 .8 9 5.47 5 .4 5 5 .9 8 + .1 7 6 . 2 6+ .19 

149Sm (6 9 + 2 )103 1 .0 % + .0 7 .7 6 5 + .0 2 1 1 .2 9 + .0 5 1 .4 4 + .0 4 1 7 .2 + 1 .1 3 .5 2 9 .0 0 5 .4 9 + .2 5 2 .3 4 4. 38 4 .8 1 4 .3 3 + .1 8 2. 54+. 07 

103Rh 221+10 3 .0 5 + .2 0 1 . 8 + . 3 5 .9 4 + .2 9 6 .6 5 + .7 0 1 .9 2 + .1 4 2 .6 9 4 .9 2 3 .7 4 + .2 5 2 .6 0 5 .0 3 5 .6 4 4 .6 3 + .3 4 1 .6 3 + .2 8 

1 5lSm (1 3 + 1 )103 .4 1 9 + .0 2 7 .3 1 4 + .0 0 8 .8 2 0 + .0 2 9 .882+.. 024 6 .9 2 ^ .4 4 1 .6 8 5 .7 0 3 .0 7 + .1 4 1.2 7 3.0 1 3 .2 6 2 .7 5 + .1 1 1 .2 6 + .0 3 

l47Pm 311+35 2 .2 6 + .0 4 1 .7 0 + .0 5 2 .1 6 + .0 7 2 .2 0 + .0 6 2 .8 3 + .2 8 2 .3 0 2 .4 7 2 .1 7 + .2 2 1 .9 5 2 .0 4 2 .0 8 2 .0 9 + .2 1 1.63+'. 16 

131Xe 153+15 2 .8 0 + .0 7 3 .5 3 + .0 8 3 .7 3 + .0 9 3 .1 2 + .0 7 1 .6 1 + .1 5 1 .8 6 2 .4 2 2 .1 3 + .2 0 1 .7 9 2 .4 0 2 .0 1 2 .4 0 + .2 8 2 .5 3 + .2 5 

133Cs 58.4 + 3 . 6 .7 8 + .1 6 5.99;+. 21 6 .9 2 + .1 7 6. 72+ .18 1 .8 2 + .1 0 1.8 7 1 .9 0 1 .8 8 + .1 1 1 .8 5 1 .8 9 1 .8 3 2 .1 6 + .1 3 2 .0 4 + .1 3 

16aSm 399¿15 .267+ .0 1 7 .2 1 3 + .0 0 6 .6 2 4 + .0 2 2 .6 9 7 + .0 1 9 1 .1 2 + .0 8 1 .1 6 2 .3 8 1. 65+. 08 1.1 1 2 .2 2 2 .4 3 2 .0 1 + .1 0 0 .9 6 + .0 4 

10BRh (1 8 + 2 )103 .9 5 + .2 0 .5 3 + .1 0 5 .4 7 + .1 6 6 .7 5 + .7 0 1 .3 0 + .2 8 0 .2 0 3 .1 6 1 .1 6 + .0 8 0 .1 2 1 .3 8 1 .7 0 1 .0 6 + .0 9 0 .1 2 + .0 3 

14eNd 61+6 3 .9 3 + .0 6 3 .3 8 + .0 6 3.06+.04 3 .2 2 + .0 4 1 .1 9 + . 12 1 .1 5 0 .9 1 1 .0 5 + .1 1 1 .1 3 0 .8 9 0 .9 4 1 .1 0 + .1 2 1 .1 0 + .1 1 

9»TC 35+4 6 . 14+. 09 5. 01+.. 10 6 .1 & + .3 6 6 .2 0 + .1 2 1 .0 3 + .1 2 1 .0 4 1 .0 3 1 .0 5 + .1 3 1 .0 3 1 .0 3 1 .0 4 1 .1 9 + .1 2 1 .0 1 + .1 2 

lS3Eu 546+2 5 .1 6 7 + .0 1 1 .1 0 5 + .0 0 5 . 3 8 + .01 .522+.022 0.48+.04 0.67 1.30 1 .0 0 + .0 6 0.73 1.47 1.79 1.43+.08 0.62+.04 

l48> pm (24+ )103 (from capture in 147 Pm) 0.94+.10 0.85 0.88 0.79+.08 0.73 0.75 0.77 0.77+.08 0.60+.06 

15BEu 4200+200 .0321+.002 .023+.005 .17+.02 .231+.022 0.40+.03 0.35 1.28 0.78+. 09 0.44 1.15 1.49 1.16+.13 0.41+.09 

160Sm 115+5 (from capture in 149 5m) 0.5%b.05 0.65 0.74 0.72+.05 0.66 0.75 0.83 0.83+.04 0.51¿ .02 

lS4Eu 1500+150 .074+.005 .046+.001 .2 8 6 + .011 .378+.010 0. 09+. 01 0.37 0. 55 0.57+.06 0.48 0 .8 9 1.10 0.97+.09 0.42+.04 

lo9Ag 185+13 .030+.006 .047+.005 1.3+0.2 2.5+. 5 0.03 0.03 1.16 0.47+.07 0.02 1.09 2.10 0.82+.13 0.04 

9'Mo 20.9+1.5 6.53+.10 6.19+.10 4 .98+ .0 8 3.98+. 09 0.15+.01 0.53 0.30 0.46+.03 0. 58 0.40 0,32 0.53+.04 0.61+.04 

a3Kr 210+10 .535+.013 1.00+.02 .295+.007 .202+.. 005 0.54+.03 0.48 0.28 0. 38+. 02 0.45 0.26 0.18 0.33+.01 0.82+.05 

>149 27.54+1.79 8.88 22.35 14.04+.65 7.54 14.88 16.90 14.39+.60 6.8 9 + .1 9 

Total F issio n product 134.4 44.8 92.0 6 1 .8 26.7 5 8 .6 61.2 57.3 41.6 

a integrated fissio n s and absorptions taken from LATREP (Nat U, Nat U+Pu, Th+a33U), pure f is s ile atom values are approximations (0.5 x barns 

per fissio n at m id-irradiation) using FISSPROD. A ll fluxfes 3 x 1013n/cmas 

b pure a36U fuel irradiated to 0.6 n/kb; Nat U (with a36U, a39Pu components) to 2.6 n A b j Nat U + Pu (with 335U, 339Pu, 341Pu components) 

to 3.6 п Д Ь ; Th+a33U to 4.0 п Д Ь . in the enriched fuels the Nat U contains 3.5 g f i s s i l e P u A s and the Th 14 g a 3 3 u A g . 

с The fraction of fissio n s contributed are as follow s - Nat U: a3BU,44.4%; a3®Pu,46.2%? a3eU .5.8^6? 341Pu.3.5% - Nat U -f Pu? a3Bu 28 !%• 

839PU,54.2%; 341P u , ll. a3eU,5.9% 

466 W ALKER

I A E A - S M -1 7 0 /3 4 

t h e h e a v y m a s s g r o u p , w i l l r e q u i r e a c o m p a r a b l e i n c r e a s e i n t h e 

y i e l d s o f o t h e r i s o t o p e s o f t h e s a m e e l e m e n t ( a s s u m i n g t h e 

i s o t o p i c a b u n d a n c e e r r o r is small) a n d a c o r r e s p o n d i n g d e c r e a s e 

i n s o m e o r a l l o f t h e o t h e r e l e m e n t s i n t h e h e a v y m a s s r a n g e t o 

k e e p Z y ^ = 1 . 0 0 0 . 

T h e u s e o f y i e l d e r r o r s t o o b t a i n u n c e r t a i n t i e s i n f i s s i o n 

p r o d u c t a b s o r p t i o n is o f c o n s i d e r a b l e i n t e r e s t s i n c e i t i n d i c a t e s 

w h e r e f u t u r e e f f o r t s c a n m o s t f r u i t f u l l y b e c o n c e n t r a t e d . 

T h e b a s i c d a t a a n d e s t i m a t e d u n c e r t a i n t i e s ( o n e s t a n d a r d 

d e v i a t i o n ) a r e s u m m a r i z e d i n T a b l e III. T h e f i r s t c o l u m n l i s t s 

t h e 2 0 m o s t i m p o r t a n t f i s s i o n p r o d u c t s i n t h e i r o r d e r o f i m p o r 

t a n c e a s d e t e r m i n e d b y t h e i r a v e r a g e a b s o r p t i o n i n n a t u r a l u r a n i u m 

i r r a d i a t e d i n a C A N D U r e a c t o r o f t h e P i c k e r i n g d e s i g n . O t h e r 

d e f i n i t i o n s o f t h e r m a l f i s s i o n p r o d u c t i m p o r t a n c e w o u l d r e q u i r e 

o n l y m i n o r c h a n g e s i n t h e o r d e r o f t h e l i s t a n d t h e n u c l i d e s 

i n c l u d e d . 

T h e s e c o n d c o l u m n l i s t s e f f e c t i v e c r o s s s e c t i o n s i n t h e 

s a m e r e a c t o r u s i n g t h e n o t a t i o n o f W e s t c o t t e t al. [6] 

л / 

cr = ct0 ( g + r s ) 

w h e r e a 0 i s t h e 2 2 0 0 m / s c r o s s s e c t i o n , g a 0 i s t h e e f f e c t i v e 

c r o s s s e c t i o n i n a M a x w e l l i a n f l u x , r is t h e e p i t h e r m a l i n d e x 

( p r o p o r t i o n a l t o t h e f r a c t i o n o f n e u t r o n d e n s i t y i n t h e e p i 

t h e r m a l r a n g e ) a n d s Œ l ' / c 0 , w h e r e I ' is t h e r e s o n a n c e i n t e g r a l 

l e s s t h e l / v c o n t r i b u t i o n f r o m g a 0 . T h e v a l u e s o f a a n d t h e i r 

a s s i g n e d u n c e r t a i n t i e s a r e b a s e d o n t h e e v a l u a t i o n o f a 0 a n d i' 

[7] a s s o c i a t e d w i t h t h e y i e l d e v a l u a t i o n d i s c u s s e d h e r e , a n d 

r = . 0 5 7 . 

T h e n e x t f o u r c o l u m n s l i s t t h e r e c o m m e n d e d y i e l d s o f [1] 

w i t h t h e i r o v e r a l l e r r o r , t a k e n a s t h e s q u a r e r o o t o f t h e s u m o f 

t h e s q u a r e s o f t h e 3 c o m p o n e n t s a l r e a d y d e s c r i b e d . 

T h e r e m a i n i n g c o l u m n s l i s t t h e c o n t r i b u t i o n s o f t h e s e 

f i s s i o n p r o d u c t s i n a v a r i e t y o f p o s s i b l e t h e r m a l r e a c t o r f u e l s - 

2 3 5 U a l o n e , n a t u r a l U , n a t u r a l U w i t h P u , a n d T h w i t h 3 3 3 u - a s 

w e l l a s i n t h e m a i n f i s s i l e c o m p o n e n t s o f t h e t w o n a t u r a l U f u e l s . 

T h e m i x e d f u e l c a l c u l a t i o n s u s e a n e w v e r s i o n [ 8 ] o f L A T R E P [9] 

a n d t h e q u o t e d v a l u e s a r e a b s o r p t i o n i n b a r n s / f i s s i o n u s i n g t h e 

t o t a l n u m b e r o f a b s o r p t i o n s i n t h e n u c l i d e d i v i d e d b y t h e p r o d u c t 

o f t h e i r r a d i a t i o n a n d t o t a l f i s s i o n s . T h e c o m p o n e n t c o n t r i 

b u t i o n s ( c o l u m n s 8, 9, 1 1 , 1 2 a n d 13) a r e a p p r o x i m a t i o n s b a s e d 

o n F I S S P R O D [ 1 0 ] c a l c u l a t i o n s u s i n g a v a l u e e q u a l t o h a l f t h e 

c a l c u l a t e d b a r n s p e r f i s s i o n a t m i d - i r r a d i a t i o n . 

T h e f i s s i o n p r o d u c t s m a y b e s e p a r a t e d f o r c o n v e n i e n c e i n t o 

t h r e e c a t e g o r i e s d e p e n d i n g o n t h e m a g n i t u d e o f (X+ct0)T, w h e r e \ 

i s t h e d e c a y c o n s t a n t , 0 i s t h e f l u x a n d T i s t h e i r r a d i a t i o n 

467

468 W ALKER 

p e r i o d . T h e t h r e e g r o u p s a r e r a p i d l y s a t u r a t i n g , p a r t i a l l y 

s a t u r a t i n g o r n o n - s a t u r a t i n g d e p e n d i n g o n w h e t h e r (\+§ 0)T i s m u c h 

g r e a t e r t h a n , o f t h e s a m e o r d e r as, o r m u c h s m a l l e r t h a n u n i t y . 

T h e d e p e n d e n c e o f t h e a b s o r p t i o n o f a p a r t i c u l a r f i s s i o n 

p r o d u c t o n i t s c r o s s s e c t i o n , a n d c o n s e q u e n t l y t h e d e g r e e t o 

w h i c h i t i s s e n s i t i v e t o A a d e p e n d s o n t h e d e g r e e o f s a t u r a t i o n . 

T h e u n c e r t a i n t y ^ i n Ù m a y b e i g n o r e d f o r r a p i d l y s a t u r a t i n g f i s s i o n 

p r o d u c t s w i t h а ф » \ , r e q u i r e s a p a r t i a l w e i g h t i n g f o r p a r t i a l l y 

s a t u r a t i n g f i s s i o n p r o d u c t s o r r a p i d l y s a t u r a t i n g f i s s i o n 

p r o d u c t s w i t h §0~\, a n d f u l l w e i g h t f o r n o n - s a t u r a t i n g f i s s i o n 

p r o d u c t s , o r i f 0 ф « \ . 

E f f e c t o f Y i e l d C o r r e l a t i o n s 

B e c a u s e o f t h e c o r r e l a t i o n s b e t w e e n y i e l d s i t is i m p o s s i b l e 

t o c a l c u l a t e t h e u n c e r t a i n t y i n t h e t o t a l f i s s i o n p r o d u c t a b s o r p 

t i o n . T o i l l u s t r a t e t h e w i d e r a n g e o f e f f e c t s t o b e e x p e c t e d 

b e c a u s e o f t h e s e c o r r e l a t i o n s c o n s i d e r t w o c a s e s a s s o c i a t e d w i t h 

1 3 S X e a n d 1 4 9 S m . 

I n t h e 1 3 5 X e c a s e , t h e y i e l d s a r e b a s e d o n s i n g l e m e a s u r e 

m e n t s o f t h e r e l a t i v e a b u n d a n c e o f t h e d a u g h t e r , 1 3 B C s , f o r e a c h 

o f t h e f i s s i l e n u c l i d e s e x c e p t S 3 S P u , w h e r e t h r e e m e a s u r e m e n t s 

a r e a v a i l a b l e . B e c a u s e n a t u r a l l y o c c u r r i n g C s i s e n t i r e l y 1 3 3 C s , 

w h i c h i s a l s o a h i g h y i e l d f i s s i o n p r o d u c t , i s o t o p e d i l u t i o n 

m e a s u r e m e n t s o f t h e r e l a t i v e y i e l d o f C s a r e d i f f i c u l t a n d t h e s e 

h a v e a n u n c e r t a i n t y e x c e e d i n g 2 % f o r b o t h f i s s i l e P u i s o t o p e s . 

I n t h e c a s e o f n a t u r a l U i t i s a r e a s o n a b l y g o o d a p p r o x i 

m a t i o n t o a s s u m e t h a t t h e u n c e r t a i n t y i s 2-|% a n d e n t i r e l y d u e t o 

t h e u n c e r t a i n t y i n t h e r e l a t i v e C s y i e l d . I t t h u s a p p l i e s t o a l l 

y i e l d s b a s e d o n C s ( m a s s e s 1 3 3 , 1 3 5 a n d 1 3 7 ) w h i c h t o t a l ~ 2 0 % 

a n d h a v e a n a b s o r p t i o n i n n a t u r a l U o f 2 4 . 7 b / f i s s i o n . T h u s , if 

t h e C s y i e l d s w e r e i n c r e a s e d t h e f u l l 2 ^ % t h e a b s o r p t i o n w o u l d 

i n c r e a s e b y 0 . 6 2 b / f i s s i o n . O n t h e o t h e r h a n d t h e r e m a i n i n g 8 0 % 

o f t h e h i g h m a s s y i e l d w o u l d h a v e t o b e r e d u c e d b y 0 . 6 % t o k e e p 

2 y. = 1 0 0 % . S i n c e t h e s e c o n t r i b u t e a b o u t 2 8 b / f i s s i o n t o t h e 

t o t a l a b s o r p t i o n , t h e n e t i n c r e a s e i n a b s o r p t i o n i s o n l y 0 . 4 5 

b / f i s s i o n , o r l e s s t h a n 3 / 4 w h a t i t w o u l d b e w i t h o u t t h e r e q u i r e 

m e n t t h a t 2 y ^ = 1 0 0 % . 

T h e s e c o n d e x a m p l e c o n c e r n s 1 4 9 S m , o r r a t h e r , a b s o r p t i o n 

i n a l l t h e m a s s e s f r o m 1 4 9 u p , s i n c e t h e s e a r e t i g h t l y l i n k e d 

t o g e t h e r b y c a p t u r e t r a n s m u t a t i o n s . I n t h e c a s e o f ЭЗБи f i s s i o n , 

t h e S m a n d E u i s o t o p i c a b u n d a n c e s w e r e m e a s u r e d r e l a t i v e t o e a c h 

o t h e r s o i n t h i s c a s e t h e r e is a d d i t i o n a l r e a s o n f o r t r e a t i n g 

t h i s g r o u p a s a s i n g l e u n i t . F u r t h e r , t h e r e a p p e a r s t o b e a g r e a t 

d e a l o f s y s t e m a t i c u n c e r t a i n t y b e t w e e n t h e d i f f e r e n t i s o t o p e 

d i l u t i o n m e a s u r e m e n t s , s o t h a t t h e r e l a t i v e S m - E u y i e l d s a r e 

a s s i g n e d a n e r r o r o f 6 % i n 2 3 5 u f u e l . S i n c e t h i s g r o u p c o n t r i 

b u t e s 2 7 . 5 b / f i s s i o n ( 2 n d t o l a s t l i n e i n T a b l e III) t h e i n c r e a s e

I A E A - S M -1 7 0 /3 4 469 

i n a b s o r p t i o n i s 1 . 6 5 b / f i s s i o n . O n t h e o t h e r h a n d , t h e t o t a l 

y i e l d f o r t h i s g r o u p i s o n l y 2 . 7 % s o t h e c o m p e n s a t i n g d e c r e a s e 

i n t h e r e m a i n i n g h e a v y m a s s e s w i l l b e s m a l l . A s s u m i n g t h e o t h e r 

y i e l d s a r e d e c r e a s e d u n i f o r m l y t h e e f f e c t is a p p r o x i m a t e l y 

0 . 0 6 x 0 . 0 2 7 x 1 0 0 o r 0 . 1 5 b / f i s s i o n , s o t h a t t h e n e t i n c r e a s e 

i s 1 . 5 b / f i s s i o n . 

I t is a p p a r e n t t h a t t h e c o r r e l a t i o n s b e t w e e n y i e l d s w i l l 

h a v e d i f f e r e n t e f f e c t s o n d i f f e r e n t f u e l s , d e p e n d i n g o n t h e 

m a g n i t u d e s o f t h e y i e l d s a n d t h e i r c o r r e s p o n d i n g a b s o r p t i o n . 

I n t h e c a s e o f i s o t o p e s o f e l e m e n t s w i t h l a r g e y i e l d s a n d l o w 

a b s o r p t i o n , f o r e x a m p l e Z r o r c e , a y i e l d i n c r e a s e m a y e v e n 

r e s u l t i n a d e c r e a s e i n a b s o r p t i o n . 

E f f e c t o f Y i e l d U n c e r t a i n t i e s i n R e a c t o r D y n a m i c C a l c u l a t i o n s 

Y i e l d u n c e r t a i n t i e s a l s o a f f e c t c a l c u l a t i o n s o f 1 3 5 X e 

o s c i l l a t i o n s i n l a r g e t h e r m a l r e a c t o r s , a n d t h e 1 3 5 X e , 1 0 S R h , 

1 4 9 S m a n d 1 5 1 S m t r a n s i e n t b e h a v i o u r f o l l o w i n g r e a c t o r s h u t d o w n . 

I n t h e s e c a s e s t h e u n c e r t a i n t y i n c r o s s s e c t i o n s c a r r y t h e i r 

f u l l w e i g h t . T h e c o s t o f t h e s e u n c e r t a i n t i e s w i l l d e p e n d n o t 

o n l y o n t h e t y p e o f r e a c t o r b u t a l s o o n t h e m e t h o d o f c o n t r o l 

u s e d ( e . g . i n s e r t i o n o f b o o s t e r s , r e m o v a l o f a b s o r b e r s ) . 

I t s h o u l d b e n o t e d , h o w e v e r , t h a t t h e c o s t o f o v e r r i d i n g 

t h e 1 3 5 X e a n d 1 0 B R h t r a n s i e n t a f t e r s h u t d o w n w i l l p r o b a b l y b e 

l e s s i n r e a c t o r s f u e l l e d w i t h 3 3 3 U , n o t o n l y b e c a u s e t h e c u m u 

l a t i v e y i e l d s o f b o t h n u c l i d e s a r e s m a l l e r , b u t b e c a u s e t h e 

d i r e c t y i e l d o f 1 3 6 X e i s m u c h l a r g e r i n t h i s f u e l t h a n in 

n a t u r a l U - 2 2 % d i r e c t t o X e , o n l y -%-78% c u m u l a t i v e t o I [ 1 1 , 12] 

T o c o n c l u d e t h i s s e c t i o n o n t h e e f f e c t s o f y i e l d u n c e r t a i n 

t i e s , I w o u l d l i k e t o n o t e t h a t a n e s t i m a t e o f u n c e r t a i n t i e s in 

f i s s i o n p r o d u c t a b s o r p t i o n w a s m a d e p r e v i o u s l y [ 1 3 ] a l t h o u g h 

t h e s c o p e w a s r e s t r i c t e d t o S 3 3 u, 3 3 5 U, a 3 s P u a n d n a t u r a l U. 

I n c o m p a r i s o n w i t h t h a t a n a l y s i s , i t w o u l d a p p e a r t h a t w e a r e a 

l i t t l e l e s s s u r e o f t h e m a g n i t u d e o f f i s s i o n p r o d u c t a b s o r p t i o n , 

m a i n l y b e c a u s e o f t h e i n c r e a s e ( b y a f a c t o r o f t w o ) i n t h e 

u n c e r t a i n t y i n S m y i e l d s i n 3 3 5 U f i s s i o n . T h i s , i n t u r n , c a n 

b e a t t r i b u t e d t o t h e i n c l u s i o n o f t h e 1 9 7 0 r e s u l t s o f L i s m a n e t 

al. [ 4 ] . 

F U T U R E R E Q U I R E M E N T S 

T a b l e III i s a u s e f u l i n d i c a t o r o f w h e r e t h e m a j o r e f f o r t 

i n i m p r o v i n g f i s s i o n p r o d u c t y i e l d s is r e q u i r e d , a l t h o u g h i t 

d o e s n o t c o v e r a l l t h e s h o r t c o m i n g s i n y i e l d m e a s u r e m e n t s . 

T a b l e I V l i s t s t h e s i x f i s s i o n p r o d u c t s h a v i n g t h e g r e a t e s t 

u n c e r t a i n t y i n a b s o r p t i o n i n n a t u r a l U f u e l , w i t h t h e i r u n c e r 

t a i n t i e s i n n a t u r a l U , n a t u r a l U p l u s P u a n d T h p l u s 2 3 3 U. F o r

470 W ALKER 

T A B L E IV. M A J O R S O U R C E S O F U N C E R T A I N T Y IN A B S O R P T I O N 

IN R E A C T O R F U E L S 

N u c l i d e A b s o r p t i o n U n c e r t a i n t y ( b a r n s / f i s s i o n ) i n 

N a t u r a l U N a t u r a l U + P u T h + 2 3 3 U 

> 1 4 9 0 . 6 5 0 . 6 0 0 . 1 9 

(1 4 9 S m ) ( 0.25) ( 0 . 1 8 ) ( 0.07) 

1 3 5 X e 0 . 4 4 0 . 5 0 0 . 3 2 

1 0 3 R h 0 . 2 5 0 . 3 4 0 . 2 8 

1 4 7 P m * 0 . 2 2 0 . 2 1 0 . 1 6 

1 3 1 X e * 0 . 2 0 0 . 2 8 0 . 2 5 

1 4 3 N d * 0 . 1 9 0 . 1 7 0 . 1 9 

* M o s t o f t h e u n c e r t a i n t y i s c o n t r i b u t e d b y t h e c r o s s s e c t i o n 

s e v e r a l o f t h e s e n u c l i d e s t h e m a j o r c o n t r i b u t o r t o t h e u n c e r 

t a i n t y i s t h e c r o s s s e c t i o n a n d t h e s e a r e i d e n t i f i e d w i t h a n 

a s t e r i s k . 

T h e u n c e r t a i n t i e s i n t h e > 1 4 9 m a s s g r o u p a n d 1 3 5 X e a r e 

d u e p r i m a r i l y t o u n c e r t a i n t y i n t h e y i e l d s o f S m a n d C s , 

r e s p e c t i v e l y , r e l a t i v e t o N d . F o r 1 0 3 R h t h e y i e l d is b a s e d o n 

l i m i t e d r a d i o m e t r i c d a t a . 

T h e s e a r e t h e t h r e e m a j o r s o u r c e s o f u n c e r t a i n t y . O f 

s o m e w h a t l e s s i m p o r t a n c e a r e t h e u n c e r t a i n t i e s ( ~ 1 0 % ) i n t h e 

1 4 7 P m a n d 1 3 1 X e c r o s s s e c t i o n s . I n t h e c a s e o f 1 4 3 N d , t h e l a s t 

e n t r y , t h e c r o s s s e c t i o n is a l r e a d y k n o w n t o +_ 3%, s o t h a t a 

m a j o r e f f o r t w o u l d b e r e q u i r e d t o r e d u c e t h i s u n c e r t a i n t y 

s i g n i f i c a n t l y . . ■ 

I n a d d i t i o n t o t h e u n c e r t a i n t i e s i n t h e C s a n d S m y i e l d s 

t h e r e a r e l a r g e d i f f e r e n c e s i n m a s s s p e c t r o m e t r i c m e a s u r e m e n t s 

o f t h e 1 3 8 B a y i e l d s f o r b o t h 2 3 9 P u (15%) a n d 2 4 1 P u ( 7 . 5 % ) [ 1 ] . 

N o r c a n t h e 2 4 1 P u y i e l d s b e c o n s i d e r e d s a t i s f a c t o r y f o r m a n y o t h e r 

m a s s e s . T h e r e i s o n l y o n e s e t o f m a s s s p e c t r o m e t r i c m e a s u r e m e n t s 

f o r t h e l i g h t m a s s e s [ 4 ] . T h e s e d o n o t i n c l u d e M o , w h i c h c o v e r s 

t h e l i g h t m a s s p e a k , a n d t h e R u y i e l d s w e r e d e t e r m i n e d r a d i o - 

m e t r i c a l l y r e l a t i v e t o 1 3 7 C s . A l s o t h e r e a r e o n l y t h r e e r a d i o - 

m e t r i c m e a s u r e m e n t s c o v e r i n g t h e m a s s r a n g e f r o m 1 0 7 t o 1 3 0 s o 

t h a t t h e r e is c o n s i d e r a b l e u n c e r t a i n t y i n t h e f i n a l n o r m a l i z a t i o n 

o f m a s s s p e c t r o m e t r i c d a t a . 

W h a t i s r e q u i r e d t o m i n i m i z e t h e r e m a i n i n g u n c e r t a i n t i e s is 

a t w o - p r o n g e d a s s a u l t u s i n g m a s s s p e c t r o m e t r i c m e t h o d s t o i m p r o v e 

S 3 6 U y i e l d s a n d r a d i o m e t r i c m e a s u r e m e n t s o f y i e l d s o f 2 3 3 U, 2 3 9 P u 

a n d 2 4 1 P u r e l a t i v e t o t h o s e o f 23Би.

M a s s S p e c t r o m e t e r M e a s u r e m e n t s 

I A E A - S M -1 7 0 /3 4 

S i n c e t h e m a i n s o u r c e o f u n c e r t a i n t y i n m a s s s p e c t r o m e t r i c 

d e t e r m i n a t i o n s o f C s , B a a n d S m y i e l d s a p p e a r s t o b e s y s t e m a t i c 

d i f f e r e n c e s i n t h e i s o t o p e d i l u t i o n m e t h o d , a m o r e p r o m i s i n g 

a p p r o a c h i s t o u s e i s o b a r i c c o u p l i n g . S i n c e t h i s i s a m e t h o d 

u s e d p r e v i o u s l y b y F a r r a r a n d T o m l i n s o n [ 1 4 ] f o r a 3 5 u y i e l d s , 

I a m , t h e r e f o r e , s u g g e s t i n g a n i n d e p e n d e n t c h e c k o f t h e i r r e s u l t s . 

I f g o o d a g r e e m e n t is o b t a i n e d I f e e l t h e s e r e s u l t s s h o u l d b e u s e d 

i n p r e f e r e n c e t o t h o s e o b t a i n e d b y i s o t o p e d i l u t i o n . 

T h e l i n k s t o b e u s e d a r e s h o w n i n F i g u r e 1 ( a ) , n a m e l y 1 3 7 C s - 

1 3 7 B a , 1 4 0 B a - 1 4 0 C e , a n d 1 4 7 N d - 1 4 7 S m . B e c a u s e o f t h e l o n g h a l f - 

l i f e o f 1 3 7 C s ( 3 0 y) a n o l d s a m p l e o f i r r a d i a t e d 3 3 5 U w o u l d b e 

b e s t f o r m e a s u r i n g t h e 1 3 7 B a r e l a t i v e a b u n d a n c e . 

T h e s h o r t - i r r a d i a t i o n B a m e a s u r e m e n t t o o b t a i n t h e 1 4 0 B a 

r e l a t i v e a b u n d a n c e s h o u l d a l s o b e u s e d t o c h e c k w h e t h e r n a t u r a l 

B a is p r e s e n t s i n c e t h i s is a p o s s i b l e e x p l a n a t i o n o f s o m e o f 

t h e d i s c r e p a n c i e s o b s e r v e d . 

T h e u n c e r t a i n t y i n t h e m a s s 1 0 3 y i e l d f r o m 23Би f i s s i o n i s 

d u e t o a l a c k o f a n y m a s s s p e c t r o m e t r i c d a t a , a n d i t s h o u l d b e 

q u i t e s t r a i g h t f o r w a r d t o d e t e r m i n e t h e r e l a t i v e a b u n d a n c e o f 

4 0 - d 1 0 3 R u a s h a s a l r e a d y b e e n d o n e f o r t h e r m a l f i s s i o n o f s 3 9 P u 

[ 1 5 ] . 

S i n c e t h e r e h a s b e e n o n l y o n e i s o t o p e d i l u t i o n m e a s u r e m e n t 

g i v i n g t h e y i e l d o f R u r e l a t i v e t o Z r i n a 3 5 u f i s s i o n [ 4 ] , i t is 

u n f o r t u n a t e t h a t t h e r e is n o c o n v e n i e n t i s o b a r i c l i n k b e t w e e n M o 

a n d Zr. T h i s i s b e c a u s e t h e t w o l o n g e s t - l i v e d f i s s i o n p r o d u c t 

i s o t o p e s o f M o a r e 6 6 - h 9 9 M o a n d 1 4 . 6 - m 1 0 1 M o . T h e l a t t e r is t o o 

s h o r t - l i v e d a n d t h e f o r m e r d e c a y s t o 1 0 6 - y 9 S T c w h i c h i n t e r c e p t s 

t h e l i n k t o R u . 

R a d i o m e t r i c M e a s u r e m e n t s 

A s s u m i n g t h a t t h e a b o v e r e c o m m e n d a t i o n s a r e a c t e d o n a n d a r e ■ 

s u c c e s s f u l i n r e d u c i n g u n c e r t a i n t i e s i n 2 3 S u y i e l d s , t h e s e c o n d 

p r o n g o f t h e a t t a c k i s t h e r a d i o m e t r i c m e a s u r e m e n t o f y i e l d s o f 

a w i d e r a n g e o f r a d i o a c t i v e n u c l i d e s f o r o t h e r f i s s i l e n u c l i d e s 

r e l a t i v e t o t h o s e i n 3 3 E u t h e r m a l f i s s i o n . 

T h e m e a s u r e m e n t o f r e l a t i v e y i e l d s r a d i o m e t r i c a l l y is b y n o 

m e a n s n e w . H o w e v e r , i n c o m p a r i n g t h e r e s u l t s o f r e l a t i v e r a d i o - 

m e t r i c y i e l d m e a s u r e m e n t w i t h m a s s s p e c t r o m e t r i c y i e l d s w h e r e 

t h a t is p o s s i b l e , t h e r e a r e e n o u g h d i s a g r e e m e n t s t o c o n v i n c e m e 

t h a t a s i g n i f i c a n t f r a c t i o n i s f r e q u e n t l y l o s t , f r o m o n e s a m p l e 

o r t h e o t h e r , i n e x t r a c t i n g a p a r t i c u l a r e l e m e n t f r o m d i f f e r e n t 

f i s s i l e s a m p l e s . 

A t y p i c a l p h y s i c i s t ' s a p p r o a c h t o t h i s d i f f i c u l t p r o b l e m i s 

s i m p l y t o l e a v e t h e f i s s i l e s a m p l e s e a l e d a n d u s e a G e ( L i ) 

471

472 W ALKER 

d e t e c t o r t o s o r t o u t t h e y - r a y s . F o r t h o s e w h o b e l i e v e t h a t 

t h i s a p p r o a c h is i n c a p a b l e o f s u f f i c i e n t a c c u r a c y I n o t e t h a t 

i t w a s u s e d s u c c e s s f u l l y a s l o n g a g o a s 1 9 6 5 t o d e t e r m i n e t h e 

d i r e c t y i e l d s o f 1 3 5 X e i n t h e r m a l f i s s i o n o f 2 3 3 U , 3 3 S U , 2 3 9 P u 

a n d 3 4 1 P u [ 1 2 ] . 

F i g u r e 2 i s a c o m p o s i t e o f f i g u r e s f r o m t h a t p a p e r a n d 

s h o w s t h e s e p a r a t i o n a n d a c c u r a c y a c h i e v a b l e w i t h a r e s o l u t i o n 

o f o n l y 3 . 4 k e V ( F W H M ) a t 2 5 0 k e V . W i t h t h e r e s o l u t i o n s n o w 

a v a i l a b l e , a n d i m p r o v e d e l e c t r o n i c s , r a t i o s o f 1 - 2 p e r c e n t 

a c c u r a c y s h o u l d b e p o s s i b l e , e s p e c i a l l y u s i n g h i g h e r e n e r g y 

Y ~ r a y s a n d s o m e w h a t l o n g e r l i f e t i m e s . 

T h e p u r p o s e o f t h e s e m e a s u r e m e n t s w o u l d b e t o c h e c k t h e 

m a s s s p e c t r o m e t r i c a l l y d e t e r m i n e d r e l a t i v e e l e m e n t y i e l d s a t 

m a n y p o i n t s i n b o t h l i g h t a n d h e a v y m a s s p e a k s w i t h t h e m a i n 

e m p h a s i s o n r e s o l v i n g t h e d i s c r e p a n c i e s d i s c u s s e d . 

T a b l e V l i s t s s o m e o f t h e n u c l i d e s w i t h h a l f - l i v e s ( g e n e r 

a l l y > 1 d a y ) a n d Y _ r a y y i e l d s s u i t a b l e f o r t h e s e m e a s u r e m e n t s . 

I n t h e l i g h t m a s s r a n g e t h e u s u a l r e f e r e n c e n u c l i d e h a s b e e n 9 9 M o 

b u t 9 1 S r i s p r e f e r a b l e f o r t h e s e m e a s u r e m e n t s b e c a u s e i t i s a n 

i s o b a r o f 9 1 Z r , a n d Z r h a s b e e n m e a s u r e d m a s s s p e c t r o m e t r i c a l l y 

f o r a l l f o u r f i s s i l e n u c l i d e s a n d h a s b e e n u s e d a s t h e n o r m a l 

i z i n g e l e m e n t in [ 1 ] . 

I n t h e h e a v y m a s s r a n g e 1 4 0 B a is t h e u s u a l r e f e r e n c e 

s t a n d a r d a n d h a s c o n s i d e r a b l e m e r i t s i n c e i t c a n b e t i e d t o t h e 

C e y i e l d s t h r o u g h 1 4 0 C e . H o w e v e r , t h e C e y i e l d s a r e l e s s a c c u r a t e 

t h a n t h e N d y i e l d s , a n d 1 4 3 C e w o u l d b e a b e t t e r c h o i c e . 

O u t s i d e t h e m a s s s p e c t r o m e t e r m a s s r a n g e (83 t o 1 0 6 a n d 1 3 1 

t o 154) m o s t o f t h e y i e l d s a r e s m a l l a n d c h e m i c a l s e p a r a t i o n w i l l 

b e n e c e s s a r y b e c a u s e i n a s e a l e d c o n t a i n e r t h e i r y - r a y s w o u l d 

a l m o s t c e r t a i n l y b e s u b m e r g e d i n b a c k g r o u n d r a d i a t i o n . 

R e p o r t i n g o f R e s u l t s 

T o c o n c l u d e , I w o u l d l i k e t o m a k e a p l e a f o r f u l l d o c u m e n 

t a t i o n o f i r r a d i a t i o n c o n d i t i o n s , e l a p s e d t i m e s , c o r r e c t i o n 

f a c t o r s a n d a s s u m e d c o n s t a n t s in p r e s e n t i n g y i e l d d a t a i n o r d e r 

t o m a k e l i f e e a s i e r f o r f u t u r e e v a l u a t o r s , a n d , i n c i d e n t a l l y , t o 

e n s u r e t h a t t h e r e s u l t s w i l l n o t b e d i s c a r d e d . 

M a n y o f t h e e a r l y m e a s u r e m e n t s h a v e n o t b e e n u s e d b e c a u s e 

o f l a c k o f i n f o r m a t i o n o n c o r r e c t i o n s . A s t a t e m e n t t h a t t h e y i e l d 

h a s b e e n c o r r e c t e d " f o r d e c a y o f 2 8 2 - d a y 1 4 4 C e " is n o t m u c h u s e 

m a n y y e a r s l a t e r w h e n t h e h a l f - l i f e h a s c h a n g e d t o 2 8 4 . 4 d a y s .

RELATIVE COUNTING RATE-LINEAR SCALE 

I A E A - S M -1 7 0 /3 4 473 

GAMMA RAY ENERGY - keV 

F IG . 2 . F ission p r o d u c t y -r a y s fr o m ir ra d ia te d 233U a t 5 , 10 and 20 h ou rs a fte r th e en d o f th e ir r a d ia tio n . 

In set: G aussian fit to 135X e y - r a y .

474 W ALKER 

T A B L E V . N U C L I D E S F O R R A D I O M E T R I C M E A S U R E M E N T W I T H 

G e (Li) D E T E C T O R S 

N u c l i d e H a l f - l i f e M a i n Y - r a y s w i t h e n e r g i e s i n k e V 

a n d y i e l d s i n y ' s p e r 1 0 0 d e c a y s ( i n b r a c k e t s ) * 

9 x S r 9 . 6 7 h 5 5 1 ( 7 2 ) , 6 4 5 ( 1 4 ) , 7 4 8 ( 2 9 ) , 1 0 2 5 ( 3 0 ) , 1 4 1 3 ( 7 ) 

9 3 y 

1 0 . 2 h 2 6 7 ( 5 ) 

9 5 Zr 6 5 . 5 d 7 2 4 ( 4 4 ) , 7 5 7 ( 5 4 ) 

9 6 N b 3 5 . 1 d 7 6 5 ( 1 0 0 ) 

9 9 M O 2 . 7 8 d 7 5 0 ( 1 4 ) ; 1 4 9 ( 9 0 ) 

1 0 3 R u 3 9 . 8 d 4 9 7 ( 8 9 ) , 6 1 0 ( 5 ) 

1 06 R u 1 . 0 1 y n i l ; 5 1 2 ( 2 1 ) , 6 2 2 ( 1 0 ) 

1 3 1 I 8 . 0 7 d 3 6 4 ( 8 2 ) 

1 3 2 T e 3 . 2 5 d 5 0 ( 1 3 . 9 ) , 2 2 8 ( 8 5 ) ; 5 2 3 ( 1 7 ) , 6 3 0 ( 1 4 ) , 6 6 8 ( 1 0 1 ) 

7 7 3 ( 7 8 ) , 9 5 5 ( 1 9 ) 

1 3 a j 

2 1 h 5 3 0 ( 8 9 ) 

1 3 3 m x e 2 . 2 6 d 2 3 3 ( 1 4 ) 

1 3 3 X e 5 . 2 7 d 8 1 ( 3 7 ) 

13 7 C s 3 0 . 2 y 6 6 2 ( 8 5 ) 

1 4 0 B a 1 2 . 8 d 5 3 7 ( 2 4 ) ; 3 2 8 ( 2 4 ) , 8 1 6 ( 2 6 ) , 1 5 9 7 ( 1 1 0 ) , 2 5 2 2 ( 4 ) 

141 C e 3 2 . 5 d 1 4 5 ( 4 9 ) 

1 4 3 C e 1 . 3 8 d 5 7 ( 1 2 ) , 2 9 3 ( 4 0 ) , 6 6 8 ( 6 ) , 7 2 5 ( 7 ) 

1 4 4 C e 2 8 4 . 4 d 1 3 4 ( 1 1 ) ; 6 9 6 ( 1 . 5 ) , 2 1 8 6 ( 0 . 7 ) 

1 4 7 N d 1 1 . 0 6 d 9 1 ( 3 0 ) , 5 3 1 ( 1 3 ) 

149 P m 2 . 2 1 d 2 8 6 ( 3 ) 

1 6 1 P m 1 . 1 8 d 3 4 0 ( 2 3 ) 

1 5 3 S m 1 . 9 5 d 6 9 ( 6 ) , 1 0 3 ( 3 2 ) 

S e m i c o l o n s s e p a r a t e t h e d i r e c t Y - r a y s f r o m t h o s e o f s h o r t - l i v e d 

d a u g h t e r s t h a t a r e i n e q u i l i b r i u m w i t h t h e p a r e n t . 

* V a l u e s i n o r i g i n a l t a b l e w e r e c o r r e c t e d a f t e r t h e m e e t i n g . 

T h e d a t a s h o w n i s t a k e n f r o m M . J. M a r t i n a n d P. B. B l i c h e r t - T o f t 

( R a d i o a c t i v e a t o m s , A u g e r - e l e c t r o n , a- , ß-, y - , a n d x - r a y d a t a , 

N u c l e a r D a t a T a b l e s J3 ( 1 9 7 0 ) 1 ) s u p p l e m e n t e d b y C . M . L e d e r e r , 

J . M . H o l l a n d e r a n d I. P e r l m a n ( " T a b l e s o f I s o t o p e s " , 6 t h ed. ( 1 9 6 7 ) 

W y l i e a n d S o n s ) .

I A E A - S M -1 7 0 /3 4 475 

O n t h e o t h e r h a n d s o m e e a r l y m a s s s p e c t r o m e t e r m e a s u r e 

m e n t s o f S m r e l a t i v e a b u n d a n c e s i g n o r e d t h e h o l d - u p i n 1 1 - d 

1 4 7 N d a n d u s e d a n o u t - o f - d a t e h a l f - l i f e f o r 2 . 6 2 - y 1 4 7 Pm. 

H o w e v e r , b e c a u s e t h e i r r a d i a t i o n a n d c o o l i n g p e r i o d s w e r e 

s p e c i f i e d , c o r r e c t i o n s o f 2 . 4 % t o 8 % w e r e m a d e w h i c h b r o u g h t t h e 

a p p a r e n t l y d i s c r e p a n t r e s u l t s i n t o e x c e l l e n t a g r e e m e n t . 

R E F E R E N C E S '* 

[1] W a l k e r , W . H . , F i s s i o n p r o d u c t d a t a f o r t h e r m a l r e a c t o r s , 

A E C L - 3 0 3 7 , P a r t I I - Y i e l d s , ( 1 9 7 3 ) . 

[2] W a l k e r , W . H . , T h e e v a l u a t i o n o f f i s s i o n p r o d u c t y i e l d s , 

p r o c e e d i n g s o f t h e s e c o n d I A E A c o n f e r e n c e o n N u c l e a r 

D a t a f o r R e a c t o r s , ¿ ( 1 9 7 0 ) . 

[3] M e e k , M . E . , a n d R i d e r , B. F . , C o m p i l a t i o n o f f i s s i o n 

p r o d u c t y i e l d s , V a l l e c i t o s N u c l e a r C e n t e r - 1 9 7 2 

N E D O - 1 2 1 5 4 ( 1 9 7 2 ) . 

[ 4 ] L i s m a n , F. L . , A b e r n a t h y , R . M . , M a e c k , W . J . , R e i n , J. E . , 

F i s s i o n y i e l d s o f o v e r 4 0 s t a b l e a n d l o n g - l i v e d f i s s i o n 

p r o d u c t s f o r t h e r m a l n e u t r o n f i s s i o n e d 3 3 3 U , S 3 E U, 

a 3 9 P u a n d 3 4 1 P u , a n d f a s t r e a c t o r f i s s i o n e d 3 3 5 u a n d 

3 3 9 P u , N u c l . S e i . E n g n g 42^ ( 1 9 7 0 ) 1 9 1 . 

[5] S t e i n b e r g , E. P . , G l e n d e n i n , L . E . , S u r v e y o f r a d i o c h e m i c a l 

s t u d i e s o f t h e f i s s i o n p r o d u c t s , P r o c e e d i n g s o f t h e 

F i r s t G e n e v a C o n f e r e n c e o n P e a c e f u l U s e s o f A t o m i c 

E n e r g y 1_ ( 1 9 5 5 ) 3. 

[6] W e s t c o t t , C. H . , W a l k e r , W . H . , A l e x a n d e r , T . K . , 

E f f e c t i v e c r o s s s e c t i o n s a n d c a d m i u m r a t i o s f o r t h e 

n e u t r o n s p e c t r a o f t h e r m a l r e a c t o r s , P r o c e e d i n g s o f 

t h e S e c o n d G e n e v a C o n f e r e n c e o n P e a c e f u l U s e s o f 

A t o m i c E n e r g y 1 6 , 7 0 ( 1 9 5 8 ) . 

[7] W a l k e r , W . H . , F i s s i o n p r o d u c t d a t a f o r t h e r m a l r e a c t o r s , 

A E C L - 3 0 3 7 P a r t I - C r o s s S e c t i o n s ( 1 9 7 2 r e v i s i o n ) . 

[ 8] M i l g r a m , M . , T h e r e v i s i o n i n c l u d e s t h e p r o d u c t i o n a n d 

r e m o v a l o f 4 5 f i s s i o n p r o d u c t s a n d a d d i t i o n a l h e a v y 

e l e m e n t s f r o m T h t o C f . 

[ 9] P h i l l i p s , G. J . , G r i f f i t h s , J . , L A T R E P u s e r s m a n u a l , 

A E C L - 3 8 5 7 , ( 1 9 7 1 ) . 

[ 1 0 ] L a n e , F . , F I S S P R O D , a g ~ 2 0 c o m p u t e r p r o g r a m , A E C L - 3 0 3 8 

( 1 9 6 9 ) . 

A E C L -X X X X : R eport p u b lis h e d b y A t o m i c E n ergy o f C a n a d a L im ite d .

476 W ALKER 

[1 1 ] H a w k i n g s , R. C . , E d w a r d s , W . J . , O l m s t e a d , W . J . , 

I n d e p e n d e n t y i e l d s o f m a s s 1 3 5 x e n o n s i n t h e t h e r m a l 

n e u t r o n f i s s i o n o f 2 3 3 U , 2 3 5 U , 2 3 9 P u a n d a 4 1 P u , C a n . J. 

P h y s . 4 9 ( 1 9 7 1 ) 7 8 5 . 

[ 1 2 ] O k a z a k i , A . , W a l k e r , W . H . , B i g h a m , C. B . , T h e r a t i o o f 

t h e d i r e c t t o t h e c u m u l a t i v e y i e l d o f 13БХе i n t h e 

t h e r m a l n e u t r o n f i s s i o n o f 2 3 3 U , 2 3 B U , 2 3 9 P u a n d 2 4 1 P u , 

C a n . J. P h y s . 4 4 ( 1 9 6 6 ) 2 3 7 . 

[ 1 3 ] W a l k e r , W . H . , F i s s i o n p r o d u c t a b s o r p t i o n i n t h e r m a l 

r e a c t o r s , P r o c e e d i n g s o f t h e F i r s t I A E A C o n f e r e n c e o n 

N u c l e a r D a t a f o r R e a c t o r s JL ( 1 9 6 6 ) 521. 

[ 1 4 ] F a r r a r , H . , T o m l i n s o n , R. H . , C u m u l a t i v e y i e l d s o f h e a v y 

f r a g m e n t s i n 23Би t h e r m a l n e u t r o n f i s s i o n , N u c l . P h y s . 

3 4 ( 1 9 6 2 ) 3 6 7 . 

[ 1 5 ] F i c k e l , H . R . , T o m l i n s o n , R. H . , T h e c u m u l a t i v e f i s s i o n 

y i e l d s o f l i g h t m a s s f r a g m e n t s i n t h e t h e r m a l n e u t r o n 

f i s s i o n o f 3 3 9 P u , C a n . J. P h y s . _37 ( 1 9 5 9 ) 9 1 6 . 


W . F . S T U B B I N S : W h ich fissioning isotopes have been adequately 

analysed, i. e. to the extent that the fragment spectra are known well 

enough to permit their use in calculations? 

W . H . W A L K E R : O f the four fissile nuclides covered in m y evaluation, 

the yields are generally well m ea su re d over the m ain part of the light and 

heavy m a s s peaks, i. e. by m a s s spectrometry. This is not the case for 

the light m a s s peak in 241P u fission and in the valley between the light and 

heavy peak there are only three radiometric yields. The result is that 

about 4 0 % of the yield of the light m a s s peak is interpolated. The effect 

on calculations of fission product absorption is not very great (in thermal 

reactors) because m ost absorption is by the heavy m e a ss fission products. 

J. B L A C H O T : I a m in agreem ent with the view expressed in your 

paper that G e / L i g a m m a spectrometry can in certain cases supplement 

m a s s spectrometric m easu rem ents. This method has two m ain advantages: 

(1) the possibility of normalization of results between heavy and light 

m a s s e s ; (2) the sensitivity of the m ethod, which requires a lower fission 

rate and therefore eliminates correction due to captures.

BIBLIOTHEQUE DE DONNEES 

RELATIVES AUX PRODUITS DE FISSION 

C. DEVILLERS* J. BLACHOT**, M. LOTT* 

B. NI MAL* N’ GUYEN VAN DAT* J.P. NOEL* 

Commissariat à l'én ergie atomique 

R. DE TOURREIL 

Institut de physique théorique, Orsay, 

France 


FILE OF D A T A RELATED T O FISSION PR O D U C T S. 

I A E A - S M -1 7 0 /6 3 

T h e authors d e s c r ib e th e d a ta n e ce s sa ry for c a lc u la t in g th e c o n c e n tr a tio n s and th e ß and y a c t iv it ie s o f 

fissio n p r o d u c ts. T h e f i l e , w h ic h is based o n th e E N D F /B fo r m a t, resu lts fr o m c o m p ila t io n and e v a lu a tio n 

o f th e a v a ila b le d a ta . It c o n ta in s : th e fis s io n y ie ld s for th e m ost c o m m o n fissio n s; is o b a r c h a in s c h e m e s ; th e 

tra n sition p r o b a b ility ta b le s and th e g a m m a sp e ctra . T h e m a in w o rk o f c o m p ila t io n and e v a lu a tio n r e la te s to 

th e d e c a y s c h e m e s , fo r w h ic h th e d a ta , g ro u p e d for 6 22 is o to p e s ( 71Z n t o I70Y b) a re as fo llo w s : th e p e r io d ; 

Q g (0 tra n sitio n e n e rg y ) and t h e in te r n a l tra n sitio n e n e r g y in th e c a s e o f is o m e r is m ; th e ß tra n sitio n p r o b a b ilit ie s and th eir 

e n e r g y ; th e r e la t iv e or a b s o lu te g a m m a ray in te n sitie s and th e ir e n e r g y ; th e r e fe r e n c e s . T h e authors p resen t resid u a l 

p o w e r m e a su re m e n ts w h ic h p r o v id e o v e r a ll c o n fir m a t io n o f th e a s s e m b le d b o d y o f d a ta . 

BIBLIOTHEQUE DE DONNEES R E LATIV E S A U X PR O D U ITS DE FISSIO N . 

O n d é c r it u n e c o m p ila t io n d e l'e n s e m b le d e s d o n n é e s n é ce s s a ir e s au c a lc u l d e s c o n c e n tra tio n s e t d e 

l 'a c t i v i t é ß e t y d e s p rod u its d e fis s io n . C e t t e b ib lio t h è q u e , b â t ie sur le fo r m a t E N D F /B , r é s u lte d 'u n e c o m p i 

la t io n e t d ’ u n e é v a lu a tio n d e s d o n n é e s d is p o n ib le s . E lle c o n t ie n t : le s re n d e m e n ts d e fis s io n pou r le s fission s 

le s p lu s c o u r a n te s ; le s s c h é m a s d e s c h a în e s is o b a re s ; le s ta b le s d e p r o b a b ilité s d e ’ tra n sitio n e t le s s p e ctre s 

g a m m a . Le p r in c ip a l tra v a il d e c o m p ila t io n e t d 'é v a l u a t i o n p o r te sur le s s c h é m a s d e d é s in té g r a tio n pou r 

le s q u e ls le s d o n n é e s r e g r o u p é e s sur 622 is o to p e s ( 71Z n à 170 Y b) sont le s su iv a n te s: la p é r io d e ; l e Q ß (é n e r g ie 

d e d é s in té g r a tio n ß ) , l ’ é n e r g ie d e tra n sition in te r n e d an s l e c a s d 'is o m é r ie ; le s p r o b a b ilité s d e tra n sition 

b ê ta e t leu r é n e r g ie ; le s in te n sité s r e la t iv e s o u a b s o lu e s d e s r a ie s g a m m a e t leu r é n e r g ie ; le s r é fé r e n c e s . 

O n p ré se n te d e s m esu res d e p u issan c e r é s id u e lle q u i v a lid e n t g lo b a le m e n t l'e n s e m b le d e s d o n n é e s re te n u e s . 

1 - INTRODUCTION - 

Ce papier présente le format et le contenu de la bibliothèque 

de données sur les produits de fission qui a été développée pour permettre 

de calculer de façon théorique la concentration, l'activité et l'énergie 

dégagée par les produits de fission dans un combustible. 

2 - APPLICATIONS DES CONSTANTES NUCLEAIRES SUR LES PRODUITS DE FISSION - 

Des calculs de puissance résiduelle d'éléments combustibles 

de compositions diverses soumis à des régimes de fonctionnement variés 

* C e n tr e d 'é t u d e s n u c lé a ir e s d e F o n te n a y -a u x -R o s e s . 

* * C e n tr e d ’ é tu d e s n u c lé a ir e s d e G r e n o b le . 

477

478 DEVILLERS e t a l. 

sont sn effet nécessaires pour déterminer le mode de refroidissement de 

ce combustible dans une gamme de temps de décroissance de l'ordre de la 

seconde à plusieurs années : 

- problèmes de sûreté en cas de dépressurisation ou de défaut 

de refroidissement dans un coeur, 

- problème du déchargement et du stockage du combustible, 

- problème du transport et du retraitement. 

Pour déterminer de façon précise la distribution des sources 

de chaleur dans le combustible et son environnement, il faut connaître 

également, comment se répartit, en fonction du temps de-décroissance, 

l’énergie émise, entre rayonnement b@ta et rayonnement gamma, ainsi que 

le spectre des gamma émis. 

Le spectre gamma permet e n ’outre de calculer la protection 

des containers de transport. 

Il est très important également, pour des problèmes de 

protection radiologique, de savoir calculer, dans un réacteur en fonc 

tionnement, l ’évolution de la concentration des produits de fission : 

- pour prévoir les conséquences radiologiques d ’un accident 

entraînant la libération des produits de fission, 

- pour évaluer la contamination du circuit de refroidissement 

par les produits de fission qui traversent les gaines défectueuses. 

Le développement de la production d'énergie nucléaire 

entraîne dans un autre domaine des études de prévision des quantités de 

produits de fission produites dans les différents types de réacteur en 

vue du conditionnement des déchets des usines de retraitement. 

L'ensemble de ces questions joue un rôle important dans la 

sûreté, l'exploitation et l'économie des réacteurs. 

Notons enfin le domaine d ’application très vaste de l'analyse 

des produits de fission, en particulier par spectrométrie gamma (Ge/Li), 

pour l'étude des combustibles irradiés.

Pour répondre à cette gamme très large de problèmes, il 

était nécessaire d ’une part de constituer une bibliothèque de données 

aussi complète que possible et d'autre part de développer des codes 

permettant de calculer la concentration et l'activité des produits de 

fission ainsi que l ’énergie émise sous forme de bita et de gamma par 

ces produits de fission (1, 2, 3). 

Les premières éditions de la bibliothèque (4, 5, B) ont été 

constituées en rassemblant les données mesurées ou évaluées, souvent 

éparses, publiées dans la littérature. 

La quantité croissante de résultats nouveaux publiés, du 

fait de l ’amélioration des techniques de mesure, nous a conduit à mettre 

au point une procédure de stockage et de mise à jour des données sur 

bande magnétique. 

I A E A - S M -1 7 0 /6 3 4 7 9 

Le format choisi pour enregistrer ces données est celui de 

la bibliothèque ENDF (73, il est décrit dans le paragraphe 3. 

TYPES DE DONNEES - 

de données : 

La bibliothèque comprend essentiellement trois catégories 

- rendements indépendants de fission 

- périodes, modes de filiation [désintégration, capture), 

énergies de désintégration, rapports de branchement 

désintégration. 

- données sur les spectres des rayonnements émis par 

Le contenu actuel de la bibliothèque comprend 622 produits 

de fission de masses comprises entre 71 et 170. 

noyaux fissiles : 

Les rendements de fission sont introduits pour trois 

235 

U : fission thermique 

fission rapide (E w 1 MeV)


. 2 3 8 

U' 

: f i s s i o n r a p i d e (E л / 1 M e V ) 

239 

Pu : fission thermique 

fission rapide CE pj 1 MeV) 

3.1. Rendements indépendants de fission 

Plusieurs compilations de rendements ds fission ont déjà été 

publiées t10, 11) et nous avons choisi celle de MEEK et RIDER (8) 

qui nous a semblé la plus complète et la plus récente. Cette 

évaluation présente de plus la bibliographie de toutes les mesures 

effectuées depuis 1940, classées chronologiquement et indexées par 

noyau. Ces informations permettraient, si besoin était, de réévaluer 

certains rendements, par exemple en se basant sur l ’étude de WALKER 

(9) . 

Dans la présente version de la bibliothèque, les rendements 

indépendants sont calculés par la formule : 

avec : 

Y (A) : valeur recommandée du rendement de fission de la 

chaîne A 

Z-0,5 

Zp (A) : valeur la plus probable de la charge des produits 

de fission de la chaîne A 

(Г(А) : paramètre de la distribution gaussiénne. 

Pour chaque chaîne de masse A, les rendements indépendants 

sont déterminés pour des charges variant de zm^n£A) à Zâx CA), 

avec la condition de normalisation suivante : 

Y (Z mini 

A) = Y (A) Y (Z, A) 

En cas d'isomérie, les rendements indépendants calculés sont en 

général divisés également entre les isomères.


Lb format ENDF permet d 'introduir^ plusieurs jeux de 

rendements indépendants suivant l'énergie des neutrons produisant 

la fission. 

Les rendements indépendants de fission ont été calculés ; 

235 

pour la fission thermique ( E nj 0) et rapide ( E m 1 MeV) pour U 

239 238 

et Pu , pour la fission rapide [ E ru1 MeV) dans le cas de U 

Le mode d ’interpolation proposé pour des fissions se produisant entre 

0 et 1 MeV est le mode linéaire, en l'absence d'autre information. 

3.2. Périodes et modes de filiation - 

Contrairement aux rendements de fission, la littérature 

relative aux données radioactives est très abondante. La Table 

des Isotopes de LEDERER et al (12) est un document très complet 

mais il ne tient compte que des travaux publiés avant 1967 ; 

or le développement des détecteurs à germanium-lithium a permis 

depuis cette date des progrès très importants dans la connaissance 

des schémas de décroissance. 

Les Nuclear Data Sheets (13) ont depuis 1966 publié huit volumes 

de données révisées. Ces publications comportent de plus des listes 

de références récentes indexées par masse qui permettent d'effectuer 

soi-même la révision des données (6). Les valeurs des énergies de 

désintégration qui n'ont pas été mesurées ont été tirées de 

l'évaluation de WAPSTRA et al.(15). 

Le choix des données reportées dans la bibliothèque est 

coordonné par le laboratoire de Chimie Nucléaire du Centre de 

Grenoble sur la base de la nouveauté, de la qualité des techniques 

expérimentales et à l'aide de mesures expérimentales de contrôle 

(14) . 

La bibliothèque contient les références de toutes les valeurs 

numériques sélectionnées. 

Un effort important reste à faire pour améliorer la connais 

sance des produits de fission de période inférieure à une heure et 

des intensités absolues des raies gamma.


Les modes de désintégration pris en compte dans la 

bibliothèque sont indiqués dans le tableau I, 

T A B L E A U I. F I L I A T I O N S P A R D E S I N T E G R A T I O N 

: Noyau Noyau Energie de Rayonnement 

’ père fils désintégration émis 

: A, Z A,Z + 1 q b f ’ ß ~, У 

A.Z - 1 QBF+ ß+, У 

A, Z + 1т q b m ’ ß~, У 

A,Z - 1m QBM+ ß+ , У 

A-1, Z + 1 o b f “ ß~, y , neutron 

A-4, Z - 2 EALPHA a , y 

: a , zm A, Z EIT У 

A, Z + 1 QBF* ß ~, У 

A.Z - 1 QBF + ß+, y 

A.Z + 1т q b m ” ß~, y 

; A.Z - "T QBM+ ß~, y 

Le format ENFB permet également d ’introduire les filiations 

par capture neutronique comme l ’indique le tableau II. 

T A B L E A U II. F I L I A T I O N S P A R C A P T U R E 

N E U T R O N I Q U E 

: Noyau 

I père 

Noyau 

fils 

Energie : 

de réaction j 

! A' z A + 1, Z Q F ; 

A ♦ 1, Zm q m ; 

; A, Zm A + 1, Z Q F ; 

A + 1, Zm q n ;

I A E A - S M -17 0 /6 3 483 

Les rapports de branchement pour les captures neutroniques 

conduisant à plusieurs isomères ont été tirés du BNL 325 (16). 

Aucune évaluation relative aux sections efficaces 

différentielles de capture n ’a été reportée dans la bibliothèque : 

leur place est prévue dans le format ENDF/B, à l ’exclusion de 

toute donnée intégrale. 

Les données intégrales, en l'absence de données 

différentielles suffisamment complètes ou détaillées sont intro 

duites au niveau des programmes d ’utilisation de la bibliothèque. 

3.3. Spectres des rayonnements bêta etogamma émis par désintégration - 

Au format ENDF/B nous avons ajouté la possibilité 

d'introduire, pour les produits de fission instables, d ’une part 

des tables de probabilité de transition bêta et d'autre part des 

tables de spectre gamma [multiplicités). 

Compte tenu du niveau inégal de connaissance de ces 

données suivant les nuclides considérés, on trouvera dans la 

bibliothèque quatre situations possibles schématisées comme 

suit : 

: Probabilités de 

] transition bêta 

Spectre gamma 

: non non 

: non oui 

: oui non 

: oui oui 

L'énergie totale de désintégration est cependant supposée 

connue pour tous les nuclides instables. 

Lorsque plusieurs modes de désintégration sont en 

compétition, par exemple, émission j$’ et , les tables introdui 

tes sont la résultante des probabilités ou spectres des divers modes.

DEVILLERS e t a l. 

Une table de probabilités de transitions bêta se présente 

sous la forme d'une suite de couples de valeurs : énergie de transi 

tion - probabilité, correspondant à chaque transition. Les probabilités 

sont normalisées à 100 en l'absence de transition interne, à 

100-XEIT dans le cas d'une transition interne de probabilité XEIT. 

L ’énergie d'une transition est aussi l'énergie maximale du spectre 

bêta émis lors de cette transition. 

Une table de spectre gamma est constituée d'une suite de 

couples de valeurs : énergie de raie-intensité, correspondant à 

l'ensemble des raies dénombrées. Les intensités peuvent être données 

en valeurs relatives, avec la valeur 100 pour la raie la plus intense, 

ou bien en valeurs absolues, normalisées à 100 désintégrations. 

FORMAT DE LA BIBLIOTHEQUE - , 

Le format choisi est celui de la bibliothèque ENDF (73 auquel 

quelques additions ont été faites pour introduire les tables de proba 

bilités de transition l(l et les spectres ^ . 

La structure générale d ’une bande ENDF est schématisée à la 

figure 1. Dans la bibliothèque des produits de fission, chaque matériau 

ne comporte qu'une seule file (MF = 1 ) . 

Un matériau est identifié par son numéro NAT et parallèlement 

par l'indice ZAP = 1000 Z + A auquel il faut adjoindre un indice de niveau 

d'excitation. Des isomères sont considérés comme des noyaux indépendants. 

comprenant : 

Chaque matériau comporte une section d'information [MT = 451) 

- des indices annonçant les sections introduites dans la suite 

et permettant aussi de différencier les matériaux fissiles des produits 

de fission, 

des données, 

chaque section. 

- des cartes commentaires comportant notamment les références 

- un dictionnaire indiquant le nombre de cartes contenues dans

Bande 

Idenlificat 

(TPID) 

Premier 

Matériau 

Matériau 

MAT 

Dernier 

Matériau 

Fin de 

Bande 

( TEND) 

Matériau 

MAT 

File 

1 

File 

2 

File 

MF 

Dernière 

File 

Fin de 

Matériau 

С MEND) 

I A E A - S M -1 7 0 /6 3 485 

File 

MF 

Section 

1 

Section 

2 

Section 

M T 

Dernière 

Section 

Fin de 

File 

(FEND) 

F I G . l . S tru ctu re g é n é r a le d ’ u n e b a n d e ENDF. 

Section 

MT 

Enregistrement 


2 


MK 

Dernier 


Fin de 

Section 

(SEND) 

Les matériaux fissiles comportent, en plus de la section MT=451 

- une section MT = 452 donnant le nombre de neutrons par fission 

6 CE) (section obligatoire), 

- une section MT = 454 donnant les rendements indépendants de 

fission (section facultative dans le format officiel ENDF). 

La section MT = 454 peut contenir un ou plusieurs jeux de 

rendements, fonction ou non de l'énergie. 

Chaque noyau produit par fission est caractérisé par : 

- ZAFP : indice égal à 1000 Z + A 

- un indice d ’état :0 ¡fondamental ; 1 : 1er état excité.... 

- le rendement indépendant de fission à l ’énergie considérée. 

La somme des rendements est égale à 2.

suivantes : 

DEVILLERS e t a l. 

Les produits de fission peuvent comporter les sections 

-Section MT = 453 : elle contient les données relatives aux 

divers modes de filiation par désintégration ou réaction neutronique 

[ou autre), en particulier, pour un noyau cible d'état donné [0 : 

fondamental ; 1 : 1er état excité j etc....) : 

-le nombre de noyaux fils produits (2 états d ’excitation du 

même noyau sont considérés comme deux noyaux fils indépendants) 

-pour chaque noyau fils produit : 

- l ’énergie de la réaction ou de la désintégration 

conduisant à ce noyau 

- l'état du noyau produit [0,1....) 

- la typa de réaction : 

Ü.O. pour une désintégration spontanée quelle qu'elle soit 

MT pour une réaction neutronique 

(MT = 102 pour une capture radiative) 

- le ZAP = 1000.Z + A du noyau produit 

- la constante de désintégration, partielle pour le mode 

de désintégration considéré conduisant à l'état particu 

lier du noyau fils considéré [0. dans le cas d ’une 

réaction provoquée) 

- les rapports de branchement pour la réaction considérée. 

Les rapports de branchement sont normés à 1 pour chaque 

type de réaction. 

- Les deux sections suivantes (MT = 456, MT = 459) ne figurent 

pas dans le format officiel ENDF et ont été créées pour les besoins 

particuliers de notre bibliothèque de produits de fission. 

- Section MT = 456 : elle contient la table das probabilités 

des transitions bêta résultant de l ’ensemble des modes de désintégration 

du matériau.


- Section MT = 459 : elle contient le spectre des raies gamma 

résultant de l ’ensemble des modes de désintégration du matériau. 

Un indice permet de spécifier si le spectre est fourni en valeur relative 

ou absolue. Dans le premier cas, il est normalisé à la valeur 100 pour la 

raie la plus intense. Dans le second cas, les intensités correspondent à 

100 désintégrations du matériau. 

L ’arrangement détaillé des données de chaque section est 

reporté dans l'annexe 1. 

Les éléments nouveaux par rapport au format officiel ENDF sont 

repérés par un astérisque. 

APPLICATION DE LA BIBLIOTHEQUE AUX CALCULS DE PUISSANCE RESIDUELLE - 

Le diagramme représenté à la figure 2 montre la procédure de 

gestion et d ’exploitation de la bibliothèque des produits de fission 

pour les calculs d'évolution et d ’activité des produits de fission et 

les calculs de puissance résiduelle. 

5.1. Retraitement de la bibliothèque ENDF 

La bibliothèque ENDF est retraitée par un programme qui aboutit 

à une bibliothèque élaborée après avoir effectué les opérations 

suivantes : 

- établissement des chaînes de filiation à partir des données 

de la section 453 (types de réaction, constantes de désintégration, 

rapports de branchement) et de sections efficaces effectives de capture 

fournies par l'utilisateur 

- calcul par le modèle de FERMI (17) des énergies moyennes des 

bêta et des neutrinos émis pour chaque transition bêta,lorsque la 

table des probabilités de transition est fournie. Calcul de l'énergie 

totale émise sous forme de bêta (EBM) et de neutrino (ENUM) pour une 

désintégration du noyau incluant tous les modes de désintégration 

possibles.


G ESTION P E L A BIBLIOTHEQUE 

Evolution P. F. 

Activité P. F. 

Spectre y par P. F. 

Puis. Res. p 

Puis . Res. y 

Spectre Global ¡f 

F I G .2 . G e s tio n et a p p lic a t io n d e la b ib lio t h è q u e . 

Calcul de l ’énergie totale gamma émise (EGI4) par l ’expression : 

EGI4 = EREL - EBM - ENUI4 

où EREL est l'énergie totale libérée par une désintégration du noyau 

incluant tous les modes de désintégration possibles. 

Lorsque la table des probabilités de transition n'est pas connue, 

les quantités EBM et ENUM sont introduites par l'utilisateur.

I A E A - S M -1 7 0 /6 3 489 

Dans le cas d ’une transition interne, l'énergie apparaît 

uniquement sous forme de gamma. 

Lorsque le spectre des gamma est connu, en valeur relative ou en 

valeur absolue, le programme renormalise les intensités des raies de 

manière que l'énergie totale gamma soit égale à EGM. 

Les approximations faites portent sur les points suivants : 

- le modèle de FERMI utilisé dans le calcul de l ’énergie moyenne 

des b§ta ne tient pas bien compte des transitions interdites. Un 

calcul pour l'ytrium-91 montre que le modèle de FERMI sousestime 

l ’énergie moyenne des bêta de 4 %. 

- dans son état actuel la bibliothèque ne distingue pas la 

désintégration ^bet la capture électronique. 

L'énergie totale correspondant à une désintégration où il y a 

compétition ^ C.E. est égale à la différence des masses entre 

noyau père et noyau fils. Dans le cas d'une désintégration ^ il y 

aurait lieu d ’ajouter l'énergie apparaissant lors de l ’annihilation 

du positon [1,02 MeV), le calcul de l'énergie totale émise est donc 

minorant. 

Dans le cas d ’une capture électronique au contraire, l ’énergie 

est emportée presque totalement par le neutrino, le calcul de 

l ’énergie totale bêta est donc majorant. 

Cette approximation ne doit pas introduire d'erreur appréciable 

dans les calculs de puissance résiduelle étant donné les rendements 

faibles des produits de fission émetteurs'(iôu C.E. 

Au contraire, il est important d ’améliorer le calcul de l ’énergie 

moyenne bêta des émetteurs 

L'amélioration des connaissances des énergies et probabilités de 

transition tb~ et des énergies et intensités des spectres gamma, 

notamment pour les corps de période courte [T < 1000 sec.) est 

évidemment souhaitable.

T A B L E A U III. E N E R G I E L I B E R E E A P R E S U N E F I S S I O N T H E R M I Q U E D E L 'U R A N I U M - 2 3 5 

T e m p s d e 

d é c r o is s a n c e 

( s e c ) 

1) Présent 

c a lc u l 

E n e r g ie b ê t a ( M e V / s ) E n e r g ie g a m m a ( M e V / s ) 

2) B A T T A T 

e t a l. [ 2 0 ] 

R apport 

( 1 / 2 ) 

1) P résent 

c a lc u l 

2) B A T T A T 

e t a l. [ 2 0 ] 

1 0 1 7 ,2 9 * 1 0 “ 2 2 ,1 8 • W 2 3 ,3 4 5 ,5 2 * 1 0 “ 2 7 ,3 6 * 1 0 - 3 7 , 5 

1 0 2 7 ,1 7 • 1 0 ' 3 5 ,1 3 • 1 0 " 3 1 ,4 0 6 , 1 1 1 0 " 3 4 ,9 3 * 1 0 “ 3 1 ,2 4 

1 0 3 4 , 4 4 • 1 0 - “ 4 ,2 0 O 

1 

R apport 

( 1 / 2 ) 

1 ,0 6 4 , 7 0 * 10 * 4 4 ,4 7 • 1 0 ’ 4 1 ,0 5 

1 0 4 2 ,4 4 • 1 0 ' 5 2 , 6 8 • 1 0 - 5 0 ,9 1 3 ,3 4 1 0 -5 3 ,1 6 • 1 0 ' 5 1 , 06 

1 0 5 1 , 2 2 * 1 0 ' 6 1 ,1 9 • 1 0 - 6 1 ,0 3 1 ,3 8 • IO " 6 1 ,3 9 * 1 0 " 6 0 ,9 9 

1 0 6 5 ,4 3 * 1 0 ' 8 5 ,4 7 • 1 0 - 8 0 ,9 9 1 ,0 3 • 1 0 " 7 1 . 1 1 * 1 0 " 7 0 , 93 

1 0 7 4 ,5 6 * 1 0 ' s 4 ,6 0 • 1 0 ‘ 9 0 ,9 9 5 ,0 9 1 0 * 9 5 ,0 1 • 10-9 1,02 

108 1 0 -Ю 1,91 * 1 ,9 4 • io-10 0,98 3 ,4 0 * 10-n 3,36 • 10’11 1,01 

109 2,65 * 10"11 2 ,6 5 • 1 0 " “ 1,00 1 ,3 5 * î o - “ 1 ,3 0 * 10“11. 1,04 

490 DEVILLERS et al.


5.2. Calcul de la puissance résiduelle pour une fission thermique de 

1 ’uranium-235 

Le programme PEPIN (11 résout les équations différentielles 

gouvernant l ’évolution des produits de fission soit avec une source 

continue correspondant à une irradiation constante de 1 watt de 

durée quelconque d'un échantillon constitué d'un seul nuclide 

fissile, soit dans le cas d'une source instantanée de produits de 

fission créée par une fission d'un nuolide fissile donné. 

Il fournit dans les deux cas pour divers temps de décroissance 

l'évolution des produits de fission, de leur activité et de l'énergie 

libérée sous forme de bêta et de gamma par l ’ensemble des produits 

de fission. 

Les résultats d ’un calcul de puissance résiduelle pour une 

fission thermique de 1 ’uranium-235 sont présentés ici. 

□e nombreux calculs similaires ont été publiés dans la littérature 

(16-21) qui se distinguent par la rigueur du traitement numérique ou 

le caractère plus ou moins complet [nombre de produits de fission) 

ou plus ou moins récent des données. 

Dans le tableau III nous présentons la comparaison entre notre 

calcul et le calcul de BATTAT et al. [20) pour des temps de décrois- 

g 

sanee variant de 10 à 10 secondes. 

On notera pour les temps inférieurs à 1000 secondes l'augmentation 

résultant de l ’introduction dans notre calcul de produits de fission 

de période courte alors que BATTAT et al. ne considèrent que des nuclides 

de période supérieure à 10 secondes. Au-delà de 1000 secondes, l'accord 

est satisfaisant, à mieux de 5 % près. 

Les calculs PEPIN ont été comparés à une mesure calorimétrique 

effectuée à Fontenay-aux-Roses (22) sur un échantillon d ’uranium-235 

irradié en neutrons thermiques pendant 100, 1000, 5000, 105 et 

6.105 secondes. 

Une courbe de décroissance de la puissance résiduelle a été 

ajustée sur l ’ensemble des mesures,corrigées des fuites d ’énergie ï .


F I G .3 . D é c r o is s a n c e d e l 'é n e r g i e lib é r é e par le s p rod u its d e fissio n th e r m iq u e d e r u r a n iu m - 2 3 5 ( 1 fission 

in s ta n ta n é e ). 

La comparaison entre le calcul et la mesure est reportée à 

la figure 3. De 100 à 600 secondes, le calcul est supérieur de 

g 

18 à 0 % à la mesure, de 600 à 7.10 secondes il est inférieur de 

0 à 7 %. Le dépouillement d ’autres mesures correspondant à des 

temps d ’irradiation de 10 et 50 secondes respectivement permettront 

de recouper les points expérimentaux vers 100 secondes.

I A E A - S M -1 7 0 /6 3 

La précision annoncée de la mesure est + 5 %. Le nombre de 

fissions intégrées par l ’échantillon est mesuré par comptage de 

Ba-La 140 et recoupement par comptage de Cs 137. 

L'écart entre le calcul et la mesure au-delà de 1000 secondes 

est donc significatif et quasi systématique. Il ne peut être imputé 

au traitement numérique des équations étant donné le bon accord de 

4 

notre calcul avec celui de BATTAT et al. au-delà de 10 secondes ; 

il est à affecter soit aux données nucléaires et à leur traitement, 

soit à la mesure. 

Calcul de la puissance résiduelle du combustible d ’un réacteur à 

neutrons rapides 

□ans le cas d'un combustible complexe constitué d'un mélange 

de nuclides fissiles en évolution et soumis à une irradiation 

irrégulière, le programme PICFEE (2-3) permet de calculer l ’évolution 

des produits de fission, de leur activité, de leur spectre gamma et de 

la puissance résiduelle après l'arrêt du réacteur. 

Le programme calcule l'évolution du combustible au cours de 

l'irradiation à partir de sections efficaces effectives, variables 

en fonction du temps, qui sont fournies par l ’utilisateur. Il 

intègre ensuite les courbes correspondant à une fission élémentaire , 

fournies par le code PEPIN respectivement pour U235, U238 et Pu239, 

après avoir effectué les interpolations nécessaires pour tenir compte 

de l ’énergie moyenne des neutrons provoquant les fissions. 

Des comparaisons ont été faites entre des calculs de puissance 

résiduelle effectués par le code PICFEE et des mesures calorimétriques 

réalisées sur des aiguilles combustibles irradiées dans RAPSÜDIE à des 

taux moyens de combustion d ’environ 9600, 37000, 47000 et 52000 MWJ 

par tonne de métal. Les nombres de fissions intégrées par les aiguilles 

ont été déterminés par mesure du néodyme formé, la précision est de 

+ 5 %. 

Les mesures calorimétriques ont eu lieu après des temps de 

décroissance longs, de 1 à 4 ans. 

Des comparaisons pour des temps de refroidissement plus courts 

(20 à 80 jours) ont été effectuées par COSTA et al. (23). 

493


T A B L E A U IV . P U I S S A N C E R E S I D U E L L E D 'U N C O M B U S T I B L E D E 

R E A C T E U R A N E U T R O N S R A P I D E S 

A ig u ille 1 2 3 4 

T a u x d e co m b u s tio n (% ) 0 ,9 7 2 3 ,9 7 4 ,8 2 5 5 ,8 1 

T e m p s d ’ ir r a d ia tio n * ( jours) 257 537 670 553 

T e m p s d e d é c r o is s a n c e * (jo u r s ) 1 5 2 0 1 2 5 0 1 1 2 5 2 3 4 

P u issan ce ß + y c a lc u lé e (w a tt) 0 ,0 4 0 2 7 0 ,2 0 4 4 0 ,2 6 7 1 1,2111 

P u issan ce a c a lc u lé e (w a tt) 0 ,0 5 6 4 0 ,0 5 7 4 0 ,0 5 7 4 0 ,0 5 1 0 

A c t iv it é d e s g a in e s m e s u r é e (w a tt) - 0 , 0 0 0 6 - 0 , 0 0 3 5 - 0 , 0 0 5 0 

M esu re g lo b a le (w a tt) 0 ,1 0 6 6 0 ,2 8 0 0 0 ,3 3 5 6 1 ,3 1 4 

M e s u r e * * c o r r ig é e (w a tt) 0 ,0 5 0 7 1 0 ,2 2 3 5 0 ,2 7 8 4 1 ,3 0 2 

C a lc u l m esu re 0 ,7 9 5 0 ,9 1 5 0 ,9 6 0 0 , 930 

* L e te m p s d 'ir r a d ia t io n co m p r e n d e t l e te m p s d e d é c r o is s a n c e n e co m p r e n d pas un te m p s d e s to c k a g e 

d 'e n v ir o n 90 jou rs a 2 , 1 "la d e la p u iss a n c e m a x im a le . 

* * La m e su re est c o r r ig é e d e l ’ a c t iv it é a , d e Г a c t iv it é d e s g a in e s e t d e s fu ite s hors d u c a lo r im è t r e . 

Les résultats de la présente comparaison sont reportés dans le 

tableau IV. 

Compte tenu de la précision C+ 2 %) de la mesure calorimétrique 

elle-même, de l'incertitude sur le taux de fission t+ 5 %) et des 

corrections importantes effectuées sur les mesures pour soustraire 

l ’énergie résultant de l ’activité o

I A E A - S M -1 7 0 /6 3 495 

Le programme PICFEE calcule l ’évolution des produits de fission, 

de leur activité et de l'énergie qu'ils émettent après des irradiations 

complexes d'échantillons comportant des mélanges de nuclides fissiles 

évoluant j il a déjà fait l'objet d'applicationstrès variées allant de 

la prévision de la composition chimique d'un combustible irradié au 

calcul des sources de rayonnement déterminant les conditions de 

manutention des combustibles irradiés. 

L'ensemble des données et des programmes .a été éprouvé sur certains 

problèmes dont quelques-uns ont été présentés ici. C'est la précision 

souhaitée par les utilisateursdans les diverses applications et la 

comparaison avec l'expérience qui déterminera l'effort à poursuivre dans 

la mesure ou l'évaluation des données nucléaires. En ce qui concerne las 

questions de puissance résiduelle examinées ici, les prévisions théoriques 

sont correctes à mieux de 10 % près pour des temps de décroissance supérieurs 

à 200 secondes, et par conséquent on peut estimer que les données nucléaires 

qui interviennent : rendements, schéma de désintégration, spectres des 

rayonnements sont suffisamment bien connus. Le perfectionnement du calcul 

des énergies moyennes des bêta sera néanmoins poursuivi en tenant compte 

des spectres des transitions permises. 

Pour des temps inférieurs, l'amélioration de la connaissance des 

rendements, schéma da désintégration et spectres de rayonnements des 

produits de fission de période inférieure à 1000 secondes est encore nécessaire. 

Il faut noter que les sections efficaces d'interaction des 

neutrons (n, (n, n ’), tn, p) avec les produits de fission n'ont 

été considérées en détail ni dans la bibliothèque ni dans les appli 

cations mentionnées ici. Leur influence est en effet négligeable pour 

la majorité des problèmes de puissance résiduelle et d'activité. Le 

programme PEPIN utilise cependant das sections efficaces de capture 

effectives fournies par l'utilisateur. 

L'introduction dans la bibliothèque des valeurs évaluées 

disponibles des sections efficaces différentielles de capture des 

produits de fission permettra de déterminer les sections efficaces 

effectives dans différents spectres de réacteurs et d'indiquer par 

des études de sensibilité pour quels isotopes des mesures ou des 

évaluations sont nécessaires.

4 9 6 DEVILLERS e t a l. 

F i l e 1 

ANNEXE 1 

NT = 451 (Indices et informations générales) 

A N N EXE 1 (1). 

: Zone 1 Zone 2 Zone 3 Zone 4 Zone 5 Zone 6 Type : 

d'enregistrement 

: ZA AWR LRP LFI b NXC HEAD : 

: b b LDD LFP NWD NBG % LIST : 

: Г n°1 : 

: Cartes commentaire J n°2 : 

; (. n° NWD ; 

I b b MF1 MT1 NC1 b C0NT ; 

; b b MF2 MT2 NC2 b c0NT ; 

b b MF NXC 

MT NXC 

n c n x c 

b c0NT ; 

: b b b b b b SEND : 

ZA : 1000.Z + A 

AWR : masse atomique : rapport de la masse nucléaire du matériau 

à celle du neutron (masse du neutron : 1.008665 dans le système 

C12) 

LRP : = 0 rien 

= 1 des paramètres de résonance sont fournis dans la file 2 

LFI : = 0 matériau non fissile 

= 1 matériau fissile 

NXC : nombre de cartes constituant le dictionnaire : une carte par 

s e c t i o n c o m p o r t a n t :

LDD : = 0 rien 

LFP : = 0 rien 

NWO : nombre de cartes commentaire 

NBG* 

HF : n° de file 

MT : n° de section 

NC : nombre de cartes de la section 

I A E A - S M -1 7 0 /6 3 4 9 7 

= 1 des données de filiation sont fournies dans la section 

MT = 453 

= 1 des rendements de produits de fission sont donnés dans la 

: = 0 rien 

section MT = 454 

= 1 tables de probabilité de transition bêta dans la section 

MT = 456 

= 2 spectres gamma dans la section MT = 459 

= 3 à la fois 1 et 2

4 9 8 DEVILLERS e t a l. 

F i l e 1 

MT = 4 5 2 [ n o m b r e t o t a l d e n e u t r o n s p a r f i s s i o n ) 

A N N E X E 1 ( 2 ) 

LNU = 1 représentation polynominale : C E ) = Cn E 

: Zone 1 Zone 2 : Zone 3 : Zone 4 Zone 5 Zone 6 

n = 1 

Type 

d 'enregistremeni 

: ZA AWR : b : LNU=1 b b HEAD 

' b cr 

cr 

cr 

: C1 C2 : ------ : ----- 

NC b LIST 

: b b : b : b b b SEND 

LNU : = 1 représentation polynominale 

CNC 

NC : nombre de termes du développement polynominal 

Cn : coefficients du polynome 

LNU = 2 valeurs tabulées de u [E) 

: ZA AWR b LNU=2 b b HEAD : 

i b 

: NBT (1) 

b 

INT (1) 

b 

NBT (2) 

b 

INT (2) 

: E1 1) CE1) E2 ô(E2) 

NR 

NBT (NR 

NP 

INT (NR) 

e n p ^ (e n p ] 

t a b i ; 

I b b b b b b SEND j 

LNU : = 2 tabulation 

NR : nombre de domaines d'interpolation 

NP : nombre total de points d ’énergie de la tabulation 

NBT(I), INT (I) : mode d ’interpolation pour ^ (E) 

V(E^) : nombre total moyen de neutrons (prompts + retardés) par fission 

Ei : énergie (eV)

F i l e 1 

MT = 453 [d o n n é e s de f i l i a t i o n ) 


’• Zon e 1 Zon e 2 Zone 3 Zone 4 Zone 5 Zone 6 

ANNEXE 1 (3) 

T y p e • : 

d 'e n r e g i s t r e m e n t 

: ZA AWR b b NS b HEAD : 

: ZA 

; ES (1 ) 

I E R E L 1 

; r t v p 1 

=ER ELNPR 

; r t y p n p r 

AWR 

ES (2 ) 

Q 1 

ZAP„ 1 

°NPR 

z a p n p r 

L I S b NE NPR 

L F S i 

D ci 

LFS 

NPR 

d c n p r 

b 

BR (1 ) 

b 

b r n p r m 

NE + 3 , 

S 

ES (N E ) 

b 

BR (N E ) 

NE + 3 b 

BrNPr (NE) 

L I S T 1 : 

L I S T 2 

L I S T 2 : 

: b b b b b b SEND ; 

Ж 

NS : nom bre d ’ é t a t s e x c i t é s du noyau c i b l e : (N S = 1 ) dan s n o t r e b i b l i o t h è q u e 

L I S : é t a t du noya u c i b l e , 0 : fo n d a m e n ta l j 1 : 1 e r é t a t e x c i t é ; 

2 : 2ème é t a t e x c i t é 

NE : nom bre d ’ é n e r g ie s p o u r l e s q u e l l e s s o n t i n t r o d u i t s le s r a p p o r t s de 

b ra n c h e m e n t (N E = 2 )* 

NPR : nom bre t o t a l de n o ya u x p r o d u i t s (d e s is o m è r e s s o n t com pté s comme des 

n o ya u x in d é p e n d a n t s ) 

ES ( 1 ) , ES ( 2 ) : é n e r g ie s p o u r l e s q u e l l e s s o n t i n t r o d u i t s l e s r a p p o r t s de 

7 

b ra n c h e m e n t ; p o u r l e s d é s i n t é g r a t i o n s : (E S ( 1 ) = 0 ; ES ( 2 ) = 2 .1 0 e V ) 

EREL : é n e r g i e t o t a l e l i b é r é e p a r l e mode de d é s i n t é g r a t i o n c o n s id é r é (gamma + 

p a r t i c u l e s ) (e V ) 

Q : Q de l a r é a c t i o n c o n s id é r é e (e V ) 

LFS : é t a t du noyau p r o d u i t : 0 , f o n d a m e n t a l, 1 . . . . 

RTYP : t y p e de r é a c t i o n : 0 . : d é s i n t é g r a t i o n 

MT : r é a c t i o n ( p . e x : MT = 1 0 2 . p o u r c a p t u r e r a d i a t i v e ) 

ZAP : 1 0 0 0 .Z + A du noya u p r o d u i t 

-1 

DC : c o n s t a n t e de d é s i n t é g r a t i o n p a r t i e l l e (s e c ) p o u r l a f i l i a t i o n c o n s id é r é e 

BR ( 1 ) , BR ( 2 ) . . . . : r a p p o r t s de b ra n c h e m e n t p o u r l e s d é s i n t é g r a t i o n s : (B R ( 1 ) = B R ( 2 ) )*

500 DEVILLERS et al. 

F i l e 1 

MT = 454 (re n d e m e n ts de f i s s i o n in d é p e n d a n t s ) 

: Zone 1 Zone 2 Zone 3 Zone 4 Zone 5 Zone 6 

: ZA AWR ! m+ 

: E1 

: Z AFP 1 

! Erj 

: ZAFP 

: 1 

b 

F P S . 1 

b 

F P S , 1 

LE 

YLD 1 

YLD 1 

ANNEXE 1 (4) 

T y p e 

b b b HEAD 

b N1 NFP 

z a f p n f p f p s n f p y l d n f p 

d ' e n r e g is t r e m e n t 

L I S T 

b N1 NFP L I S T 

z a f p n f p f p s n f p 

YLD NFP 

: b b b b b b SEND 

N1 : = 3 X NFP 

NFP : nom bre de p r o d u i t s de f i s s i o n p o u r le s q u e ls le s re n d e m e n ts s o n t donnés 

E i : é n e r g i e d es n e u tr o n s p ro v o q u a n t l a f i s s i o n (e V ) 

LE : = 0 : un s e u l j e u de re n d e m e n ts e s t donné 

^ 0 : (L E + 1 ) j e u x de re n d e m e n ts s o n t don né s p o u r LE + 1 v a l e u r s 

d 'é n e r g i e 

1^ : mode d ' i n t e r p o l a t i o n u t i l i s é e n t r e le s é n e r g i e s E ^ .^ e t E^ 

(1 ^ = 2 l i n é a i r e ) * 

Z A F P , Y L D , FPS : p o u r ch aq ue p r o d u i t de f i s s i o n 

- 1 0 0 0 .Z+A 

- re n d e m e n t in d é p e n d a n t 

- é t a t du noya u p r o d u i t : 0 fo n d a m e n ta l 

1 1 e r é t a t e x c i t é 

2 2ème é t a t e x c i t é

F i l e 1 

HT = 456 * ( p r o b a b i l i t é s de t r a n s i t i o n b ê t a ) 


: Zone 1 Zone 2 Zone 3 Zone 4 Zone 5 Zone 6 

ANNEXE 1 (5) 

T y p e ; 

d ' e n r e g i s t r e m e n t 

: ZA AWR b b b b HEAD : 

I b b b 

: e t ( i ) P B ( 1 ) 

b 

b 

b 

NR = 1 

b 

E T (N P ) 

NP 

b 

PB (N P ) 

t a b i ; 

I b b b b b b SEND j 

NR : nom bre de d o m a in e s d ' i n t e r p o l a t i o n 

NP : nom bre de t r a n s i t i o n s b ê ta ( V e t !¡y* ou c a p t u r e é l e c t r o n i q u e ) 

NBT ( 1 ) , IN T ( 1 ) : mode d ’ i n t e r p o l a t i o n (s a n s o b j e t ) 

E T ( i ) , PB ( i ) : é n e r g i e (e V ) e t p r o b a b i l i t é de t r a n s i t i o n 

MT = 459 * ( s p e c t r e s gamma) 

: ZA AWR LR b b b HEAD : 

: b b b b NR = 1 NG TA B 1 : 

: EG ( 1 ) X G (1 ) 

b b b 

EG (N G ) 

b 

X G (N G ) 

; b b b b b b s e n d ; 

NG : nom bre de r a i e s 

LR : = 0 s p e c t r e en v a l e u r s r e l a t i v e s 

= 1 s p e c t r e en v a l e u r s a b s o lu e s 

E G ( i ) , X G ( i ) : é n e r g i e (e V ) e t i n t e n s i t é du s p e c t r e V t o t a l c o r r e s p o n d a n t 

à l'e n s e m b le des modes de d é s i n t é g r a t i o n du m a t é r i a u . 

REFERENCES 

(1 ) R . de T O U R R E IL , Program m e de c a l c u l de l ’ a c t i v i t é des p r o d u i t s de 

f i s s i o n . N o te C E A .N .8 2 4 (O c t o b r e 196 7)

502 DEVILLERS et al. 

(2) 

(3 ) 

(4 ) 

(5) 

(6) 

(7 ) 

t8) 

(9 ) 

(10) 

(11) 

(12) 

(1 3 ) 

(1 4 ) 

B . BARRE, P IC F E E : program m e d ’ i n t é g r a t i o n de c o u rb e s de f i s s i o n s 

é lé m e n t a ir e s t e n a n t com pte de l ' é v o l u t i o n des n u c li d e s f i s s i l e s , 

N o te C E A .N .1 2 0 3 (O c t o b r e 1 9 6 9 ) 

C . D E V IL L E R S , N ’ GUYEN VAN D A T , P IC F E E 2 : program m e de c a l c u l de la 

c o n c e n t r a t i o n e t de l ' a c t i v i t é des p r o d u i t s de f i s s i o n e t de la p u is s a n c e 

r é s i d u e l l e dans un c o m b u s t ib le i r r a d i é , r a p p o r t SERMA № 118/S 

( J a n v i e r 1 9 7 3 ) 

B . BARRE, R . de T O U R R E IL : B ib l i o t h è q u e des a c t i v i t é s ^ e t 'S des p r o d u i t s 

de f i s s i o n . N o te C E A .N .1 2 6 9 ( A v r i l 1 9 7 0 ) 

B . BARRE, R . de T O U R R E IL : B i b l i o t h è q u e de d on né es n u c l é a i r e s r e l a t i v e s 

aux p r o d u i t s de f i s s i o n (2ème v e r s i o n ) . N o te C E A .N .1 4 2 3 (M a rs 1 9 7 1 ) 

J . B LAC H O T, R . de TO U R R E IL : b i b l i o t h è q u e des don né es n u c l é a i r e s r e l a t i v e s 

aux p r o d u i t s de f i s s i o n (3ème é d i t i o n ) . N o te C E A .N .1 5 2 6 (M ars 197 2) 

Г1.К. DRAKE, D a ta F o rm a ts and P r o c e d u r e s f o r th e ENDF N e u tr o n C ro s s 

S e c t io n L i b r a r y , BNL 5 02 7 4 , ENDF 102 v o l 1_ (1 9 7 0 ) 

M .E . MEEK, B . F . R ID E R , C o m p i la t io n o f F i s s i o n P r o d u c t Y i e l d s 

N E D O -1 2154 (1 9 7 2 ) 

W . H. W ALK ER , «The evaluation of fission product yields», Nuclear Data 

for Reactors (Compt. Rend. C on f., Helsinki, 1970) A IEA, Vienne (1970) 

685. 

C . M E IX N ER , J Ü 1 -8 1 1 , 8 1 2 , 813 (1 9 7 1 ) 

A . T O B IA S , RD/B/M 2356 (1 9 7 2 ) 

C .M . LEDER ER , J . M . HOLLANDER, I . PERLMAN, T a b le o f Is o t o p e s (6ème é d i t i o n ) 

J o h n W IL E Y , so ns (1 9 6 7 ) 

N u c le a r D a ta S h e e t s , A c a d e m ic P re s s In c .V o lu m e B 1 -B 8 

J . B LA C H O T, L . C . CARRAZ, 0* MARBACH, R a ie s gamma é m ises p a r q u e lq u e s 

K r y p t o n e t xen on de f i s s i o n , r a p p o r t C E A -R . 4437 (1 9 7 3 ) 

(1 5 ) A .H . W APSTRA, N . B . GOVE, N u c l e a r D a ta T a b l e s , v o l . A 9 , 267 (1 9 7 1 )

(1 6 ) BNL 325 

(1 7 ) В . BARRE, R . de T O U R R E IL , E n e r g ie m oyenne ém ise p a r le s n u c li d e s ^3“ 

i n s t a b l e s - N o te C E A .N . 1265 (1 9 7 0 ) 

(1 8 ) J . F . P E R K IN S , R .W . K IN G , N u c l . S o i . E n gn g 3 , 726 (1 9 5 8 ) 

(1 9 ) J . F . P E R K IN S , R R - T R - 6 3 - 1 1 (1 9 6 3 ) 

(2 0 ) M .E . B A T T A T , D . J . D U D Z IA K , H .R . H IC K S , L A -3 9 5 4 (1 9 6 8 ) 

(2 1 ) J . S C Q B IE , R .O . S C O T T , J l o f N u c l . E n e r g y 2 5 , 339 (1 9 7 1 ) 

(2 2 ) A p a r a î t r e 


(2 3 ) L . C O S TA , J . R A S T O IN , R . de T O U R R E IL , J l o f N u c l . E n e r g y 2 6 , 431 (1 9 7 2 )

DISCUSSION OF FISSION-PRODUCT YIELD 

EVALUATION METHODS 

AND A NEW EVALUATION 

M. LAMMER*, O.J. EDER 

Österreichische Studiengesellschaft für Atomenergie, 

Seibersdorf, Austria 

Abstract 

DISCUSSION OF FISSION-PRODUCT YIELD EVALUATION METHODS AND A NEW EVALUATION. 

Reliable data on fission product yields are necessary for interpretation of gammaspectrometiic 


measurements on burnt fuel elements. Discrepancies among sets of fission yields recommended by different 

evaluators led to a detailed study of published experimental data. A new evaluation was performed. After 

a comprehensive description of the present state of experimental methods for obtaining fission product yields 

the previously adopted evaluation procedures are critically reviewed. An evaluation procedure is proposed 

which takes into account sources of experimental errors and accuracies of methods used. Examples of recently 

evaluated fission product yields for thermal fission of Z33U, 2 35u and^Pu and for fast fission of ^ T h are 

presented. Data for °*u fast fission and z41Pu thermal fission are in preparation. 

1. DîTROroCTION 

Рог a number of years research work on fuel Ъит-ир analysis has Ъееп 

done at the Research-Centre Seibersdorf [1-3]. With the use of high 

resolution semiconductor detectors the identification of many more fission 

products via gamma-spectrometry of irradiated fuel elements has been 

possible, than by application of Nal detectors. The aim of a fuel burn-up 

analysis is either to calculate fission product inventories and fuel 

burn-up (forward calculation) or to derive an appropriate fuel history 

from measured fission product gamma-spectra (backward calculation). 

A survey of recent work in this direction will be presented in a 

separate paper at this conference [4]. Here it should only be noted that 

we are interested in fission products that can be identified by gamma 

spectrometry. Especially important for this work (see [4]) are fission 

yields for 95Zr, 9 9 m o , 134cs, ■l5^Ru> 10^Ru> ^ C s (capture product 

134cs), 137cs, ^4®Ba, 141ce, l44Ce an(j. 147щ. jn addition several yields 

for fission products in the mass range from 149 "to 153t which contribute 

to the activity of ^54e u (activation product) through a series of neutron 

capture processes, are of importance in this context. 

Checking the reliability of published fission product yields, that 

serve as input to our calculations, we found several discrepancies in recommended 

values of evaluations and recent experimental results^^]. In 

trying to find out the reasons for these discrepancies, we were naturally led 

to the consideration of: 

- how are recommended values for fission product yields reached 

- what are the experimental methods and the respective correction 

procedures. 

* Present address: Nuclear Data Section, IAEA, Vienna, Austria. 

505

506 LAMMER and EDER 

2. SURVEY OP FISSION YIELD EVALUATIONS UP TO I969 

2 .1 . Information included in the evaluations 

I f the user of fissio n product yield evaluations does not want to just 

adopt one set o f recommended yield s at random, he wants to be given the 

following information: 

- what is the general evaluation procedure 

- which experiments (together with references) have been preferred for 

calculating recommended yields 

- any.information that allows a check on the r e lia b ility of yield values 

used, preferably a l i s t of the individual experimental data together 

with references 

- an indication of any changes of original experimental values and the 

nuclear data used by the evaluator to apply corrections 

- uncertainties of recommended yields 

Guided by these considerations evaluationsâvailable up to I969 are 

surveyed. Fission product yield data for an¿ 239pu have been 

compiled in the works quoted, except where noted. 

Steinberg and Glendenin [7 ] reviewed only very early measurements and 

w ill not be considered here in more d etail. 

K atcoff' s [8 ] evaluation includes experimental data up to I960, 

among these the fir s t extensive series of mass spectrometric measurements, 

carried out at McMaster University, Canada [9 - 17]* A short introduction 

to the tables reviews the experimental methods. Mass-spectrometric data are 

preferred for recommended yield s. 

The tables contain recommended values. A l i s t of references is given 

for each f is s ile nuclide. Adopted h a lf -life values are also given. No 

information on original experimental data and methods or correction procedures 

is given. Uncertainties have not been assigned. 

233 

Ferguson and 0 'Kelly [l8 ] evaluated U yield s only. Their report 

contains a detailed description of the data treatment and the evaluation 

procedure. They averaged readjusted mass spectrometric yield s and fin ally 

normalized each mass peak to 100 $ with the aid of radiometric and interpolated 

data. 

This report contains separate tables for a ll original experimental 

data compared and adjusted values together with the recommended yield s. 

The data sets are given with the respective references. Uncertainties are 

assigned as standard deviations only in those cases, where more than one 

experimental value was used for the fin al yield . 

Croall [ 19] gives a more extensive discussion of experimental methods 

and correction procedures. He preferres mass-spectrometric data and experiments, 

where more than one yield has been measured. Corrections for 

new h a lf -life values were applied, where possible. 

The tables contain references together with each recommended yield 

and a l i s t of adopted h a lf-liv e s is also given. However, no information 

on preferred individual experimental data is included. Some highly discrepant 

values are given without comment for different isotopes belonging 

to the same mass chain in cases, where a ll o f them represent essentially 

total chain y ie ld s. For each yield the 95$ confidence lim it is estimated. 

Rider et a l. [20] made a few renormalizations o f relative y ield s, 

which they describe in d e ta il. Their tables show original experimental 

data (and in some cases calculated y ield s) with references together with 

recommended values. For each yield the 9 ^ confidence lim it is estimated.


In their evaluation the authors included their own measurements [5 ] 

as well as those of Lisman et a l. as published up to March 1967 (see [ 6 ] ) . 

These contain mass-spectrometric yield s of the isotopes of Kr, Ru, Xe, Ce, 

Nd and Sm, the yield of 99tc determined spectrophotrometrically and of 

137Cs determined by gamma spectrometry, for ^ЗЗц 2з5и fissio n . However, 

the Kr yield s of 235u have been revised later by Lisman et a l .[ 2 l ] . 

The evaluation of Meek and Rider [22] was not available to us until 

recently. This work is based on [2 0 ], but contains yields of the isotopes 

o f Rb, Sr, Zr and Cs and of 138;ga f or 235u measured mass-spectrometrically 

by Lisman et a l. [ 6 ]. It also includes the ^39pu y ield s, as published in 

IN-1189, which were, however, completely revised in IN-1277 (see [6 ])- 

233u yield s are not evaluated in 'th is work. Meek and Rider have, with one 

exception, simply averaged published experimental yields from thermal 

fissio n . The tables include original experimental data with references, 

together with the recommended values, but also cumulative yield s for 

the respective decay chains for a given mass number. No uncertainties are 

assigned. 

Allen and Drake [23] give a more recent survey o f U fission y ield s, 

which was not published at the time of the preparation o f the present paper. 

2 . 2 . Survey of discrepancies 

Table I shows a survey o f discrepancies among fissio n yield data from 

literature for the isotopes liste d in the introduction. Some other important 

long lived fission products are also included. This table should 

re fle ct the situation at the time, when this evaluation was started. Therefore 

evaluations are also compared to the measurements of Lisman et a l. 

[ 6 , 2 1 ] . Discrepancies are given in percent of the lowest value in 

column 3 and in percent of yield s of Lisman et a l. in column 4. 

The evaluations compared are: 

235u: References 

233u: References 

239pu: References 

19, 20, 22] 

1 8, 1 9, 2 0, 23] 

8, 19, 20, 22] 

Other yields for Pu-241 thermal fission and U, U, U, Th 

and ^39pu fast fission are not considered here, as published experimental 

results were rather scarce in the past and the most recent measurements 

[2 1 , 24, 25, 26] axe not included in the evaluations mentioned. 

235 

The overall agreement of compared yields is best for U, which is , 

to a lesser extent also reflected in the values o f table I. 

3. EXPERIMENTAL METHODS FOR MEASURING FISSION YIELDS AND THEIR SOURCES OF 

ERROR: 

In th is chapter the mass spectrometric, the radiochemical and the 

ratio measurement technique are reviewed together with the sources of 

error and a discussion of the p o ssib ility for the evaluator to check and 

correct published experimental data. Based on these considerations, the 

previous evaluations w ill be discussed in 5* and new evaluation procedures 

are proposed in 6.


TABLE I. SURVEY OF DISCREPANCIES 

F issile Mass no. Discrepancies (percent of fissio n yield ) 

isotope fission 

product 

between evaluations 

(maximum) 

2350 9 ° Sr < 4 $ [19] - Г20] 

233и 

> 5 $ [19] - [2 2 ]a) 

between evaluations 

and Lisman et a l.[6 ] 

no 

ro 

0 

1_______ 1 

1 

H-* 

40 

1_________ 1 

95 < 4$ Г8] - [ 19] < 1$ [ 1 9 , 20, 22] - 3$ [ 8] 

99 about 1$ about 1$ 

106Ru > 2$[ 8, 19] - [ 20, 22] а^Ъ ^ 0$ [ 20, 22] - 2$ [8 , 19] 

1 ?5sb « 0 ( a ll) w40$ (a ll) 

131 

«0 ( a ll) 

6$ I > Xe[ 19] 

4$ ( a ll) 

133 within 1 . 5$ (a ll) within 2$ (a ll) 

137Cs < 1$ ( a ll) within 25*0 ( a ll) 

140 within 2$ ( a ll) within 2$ ( a ll) 

141Ce 

141 

5$ [ 20] - [ 22] 

^>10$ difference La>Pr[l9] 

144 >5$ [8 ,1 9 ] -[2 0 ]а)Ъ) 

147 

8$ [ 8] - [ 22] a) 

~ W f o Md - Pm [19] 

5.5$ [2 0 ]- 1C$[22] 

С$ [2 2 ]-4 $ [8 ,1 9 ] 

3. 5[ 22] 8$ [ 19] , 11$ [ 8] 

149 11$ [ 19] - [ 22] 

4$[22],9^ [20 ],15$ [19] 

152 « 2С$ [ 8] - [ 22] 1 C$ [22],15$[20],2C $[19] 

86 11$ [ l 9 ] -[2 0 ] b) 2$ [ 20] - 13$ [19] 

9°Sr 3$ [18] - [23] 8$ [23] - 11$ [18] 

95 3$ [ 18] - [ 23] 3$ [18] - 6$ [23] 

99 7$ [ 2 0 ]-[23] 0$ [20] - 7$ [23] 

106Ru 13$ [2 0 ]-[1 8 ,2 3 ]Ъ) 5$[ 20], IC / f l 19] , 18$[ 18,23] 

1?5sb 100$ [2 0] - [18,23] 16$ [18,23]Г5С^[19],8С$ 

[20] 

131 4$ [23] - [19] 

>1$ [19] -2$ [23] - [20] 4$ [19] ->5$ [20] 

140 > 3 $ [ 23] - [ 18] 

> 7 $ Ba - Ce [19] 

яО [23] -

T A B L E I (continu ed) 


F is s ile Mass no. Discrepancies (percent o f fis s io n y ie ld ) 

isotope fis s io n between evaluations between evaluations 

product (maximum) and Lisman et a l. [ 6] 

141 

[2 3 ,l8 ]-[2 0 ] 

144 2 .% [l8 ]-[2 0 ,2 3 ] > l$ [2 0 ,2 3 ]-3 .5 $ [l8 ] 

147 < 4 1 [2 0 ]-[1 8 ]Ъ) > 4$[20] - > 8$ [ 18] 

149 й 9 ^ [2 3 ]-[1 9 ]Ъ) W0 [20] - > 5 $ [23] 

152 30$ [23] - [1 8 ]Ъ) 8$[20],О.С$[23],18$[18] 

239„ 

^Pu 9°sr * 7 # [l9 ]-[2 0 ,2 2 ] 2$ [ 19] - 5$ [ 20, 22] 

95 2.5/» [l9 ]-[2 0 ,2 2 ] 6io [20,22] 

99 6$ [ 20] - [ 8, 19] < 4 io [8 ,1 9 ]-9 .5 $ [20] 

137Cs 14i [19] - [8 ]


3 .1 . Mase-spectrometric measurements 

3 .1 .1 . Description of techniques 

Up to now mass spectrometric measurements of fission yields have 

been carried out for all stable and reasonably long lived fission products. 

Most commonly the isotopes of Kr, Sr, Zr, Mo, Ru, Xe, Cs, Ba, Ce, Nd and 

Sm have been studied, in some cases also isotopes of Y, Cd, Sn and Eu. 

The range of isotopes studied mass-speotrometrically can be extended by the 

use of on-line mass-spectrometers [27]. 

There are essentially two procedures used. Either the element to be 

investigated is chemically separated from the other fission products and 

the fissile element prior to mass-spectrometric analysis. Or, after separation 

from heavy elements like U or Pu, the sample containing all fission 

products is mounted on the filament of the mass spectrometer, making use of 

the different ionisation energies of the elements and thereby investigating 

the elements in succession. In the latter method complete separation of 

the elements is not always achieved (especially in the rare earth region) and 

careful corrections have to be applied for interference effects of either 

compound ions (e.g. LaO) and metal ions (e.g. 154sm). or isobaric isotopes 

(e.g. 144Ce - *44щ ). 

The mass spectrometric measurements give precise relative yields for 

the isotopes of one element. As long as the half life of an isotope is at 

least of the order of the time needed for irradiation, handling and 

measuring, it can be investigated mass-spectrometrically in the conventional 

way. This makes possible the use of isobaric fission products to link different 

elements. Examples, where errors due to decay corrections can be kept 

small under suitable conditions, are 9 5 2r - $ 5 m o , Í33xe - ^ЗЗсз, 140ga _ 

140ce, 144ce - and 147jjd _ 147sm> For the above mentioned isobars this 

way of extending relative yields to neighbouring elements is generally 

superior to other techniques. 

A suitable method to obtain the number of atoms of a particular fission 

product formed in an irradiated sample is the isotope dilution technique. 

In this technique, a known amount of a standardised solution is mixed 

thoroughly with a known amount of solution of either fission products or the 

chemically separated element under investigation. The standard solution 

contains a predetermined number of atoms of either a highly enriched 

"spike isotope" - preferably not formed in fission, or of the natural 

element. This mixture is measured again with the mass-spectrometer and 

the number of fission product atoms can be calculated by comparison with 

the pure fission product spectrograms. 

Before leaving this technique one should mention the integral mass 

spectrographic method, as applied by Anikina et al. [28-30]. After determining 

the relative ionization coefficients of the elements under study 

for the spectrometer used, the ion currents are integrated for a given 

mass position of the investigated sample. Chemical separation of elements 

contained in the samples were not performed in these experiments. Prom the 

known ionization coefficients the relative concentrations can be determined. 

Absolute concentrations can be obtained by a determination of the number of 

atoms for one mass number, e.g. by isotope dilution. 

3 .1 .2 . Sources of error, corrections and accuracy 

Rather high integrated neutron fluxes are required for accumulation 

of an amount of fission products sufficient to perform mass spectrometric 

measurements with reasonable accuracy. Therefore corrections have to be 

applied for neutron capture in fission products. If unstable isotopes are


also measured, then in -p ile and o u t-o f-p ile decay corrections have to be 

applied,as the usual neutron fluxes require longer irradiation times and 

the radioactivity o f the sample has to be su fficien tly low for handling. 

Fission products like ^35xe and some Sm isotopes have such high and rather 

uncertain capture cross-sections, which in addition depend strongly on the 

neutron spectrum that corrections can hardly be applied reliably under normal 

irradiation conditions. Therefore samples for measurements o f the 

fissio n yield s of these isotopes and their capture products have to be 

irradiated in very low fluxes. 

In many cases cross-section and h a lf -life data are known more 

accurately at the time of evaluation than when the experiment was performed. 

The correction of original yield data by the evaluator requires 

the knowledge of irradiation conditions and cooling time involved in the 

measurements, as well as either of the nuclear data used for corrections 

by the experimenter or of the uncorrected data. 

Contamination of the fissio n product sample by naturally occuring 

isotopes in the same mass range can arise from the sample i t s e lf , the 

reagents, containers and apparatus used for post-irradiation treatment, 

or even from the filament o f the mass-spectrometer, if surface 

ionization is used. Corrections can be applied to mass-spectrograms taking 

into account the abundance o f an isotope not formed in fissio n . I f th is 

is not possible, unirradiated samples have to be carefully analysed. In 

many cases the amount of contamination cannot be determined exactly and 

can distort the abundances of fissio n product isotopes. For the Sm isotopes 

it is also essential to know, whether the contamination was present 

in the sample prior to irradiation, or not. In addition low yield 152Sm 

and ^ 54 Sin are very sensitive to corrections, as they have highest abundance 

in the natural element. 

When the isotope dilution technique is applied, one has to consider 

mainly four sources of error: 

- a fractionation o f fissio n products (only partial recovery), 

- an incomplete mixing of the fissio n product solution with the standardized 

solution, 

- accuracy of the calibration of the standardized sample 

- losses due to mass transport or reactions in the solution 

Fractionation of fissio n products can be detected by measuring the activity 

of the residual solution. Also losses o f fissio n products due to diffusion 

or migration can occur, but th is can be avoided by properly encapsuled sample 

The accuracy of the determination of isotopic compositions depends on 

the amount of the investigated element, i t s ionization energy, the 

abundance of a particular isotope and the dynamical parameters o f the 

mass-spectrometer used. Standard deviations quoted for fissio n products range 

typ ically between 0.1 and 2 percent. 

Highly enriched spike solutions were used for isotope dilution by 

Lisman et a l. [ 6 , 2 1 ] . The preparation of the spike is described in detail 

in [21] and a standard deviation o f less than O .j/ o is quoted for its 

standardization, leading to values around 0 .5 percent for the determination 

of the number o f fissio n product atoms. 

The method of using the natural element for isotope dilution is less 

sensitive to changes in the isotopic composition o f the sample. Therefore 

an overall accuracy of 0 .3 to 3 percent can be assigned to the measurement 

o f the number o f fissio n product atoms present in a sample. However, in 

practice the deviations among measurements are sometimes larger, probably


due to systematic errors of the above mentioned kind. Therefore outstanding 

data can be rejected, i f su fficien t measurements are available to allow 

a check. 

3 .2 . Radiochemical measurements 

3 .2 .1 . Description of techniques 

The advantages of the radiochemical techniques are twofold: 

- Sufficient radioactive nuclei are produced in rather short irradiation 

times. This makes fissio n yield determinations possible without the 

problem o f interference caused by neutron capture processes. 

- Natural element impurities do not contribute to the error of the 

measurements, as only radioactive fissio n products are measured and 

capture products arising from impurities can be neglected. 

The fissio n products to be investigated are separated by suitable chemical 

procedures. This is done either directly after the dissolution of the irradiated 

sample, or the resulting solution is diluted to known volume and aliquots 

axe drawn from this solution for further separation. So far the method is also 

applied for the mass-spectrometric isotope dilution technique. However, 

radiochemical measurements require rather very pure samples, which is 

achieved by a series of separation procedures, and the chemical yield is 

usually determined by weighing an inactive carrier. A known amount of 

solution is then investigated for fissio n products by counting techniques. 

3 .2 .2 . Sources of error, corrections and accuracy. 

Errors arising from chemical separations can be due to : 

- undetected losses of fissio n products 

- the determination of the chemical yield 

- incomplete separation from other fissio n products. 

Other errors may arise from activity measurements, which require a 

number o f corrections. 

In earlier measurements mostly Geiger-Mlller counters were used for 

the determination of the ß -a c tiv ity . Large corrections have to be 

applied for: 

- efficien cy, deadtime and geometry of the detector assembly 

- absorption in the sample, air and detector window 

- s c a t t e r i n g o f p ~ r a y s . 

The 4 7Г counter assemblies, more commonly used la te r, require less 

corrections than the Geiger-MUller counters. Corrections for self-absorption 

in the sample and absorption in the supporting film are s t i l l d iffic u lt to 

calculate d irectly. However, the high efficiency o f 4 Xcounters makes possible 

the use of very thin samples and film s. Thus corrections can be kept 

reasonably small and be determined empirically. 

Other counters require corrections similar to those mentioned. Uncertainties 

in the determination of the counter efficiency can be reduced 

by careful calibration against standardized detectors using standard sources, 

as has been done in most recent experiments (e .g . [31])* 

Usually gross ( I -decay curves are measured at several time intervals. 

In the most straight-forward cases a suitable time interval can be chosen 

for the measurements, where the activity of the investigated fission 

product is clearly dominating and errors introduced by interfering 

activity can be kept n egligible. Far more complicated are those cases 

where several fissio n products together with their daughter products


contribute to the tota l a ctiv ity . Gross decay curves have to be resolved 

into components and fin a l resu lts depend strongly on the values used for 

the h a lf liv e s . One erroneous value a ffe c ts the other resu lts as w ell. 

Decay data o f precursors have to be taken into account, esp ecia lly for 

calcu lation s o f the a ctiv ity present at the end o f the irradiation and 

a fter chemical separations. 

Prom the evalu ator's point o f view i t is almost impossible to correct 

old data fo r better known h a lf l i f e values or decay schemes. This would 

only be p ossib le, i f a ll the data points were available in addition to 

the experimental d e ta ils , but even then attempts to do th is fo r two 

experiments [32, 33] fa ile d to improve the resu lts. Corrections can be 

applied fo r a rather long lived fis s io n product, where the origin a l decay 

correction s introduce only small errors and the h a lf l i f e used is available. 

It is d if fic u lt to malee a general statement about the accuracy o f radiochemical 

measurements. This depends too strongly on any undetected 

fa ilu res during separation procedures and the detector equipment used 

fo r measurements. Considerable discrepances can also arise from various 

errors in the h a lf-lif e values and decay schemes used, including precursors 

and daughters. 

As such errors may be d ifferen t fo r fis s io n products investigated 

within the same experiment, i t is then a question o f how many y ie ld data 

o f one isotope are available fo r intercomparison to decide, which resu lts 

are to be rejected . 

In more recent experiments the e fficie n cy ca lib ra tion o f the counters 

is accurate to about 2 percent [3 1 ]. Including correction s and chemical 

y ie ld determination, excluding undetected losses, the overall accuracy 

should be within 3 - 5 i n very early experiments up to around lOfo and 

more. 

In some experiments also gamma spectrometry is applied for the 

determination o f disintegration rates. However, absolute in ten sities o f 

gamma rays are accurately known only for a few fis s io n products, and were 

even more uncertain in the past; Further, complex spectra cannot be resolved 

by K al-detectors, which are most commonly used. E fficien cy calibration 

introduces additional uncertainties. 

The sources o f error can be reduced by measuring the gamma spectra 

re la tiv e to a standard with known disintegration rate. Another suitable 

method is the determination o f the detector e fficie n cy for the investigated 

fis s io n products by 4 JT— ß -V -co in cid e n ce counting o f pure samples o f the 

isotopes. 

Corrections can be applied by the evaluator without d iffic u lt y only for 

errors in gamma-ray in ten sities used. 

3.3. Ratio measurements 

3 .3 .1 . Description o f method 

235 

I f a set o f fis s io n y ie ld s , e.g . those for U, is assumed to be well 

known, an R-value can be measured, which is defined as 

Y. 1 

X . 

V st 

. . fis s io n y ie ld o f isotope i 

99 

. . fis s io n y ie ld o f a standard isotope (usually Mo) 

. . .the fission a b le isotope under study


These ratios can be measured precisely, i f irradiation times are either 

short compared to the h a lf-liv e s of the investigated fission products or 

equal and measurement conditions are identical. In this case an absolute 

calibration of the equipment is not required and also the determination of 

absolute disintegration rates is not necessary, which avoids errors due to uncertainties 

in decay schemes. 

3.3>2. Sources of error, corrections and accuracy 

I f the measurement conditions are identical and decay corrections of the 

same magnitude, errors depend only on the reproducibility of the chemical 

procedures, on the counting s ta tis tic s and on the accuracy of the reference 

y ie ld s. Results from this type of measurement can easily be adjusted by the 

evaluator to a new set of reference y ie ld s, i f the R-values obtained in the 

experiment are liste d or i f the reference yield s used are quoted. 

However, generally fractional independent yield s of fission products, 

defined as the ratio of independent to cumulative or total chain y ield , 

vary with fissionable isotope and neutron energy. I f the independent yield of 

an investigated fissio n product is significant in at least one type of fissio n , 

corrections have to be applied, i f the h alf l i f e o f the precursor is comparable 

to the irradiation time or the cooling time until chemical separation. 

The accuracy o f th is method can be better than 1$, but varies, depending 

on the fissio n product studied. In beta^ray measurements errors due 

to h a lf -life values used cancel, i f the gross decay curves have not too 

many components. In gamma ray measurements peak areas can be determined 

with rather high accuracy. But as fissio n products are not chemically sepa^- 

rated, gamma spectra are complex and errors can be introduced by differences 

in background subtraction or interferences of other peaks. Due to these 

d iffic u ltie s in the processing of the raw data, or any of the above mentioned 

errors, discrepancies are sometimes larger for single values. 

3 .4 . Determination of the number of fission s 

For the determination of absolute fissio n y ield s, the number of 

fissio n s, that have occurred in a sample, can be measured by essentially 

three methods. 

3 .4 .1 . Isotope dilution mass spectrometry 

The technique i t s e lf has already been described and i t s application 

for the determination of the number o f fission s shall be explained for 

the example o f 2 3 5 u . 

The isotopic composition and the number o f atoms of Uranium are 

measured before and after irradiation. I f the sample is highly enriched in 

2 3 5 u , the to ta l loss o f U is almost entirely due to fission s of 23 5 u . 

Corrections for other losses of total U can bé kept small enough to con*- 

tribute a negligible error. This method has been'applied by Lisman et a l. 

[ 6 ,2 1 ] , Rider et a l. [5 ] and Meyer et a l. [34] and requires a su fficien tly 

large number of fissio n s. 

3. 4 . 2. Flux monitors 

After measuring the neutron flux with a suitable monitor the number 

o f fissio n s is calculated for a known amount of fis s ile material using 

published fissio n cross sections. The monitors mainly used in thermal fissio n 

yield measurements are 59Co and sometimes Boron, where the change in the 

IOb/H-B ratio is measured mass-spectrometrically.

LAEA-SM-170/13 515 

The accuracy of th is method depends on the s e lf shielding corrections for 

monitor and sample,the values of the cross sections used and, in case a 59co 

monitor is used, on the h alf l i f e value used for ^ C o . Reliable s e lf shielding 

corrections cannot be applied, i f the sample is very thick, i .e . these 

corrections should not exceed 10 - 15%. 

2200 m/sc cross-section values have been used in many experiments. 

A recalculation o f the number of fissio n s, based on recent adopted cross- 

section values, would require information about the neutron spectrum, which 

i s , however, rarely available. The flux monitors usually have a l / v cross 

section but the 2200 m/sc values can be used only i f resonance absorption can 

be neglected, which i s , however, not the case in a reactor neutron spectrum. 

E.g. for r / T /T o » 0 .0 2 about 1 b arn would have to be added to th e 2200 m/s 

cross section of 59co, which is about yfo o f this value. U and Pu fissio n cross 

sections depend in addition strongly on the neutron temperature. 

3.4 .3 * Fission Counters 

In this method fissio n rates are-determined directly by counting the 

emitted fissio n fragments, which, of course, requires very thin samples. 

These are irradiated together with "th ick ” samples, which serves for 

fissio n yield measurements, but has s t i l l to be thin enough to avoid large 

self-sh ield in g corrections. 

Errors in th is method can further arise from corrections to the fission 

ra te .fo r sample thickness and in the determination of the counter efficien cy, 

which varies with sample position in the counter. 

3 .5 . Absolute fissio n yields 

In many publications resu lts are given as absolute fissio n yield s in 

percent per fissio n . The evaluator has, however, to distinguish between those 

experiments, where absolute yields have actually been measured, and those, 

where relatively measured yields have been normalized by the authors in 

order to obtain absolute y ield s. 

A measurement of absolute fissio n yield s requires that the number of 

fissio n s, that occurred in the sample, have to be determined as well as 

the absolute number of atoms, or any equivalent quantity, of a ll investigated 

fissio n products from this sample. In th is case the evaluator can only apply 

corrections for errors that have been introduced during the original processing 

of the raw data. 

In many radiochemical measurements yields are determined relatively to a 

suitable standard, mostly 99mo or Ba. The absolute fissio n yield o f the 

standard is either measured separately or the value is taken from literature. 

Sometimes absolute yields are obtained by normalizing relatively 

measured yield s with the aid o f interpolated and literature values in the 

mass ranges not covered by the experiment in such a way that the sum of 

yield s is either 100 fo for each mass peak or 200 $ for both mass peaks. In 

experiments using radiochemical techniques th is method has only been applied 

i f no absolute y ield of a suitable standard was available [ 2 6 ,3 5 * 3 6 ] . As 

many high yield masses have to be interpolated in such a work, the quoted 

absolute yield s are not very accurate and cannot be compared to other results 

without readjustment. Mass spectrometric measurements cover in general most 

o f the high yield range o f at ; least one mass peak. In th is case the r e liability 

of absolute yields depends m ainly on the number and accuracy of literature 

values in the range of yields hot:m easured in the experiment. 

A ll these resu lts from relaiive' measurements depend on earlier data and 

should therefore be renormalized'by ;the evaluator, using his own adopted values.


4. MAIN PUBLICATIONS OP EXPERIMENTALLY DETERMINED FISSION YIELDS 

When comparing published experimental fis s io n y ie ld s one finds 

that discrepancies are often larger than one would expect from the 

accuracies quoted or from those we have assigned in the previous chapter. 

These discrepancies cannot always be explained, but are mostly due to 

systematic deviations, normalization procedures and, in the case o f 

radiochemical measurements, resolu tion o f gross decay curves. Knowledge 

o f these discrepancies and o f the experim entalist's measurement and 

data analysis techniques is essen tial for a discussion o f existin g 

evaluations and evaluation procedures. Therefore those publications o f 

fis s io n y ie ld data, which receive heaviest weight in evaluations shall 

be b r ie fly surveyed. 

235 

4.1._____ U thermal fis s io n y ield s 

235 

Thermal fis s io n y ield s o f U have been determined mass spectrometrica 

lly by Farrar et a l. [3 7 ,3 8 ], who used the isob aric technique, and by 

Rider et al [5 ]i Lisman et al [6 ,2 1 ], Petruska et al [1 0 ,1 1 ], Steinberg 

and Glendenin [7 ] and Chu [39] who applied the isotope d ilu tion technique. 

Gorshkov et al [29] applied the integral mass spectrographic method. 

Rider et al Г51 and Lisman et al [6 ,2 1 ] determined the number o f 

fis s io n s by isotope d ilu tion mass spectrometry for one and four samples 

resp ectiv ely . A dditionally Lisman et al calculated a ll y ie ld s rela tiv e 

to 148щ, normalized the averaged values to lOOfo fo r the heavy mass peak 

and com pared the resulting yields to absolute yields determ ined fro m the 

num ber of fissio n s in ord er to check the relia b ility of the norm alization 

technique. 

Petruska et a l. [10,11] measured the neutron flu x with a Boron monitor. 

In addition to th eir own measurements they used the rela tiv e Kr and 

Xe y ie ld s o f Wanless and Thode [9 ] and normalized them to with the aid 

o f a known branching ra tio for ®^Kr and to 1^3(;s with the aid o f an unpublished 

13i-Xe: 133xe y ie ld ra tio resp ectively. Ce y ield s were linked 

to those o f Nd through the common y ie ld at mass 144, requiring, however, 

a rather large decay correction for 144q6> 

Farrar et al [3 7 138] normalized rela tiv e y ield s in the heavy mass peak 

to 100^> using the same Xe and Cs y ie ld s as Petruska et al [10,11] and 

interpolated values in the mass ranges not covered by th eir experiment. 

For the lig h t mass peak they used rela tiv e y ie ld s o f Kr and Rb and their 

normalization to Sr o f Petruska et al [11] and obtained absolute y ield s 

rela tiv e to th eir predetermined y ield s in the heavy mass peak with the 

aid o f an isotope d ilu tion ra tio also from [1 1 ]. Zr and Mo isotopes were 

linked to these y ie ld s by the isobaric technique. This technique depends 

on the accuracy o f decay correction s. 

Steinberg and Glendenin [7 ] used radiochemical, previous mass 

spectrom etric and interpolated y ie ld s together with th eir own measurements 

and normalized the whole y ie ld curve to 200$. Their rela tiv e Ru y ield s 

were normalized to a radiochemical value o f the 106Ru y ie ld and the overa 

ll accuracy o f absolute y ie ld s is rather low. 

Chu [39] measured only rela tiv e fis s io n y ield s in the rare earth 

region. 

Gorshkov et al [29] (see also [2 8 ]) do not in dicate, how they obtained 

absolute y ie ld s , which are given with low accuracy only.


The samples used for fissio n yield measurements at McMaster University 

[9-11* 371 38] and by Chu [39] were irradiated in low integrated neutron fluxes 

and required only minor corrections for neutron capture. Yields obtained 

in these experiments agree well with those of Rider et al [5 ] and Lisman 

et al [6 ,2 1 ] , who irradiated their samples in rather high integrated neutron 

fluxes, but used adequate nuclear data for corrections. 

Heavy mass yield s of Steinberg and Glendenin [7 ] obtained from high flux 

irradiations disagree seveialy with other mass spectrometric data, probably 

due to inadequate corrections and contamination. No d etails on irradiation 

and on cooling time are published. The same is true for the measurements 

of Gorshkov et al [2 9 ]. Although many of their absolute yield s agree 

approximately with other published data, discrepancies become evident only 

when relative yield s are compared. Sources of error due to the method 

i t s e lf are not indicated. 

4 .2 . 233U thermal fissio n yields 

235 

Lisman et al [6 ,2 1 ] and Rider et al [ 5 ] : same as for U. 

Bidinosti et al [40] made mass spectrometric measurements o f stable 

and long lived fissio n products, but used different normalization techniques. 

Only fin al resu lts are shown in the tables and no d etails on corrections and 

nuclear data used are included in their publication. The isotope dilution 

technique was applied for the isotopes of Sr, Cs, Nd and Sm and for -*-38ва> 

The isobaric technique has been used to link Ce to Nd through the common 

mass 144 and Zr to Mo through the common mass 95» but the h alf liv es used 

for decay correction are not published. Making use of the Xe yield s of 

Fleming et al [14] and Sm yield s of Melaika et al [13] the heavy mass peak 

was normalized to \O O fo. However, for tb io samples the number of fission s 

were calculated from a neutron flux measurement and yield s obtained in 

th is way were said to be 2 and 4 percent lower than those obtained from the 

normalisation technique and shown in the table. In the light mass peak Sr 

yields were calculated from the number of fissio n s. Kr yield s were taken 

from [ 14] and normalized to the -^^Cs y ield , and Rb yield s were obtained with 

the aid of the 85кг branching ra tio , which is not quoted. 

Relative Ru yields were linked to the Zr-Mo yield s by a radiochemically 

determined ratio and these relative yield s together with interpolated and 

extrapolated values were normalized to total 100$ minus the predetermined 

Sr,Rb and Kr yield s and extrapolated values below mass 83. Absolute yields 

and even isotope dilution data disagree with other mass spectrometric 

measurements. 

Steinberg et a l. quoted in [ 7 ] , have applied the method o f isotope 

dilution mass spectrometry for the isotopes of Zr, Mo and Ru and normalized 

their relative yield s to radiochemically determined values. 

Anikina et al [3 0 ,4 1 ] (summarized in [2 8 ]) have applied the isotope 

dilution and mass spectrographic method. Details on the analysis of Sr 

isotopes by the former Diethod are given in [4 1] and o f Cs isotopes and the 

rare earth fissio n products by both methods in [3 0 ]. Information on the 

irradiation of the sample can be found in [4 2 ]. The original relative 

yield s obtained by the method of isotope dilution agree after correction 

with those of [ 5] and [ 6 ] , whereas the values obtained by the integral 

method disagree. The same sample was analysed later by Gorshkov and 

Anikina. [43] for the isotopes of Zr and Sr as well as for °^Y and J^Ba 

by the integral mass spectrographic method. Relative and absolute yields 

calculated from the 233u depletion [ 42] disagree completely with other 

mass spectrometric measurements. The good agreement achieved by the


isotope d ilu tion method on the same sample in dicates, that natural element 

contamination cannot account for the discrepancies. It seems that the 

integral mass spectrographic method is not suitable for accurate fissio n 

y ie ld measurement. 

239 

4 .3 . Pu thermal fis s io n y ield s 

Rider et al [5 C] obtained absolute y ie ld s from the change in the 

isotop ic composition o f Pu in one sample, using a known capture to fis s io n 

r a tio . As for 233u and 235u rela tiv e y ie ld s obtained from the other two samples 

were normalized to agree in the sum o f y ield s with one sample, fo r which 

the number o f fissio n s have been determined. 

Lisman et al [ 6 j ] used the method o f isotope d ilu tion mass spectrometry. 

However, they found th eir y ield s too low compared to the measurements 

o f Pickel and Tomlinson Г15] and therefore revised th eir y ield s 

la ter Гбш, 21], using the normalization technique as described in 4*1« 

F ickel and Tomlinson [15] used the method o f isotope d ilu tion mass 

spectrometry. Yields in the heavy mass peak were obtained from two samples, 

irradiated in the same p osition . For one sample they measured the neutron 

flu x and the neutron temperature with the aid o f Co and Sm monitors. The 

number o f fissio n s were determined using g and s factors in the Westcott 

formalism. Yields obtained in th is manner for both samples agree well for 

the isotopes o f Nd and Ce. The y ie ld s o f Sm and Cs isotopes, and hence 

also those o f Xe, which were taken from Fleming et al [16] and normalized 

to 133cs, are about 5% lower fo r the Pu Al a lloy sample. However, their 

fin a l values were reached by a normalization o f each set o f y ie ld s to 

100$ and averaging them. 

Yields in the lig h t mass peak were obtained by isotope d ilu tion 

re la tiv e to the predetermined Cs y ie ld , but generally from samples d iffe r 

ent to those used fo r measurements o f the isotop ic compositions o f fissio n 

products. Only Zr y ield s were normalized to Mo y ield s at the common mass 95* 

The fin a l set o f y ie ld s contains also the Kr y ield s measured by Fritze et al« 

[17] and normalized to ®5Rb with the aid o f the ®5jCr branching ra tio . 

F ritze et al. [ 17] measured the absolute y ie ld o f '*'3'*'Xe by the isotope 

dilu tion technique together with a determination o f neutron flu x and temperature. 

Further, they measured rela tiv e Kr y ield s and the ra tio o f fissio n 

product Xe to Kr. Use was made o f the rela tiv e y ield s o f Fleming et al [16] 

to obtain absolute Xe and Kr y ie ld s. 

Krizhansky et al ['44»45] applied the method o f isotope d ilu tion mass 

spectrometry (resu lts o f isotope d ilu tion measurements are given in [2 8 ]. 

Although there are several discrepancies among the other mass spectrometric 

measurements already mentioned, the resu lts o f Krizhansky et al disagree 

much more seriou sly. Even re la tiv e abundances o f fis s io n product elements 

cannot be compared to other measurements. 

F inally the radiochem ically determined y ield s o f Marsden and Y affef 46] 

should also be mentioned, as heavy weight was given to th eir data in the 

la ter evaluations [1 9 ,2 0 ,2 2 ]. Marsden and Yaffe measured the neutron flu x 

with a Co monitor and calculated the number o f fissio n s from the 2200 m/sec 

value o f 742 barn fo r the fis s io n cross-section o f 239pu, This has been 

common pra ctice in many gxperiments, but can introduce considerable error 

in the determination o f Pu fis s io n y ield s due to it s strong 0.3 eV 

resonance. The smallest p ossible value for a reactor neutron spectrum cross 

section (pure maxwellian at 20° C) is about 780 b and inclreases with increasing 

neutron temperature and contribution o f epithermal neutrons [4 7 ].

LAEA-SM-170/13 519 

An example o f the influence o f the 239pu cross section value is given in 

section 7 . 3. Surprisingly the absolute fis s io n y ield s o f Marsden and Yaffe 

agree fa ir ly well with mass spectrom etric measurements at several mass numbers. 

However, i f absolute y ield s obtained from a flu x measurement are included in 

an evaluation, the cross section data used have to be checked. 

5. DISCUSSION OP EVALUATIONS AND EVALUATION METHODS. 

In chapter 2 the information included in the previous evaluations have 

been summarized from a u ser's point o f view. Now the evaluation procedures 

themselves and the treatment o f experimental data shall be discussed in the 

lig h t o f the review o f experimental methods and the individual experiments 

described in the previous chapter. 

5.1. Treatment o f data in previous evaluations 

After a survey o f existin g fis s io n y ie ld measurements and knowledge o f 

the methods used i t is p ossible to better understand and analize previously 

used evaluation procedures. 

K atcoff [ 8] evaluated y ie ld s fo r individual fis s io n product isotopes 

within the same mass chain. He preferred mass spectrometric measurements 

where available and averaged resu lts o f equally re lia b le measurements or 

selected values he considered superior to others which avoids the averaging 

o f discrepant data. Original data were renormalized by checking the sum o f 

y ie ld s against 100$ and corrected for neutron capture. When selectin g ^35u 

fis s io n y ie ld measurements, the data o f Anikina et al [28] were not used 

and the other mass spectrometric data [7 , 10, 11, 39 ] averaged. For 233U 

and Pu the evaluation o f recommended y ie ld s is not cle a r, as these do 

not correspond to individual experimental sets o f y ie ld s , even after renormalization. 

Radiochemically determined y ield s were used fo r readioactive precursors 

o f fis s io n products measured mass spectrom etrically. Therefore d iscrepant 

y ield s are given for isotopes belonging to the same mass chain, which 

are not consistent with charge d istribu tion theory derived from measurements 

o f independent y ield s [ 48, 49] . 

Ferguson and 0 'K elley [ l 8] used mass spectrometric data onlyi for the 

mass ranges covered by these measurements. They have lowered a ll those 

y ield s reported by B idinosti et al [4 0 ],th a t had been obtained by the 

isotope d ilu tion technique, by. 3$, according to the average d ifferen ce 

between the normalization procedure and the flu x measurement (see 4. 2. ) . 

The y ield s o f Zr, Mo and Ru isotopes remained unchanged. Relative y ield s 

reported by Gorshkov and Anikina [43] and Steinberg and Glendenin [7 ] for 

the lig h t mass peak and by Anikina et al [28] for the heavy mass peak were 

readjusted to agree in the sum o f y ield s with those o f B idin osti et al 

[4 0 ]. Only the data o f [28,43] obtained by the integral mass spectrographic 

method were used and no correction s were applied to origin al data. Ferguson 

and O'Kelly used the normalization procedure, described in 3 . 5*1 to ca lculate 

absolute y ie ld s fo r each mass peak separately. 

Although the yields reported in [28] and [43] were measured at d ifferen t 

times, the same sample was used and hence the resu lts are based on the 

same number o f fis s io n s . After the readjustment made by Ferguson and O'Kelley 

the ra tio o f y ie ld s in the lig h t mass peak to those in the heavy mass peak 

is completely d ifferen t from the ra tio o f orig in a lly determined y ie ld s. 

Large discrepancies between some reported experimental y ie ld ra tio s o f 

d ifferen t elements were smoothed by the method o f matching the sums o f


y ie ld s . Although in con sistencies remained even a fter readjustment the 

y ie ld s were averaged by Ferguson and O'Kelley. However, at the time o f 

th eir work no other mass spectrometric measurements were available to allow 

a check. 

Croall [ 19] evaluated individual fission products belonging to some mass 

chain. Original data were corrected for decay and neutron capture. Relative 

measurements and R-values were readjusted to his adopted standard y ield s. The 

treatment of mass spectrometric data is not evident from the report. When 

comparing recommended yields with the original data of the references given, 

it appears that some readjustments were made, especially for discrepant 

absolute values. In some cases, where only one reference was used to obtain 

a recommended y ie ld , this does not correspond to the original value. The 

measurements of Farrar and Tomlinson [38] and others published in laboratory 

reports [5>6,34] are not included in C roall's evaluation. The selection of 

preferred yield s is also not evident, as sometimes obviously not a ll results 

from references have been used which axe liste d along with the recommended 

value. Radiochemical measurements were averaged together with mass spectrometrically 

determined y ield s. For the values reported by Marsden 

and Yaffe [46] were considered even superior over a ll other measurements 

and generally adopted as recommended y ield s. I f sets o f preferred experimental 

yield s disagreed in a certain value, they were averaged. Yields adopted 

for different isobars within the same mass chain are sometimes highly 

discrepant and not consistent with charge distribution theory [48,49]* 

Rider et al [20] proceeded on a mass by mass basis comparing a ll 

isotope y ie ld s within a mass chain that essen tially represent tota l 

chain y ie ld s . Generally no readjustments o f o rig in a lly reported absolute 

y ie ld s were made. Exceptions are pure re la tiv e y ield s that were normalized 

to adopted y ie ld s and the data o f Anikina et al [2 8 ]. The data reported for 

235u were normalized to the adopted value of their relative standard and 

those reported for ^39pu were renormalized to other measurements for mass 

142 and above. This is , however, not valid« and rather arbitrary, as the 

original normalization is established by a measurement of 142q6 relative to 

140ce [45] Md therefore genuine, although in complete disagreement with 

other measurements. 

233u fissio n yield s of [7 ,2 8 ,4 0 ,4 3 ] were used as adjusted by 

Ferguson and O'Kelley [l8 ] and yields recommended by Katcoff [8 ] were 

also included in the averaging procedure. Thus, for example, the relative 

Xe yields of Wanless and Thode [ 9] are included 3 times: as adjusted by 

Katcoff [ 8 ] , Petruska et al [10] and Farrar and Tomlinson [3 8 ]. Radiochemical 

measurements before i 960 were not used, later ones were averaged 

together with mass spectrometric data, but a few outstanding values were excluded 

from the mean. 

Meek and Rider [22] evaluated not only chain y ield s but y ield s fo r a ll 

fis s io n products by combining experimental resu lts with charge d istribu tion 

theory and decay schemes. They used essen tia lly the same experimental 

data and renormalizations as Rider et al [2 0 ], except that they included 

some more recent measurements, and therefore the discussion shall not be 

repeated. But as they separated y ield s o f isobars within the same mass 

chain sometimes lower y ie ld s o f radioactive precursors o f fis s io n products 

were allowed fo r , which are not consistent with charge distribu tion 

theory. When d ifferen ces were too large, y ie ld s o f isobars were averaged. 

In no case was the cumulative y ie ld o f a daughter allowed to be smaller 

than the cumulative y ie ld o f it s parent. As Rider et al [20] they used 

y ie ld s estimated by Weaver et al [95] f ° r masses not covered by measurements. 

These estimates are, however, based on the e a rlie r evaluation o f K atcoff 

and do not agree with in terpolation s between more recent measurements.


In the discussion of their evaluation, Meek and Rider state that 

the unweighted averaging of data is not satisfactory and should only be 

considered as preliminary. They propose for a later evaluation estimates 

of uncertainties of individual experiments to obtain weighted averages. 

They also suggest the use of improved Gaussian charge distributions and 

calculations of unmeasured y ield s. We were only recently informed that in 

the meantime Meek and Rider have published a new evaluation [4 9 ]. Unfortunately 

th is is not yet available to us and can therefore not be 

discussed for comparison. 

5 .2 . Discussion of evaluation procedures 

Discrepancies among evaluations do not only arise from the inclusion 

of different experimental data. They are also due to the procedure of 

evaluating absolute yield s on a mass by mass basis. Differences in renormalizations 

of experimental data lead to different absolute yields 

that are compared. Depending further on the number of radiochemical 

measurements included, individual yield s that show best agreement w ill 

also be different in the evaluations. I t w ill be shown which consequences 

th is procedure has and how the resulting drawbacks can be avoided. 

Mass spectrometrically determined relative yield s o f the isotopes of 

one element agree, with some exceptions, also actually within 1 % . Discrepancies 

due to decay or neutron capture can usually be corrected. Errors 

due to contamination of naturally occurring stable isotopes can often be 

detected by intercomparison of these relative yield s. 

For the linking of relative element yield s by isotope dilution, isobaric 

technique or integral mass spectrographic method,the actual agreement 

among measurements is not as good. In the case of the isobaric technique 

ratios can be adjusted with the aid of better known h alf liv e s. Relative 

yield s obtained by the fir s t two methods agree generally s t i l l within a few 

percent. The consistency of data sets can again be checked by intercom- 

parison and discrepant values can be excluded. 

Poorest agreement show absolute y ield s. Exceptions are the data for 

[1 0 ,1 1 ,3 7 ,3 8 ,5 ,2 1 ], which is also reflected in the relatively good 

agreement among evaluations, and for * Ри[5с1,6Л,21,118] . The values 

of absolute yields depend on the way, thqywere obtained. It has been 

shown in chapter 4 that these are widely different and not always straight 

forward. I f the normalization technique is used, absolute yields depend 

also on errors introduced with the linking of relative element y ield s. 

Part of the mass yield curve w ill be lower, the other part higher than 

that determined in other experiments. 

Discrepancies in absolute yield s constitute a source o f error in 

evaluations. Measurements, which show good agreement in relative y ield s, 

may disagree, i f only absolute yield s are compared. On the other hand 

measurements, which disagree in a comparison of relative yield s may 

coincide with different sets of other data at different mass numbers, 

including radiochemical measurements. These coincidences may not only 

influence renormalizations, but can lead to preferred values, which are 

not consistent with relative mass spectrometric y ield s. 

The accuracy of more recent radiochemically determined yields depends 

mainly on the accuracy o f h alf l i f e values used, the determination of 

the number of fissio n s and the decay curve resolution. I f this is satisfactory, 

absolute yield s can be o f an accuracy comparable to some single 

absolute mass spectrometric y ie ld s. But as they are measured only for 

certain mass numbers and not for stable isotopes, their inclusion in averages 

may distort relative yield s well established by mass spectrometric measurements.


In our work [4*51] the interpretation of gamma spectrometric 

measurements on burnt fuel elements is based on activity ratios of fission 

products listed in the introduction (l.). This method avoids large 

corrections that have to be applied in a determination of absolute 

activities. Therefore the accuracy of relative yields is most important 

for our work. For this reason and in order to avoid errors introduced if 

only absolute yields are compared, we concluded that the best suitable 

evaluation method would be to start with arbitrarily normalized relative 

mass spectrometric measurements and establish the shape of the yield curve 

in the peak regions in this way. These relative yields can then be normalized 

with the aid of absolute yields.Radiochemical yields should only be used 

for the final normalization and as a check of relative and absolute yields 

obtained in this manner. An evaluation based on these considerations was 

started in 1969 and the procedure used is outlined in the next chapter. 

Independent from our work Walker made an evaluation based on similar 

conclusions. The first set of evaluated yields for ^35u Was presented in 

197O [54]. This paper includes a detailed description of the treatment of 

experimental data and results of individual steps in his evaluation procedure. 

He normalized experimental mass spectrometric yields of different 

authors to agree in the sum of Zr yields for the light mass peak and in the 

sum of Nd yields for the heavy mass Peak. This selection is reasonable, as 

these elements cover the greatest parts of the respective mass peaks. By 

a selection of consistent relative yields he obtained the shape of the main 

portions of the mass peaks and normalized them as a group so that the sum 

aver each mass peak is 100$. 

Walkers evaluation would have been adequate for our work, had the results 

been available earlier. However, we learnt about the paper presented at 

the Helsinki Conference [54] only almost a year later. The evaluations 

of yields from other fissile isotopes were not published before last 

year [55^] and are still not yet available to us. These results could 

therefore not be compared to our evaluation, but will probably be presented 

at this conference [56]. Thus, our present calculation was carried out as a byproduct 

of our investigations of irradiated fuel elements. 

6. PROPOSAL OF EVALUATION PROCEDURES 

6.1. The present evaluation procedure 

The principle has already been outlined in the previous chapter. 

Some details shall be given as information to the recommended yields 

shown in tables IV to VII. The following evaluation procedure was 

adopted: 

step 1: Mass spectrometric measurements were collected first and corrected, 

where possible, for differences in cross section and half life 

values between those used in the original work and those shown in table II. 

The cross section data shown in this table are based on Walker's comprehensive 

compilation [55a] and only updated for later measurements. For 

fission products,where no measurements are available, the capture cross 

sections calculated by Cook [58] are used. The half life Values are based 

on the compilation of Martin and Blichert-Toft [52]» but several more 

recent measurements were incorporated in a new evaluation carried out by 

one of us. The complete set of fission product half lives above 1 day will 

be published later as SGAE report. Table II includes values based on publications 

issued after the fission yield evaluation was started. Readjustments 

were made later, if necessary. The corrections to the published yield


data have been calculated with the aid of the computer programme CHAIN, 

briefly described in [4], by simulating the special irradiation conditions 

as given by the authors of the yield data. 

Step 2: Corrected sets of relative mass spectrometric yields were 

compared and checked for consistencies. Lata which suffered from incomplete 

or out of date corrections, and where no readjustment was possible, were 

rejected as well as those measurements that obviously disagreed severely 

with others. 

Step 3* Relative yields of the isotopes of individual elements were 

averaged first. If sufficient measurements were available for comparison 

only consistent ratios were selected. 

Step 4s Data for linking relative element yields were compared next. 

As stated in 5*2 the agreement is not so good for these data. Therefore 

also ratio measurements (see section 3-3) were used for fissile 

isotopes other than 235u, mainly to serve as a check. In some cases they 

were also included in the average, if their accuracy is comparable to that 

of isotope dilution data. Here the selection of preferred yields was not 

so easy, due to poorer overall agreement. Individual examples will be 

given in chapter 7- 

Step 5* Relative element yields were linked according to the data 

obtained from step 4. This was adopted as especially in the experiments 

carried out at Mo Master University [9-17» 37,38,40] the samples used for 

isotope dilution measurements were not the same as those used for measurements 

of the isotopic distributions of fission products, or were even obtained 

in different experiments. Also the higher precision of xelative 

measurements can be maintained. 

During the actual evaluation this step had to be modified slightly. 

The procedure outlined above led to some disagreement between isotope 

dilution data and isobaric yields. Therefore neighbouring elements had to 

be adjusted together. But final yield ratios were always checked against 

those obtained in step 3» 

Step 6: The original idea was to normalize the groups of relative 

yields to most accurate absolute yields and was applied to the first preliminary 

results used for the calculations. We learnt from Walker's evaluation 

[54] that sum of yields not measured mass spectrometrically was 11.015$ 

(of which 6.16$ is the well known 99Mo yield,)for the light mass peak and 

only 3.635$ the heavy mass peak. Therefore this method of normalization 

seems to be well justified and was adopted in our first complete evaluation 

of 233u and 235u fission yields. 

The final normalization was checked in several ways: 

- The separate normalization of each mass peak was checked by 

comparing isotope dilution data of several isotopes firom the light and 

heavy mass peak with the adopted values. This showed systematic deviations 

of the order of 1 - 2$. 

- The adopted absolute y ie ld s were compared to most r e lia b le absolute 

measurements based on determ inations o f the number o f f is s io n s . The agreement 

w ith radiochem ical y ie ld s was w ith in the lim it o f th e ir e r ro r s . A comp 

a rison w ith mass sp ectrom etric data showed good agreement fo r the heavy 

mass peak o f 235u, but again d e v ia tio n s o f the order o f 1-2$ fo r the lig h t 

mass peak and fo r both mass peaks o f 233u.


TABLE II. RECOMMENDED FISSION PRODUCT NUCLEAR DATA 

fissio n 

product h a lf-life 

Cross-sections (barn) 

typeu thermal“ R es.In t.c 

83Kr maxw 200 150 

8^Kr 10.73+0.06 a p ile 8 

89 Sr 50. 52+0.05 d pile 0.42 

9°Sr 2 8 .6 + 0 .4 a p ile 0.8 

91* 58. 5I+O.1 2 d p ile 1.4 

6З.98+О.1 2 d p ile 1 

35.O45+O.OIO d p ile 4 

99M0 66.7 +0 .5 h p ile 2 

103Ru З9 .З5+О.1О d p ile 10 

105Rh 3 5.5 +0.2 h maxw 17000 I7 OOO 

106Ru 368.3 +2 .0 d maxw 0.15 2 

125sb 2.75+0.04 a p ile 1 .6 

131mTe 30 +2 h p ile 0.1 

! 3 ! i 

8.О5+О.О2 d d maxw 0.94 8 

131mXe П . 98+О.О5 d p ile 50 

131Xe maxw 100 83О 

!3 3 i 

20.9 +0.1 h e pile 0.005 

133mXe 54 ±2 h pile 50 f 

133Xe 5 . 29+O.OI d pile 190 

133Cs maxw 29.5 450 

135T 6. 585+О.ОО2 h p ile 0.05

T A B L E II (con tin u ed) 

fissio n 

product 

h a lf -life 


Cross sections (barn) 

type Ъ thermal** 

135Xe 9 . 172+ O.OO5 h 2200 2. 65x l06 g 

13?Cs ЗО.О + 0.2 a p ile 0 .1 1 

141Ce 32.55 + 0.02 d p ile 29 

143Pr 13.58 + 0.03 d maxw 100 150 

143Nd maxw З25 60 

Res. Int. 

144Ce 284.5 + 0 .4 d maxw 1 2 .2 

14 5Nd maxw 45 250 

14?Nd 11.00 + 0 .0 3 d p ile 100 

14?Pm 2. 623+ 0.001 a maxw 182 h 2400 h 

147 Sm maxw 61 646 

148% 40. 9 + 0.2 d 1 pile 25000 

148Pm 5 .З7 + 0 .0 1 d p ile 3000 

149pm 53*08 + 0.05 h p ile 1400 S 

14^Sm 2200 42100 g 

^ S m maxw 100 240 

2200 15000 g 

1 52Sm maxw 206 3000 

4*9 + 0 .1 a p ile 4040 

a Only fissio n products relevant for correction 

Ъ 2200 = 2000 m/s cross-sections 

maxw = maxwellian average cross-sections at 20.4 С 

p ile = reactor spectrum cross-section 

с Reduced in fin ite dilute resonance integral (above l /v ) 

d Branching to 131mXe . U K 

e Branching to ^33mXe : 2 .8 fo 

f Results o f Reynolds and Emery [53] suggest that this cross section 

might be in the order o f lo4 barn. 

g Used with g and s factors in Westcott convention 

h Production ratios 47*24$ to '*‘4®mPm, 4 )2 .1 (ifо to ^4®gPm 

, 148g 

i ¥¡o internal transition to Pm 

525 

с


Radiochemical yield s in the range o f masses 121 to 130 important for 

the fin al normalization show very large discrepancies, as can be seen for 

i n -the i as-t column of table IV. Measurements in this mass range are very 

scarce for other fi s s ile isotopes and the sum of yields in th is mass range 

much higher. This introduces considerable uncertainties in the fin al 

normalizations. To avoid discrepancies as given above and reduce the overall 

uncertainty, the fissio n yield s were reevaluated for both mass peaks together 

and fin a lly normalized by a combination o f the two procedures, which w ill 

be discussed individually in chapter 7. 

As a further check the to ta l number of neutrons (prompt + delayed), 

can be calculated from the adapted set of yield s according to : 

DT = Mp - L - H 

where ^ _ magg numker Qf fis s ile isotope + 1 

L = average mass of light fragment 

H = average mass of heavy fragment 

L + H can be calculated from: 

L = I ^ ( mass x .Yield) \ -g _ / 5L(mass x y ield ) j 

V 5. yield /l i g h t \ Slyield / heavy 

The calculated value of can be compared to recommended values 

[4 7 ]. This is , however, not a very meaningful check. On the one hand the 

value o f U j derived in this manner is rather sensitive to changes of 

individual y ield s. On the other hand errors may cancel. This can be seen from 

table I I I , where й ^ calculated from fissio n yield s is compared to [4 7 ]. 

For 235u was also calculated for the fissio n yields recommended by Meek 

and Rider [22] and by Walker [5 4 ]. Differences in L among the evaluations are 

compensated by differences in H . The only conclusion that can be drawn from 

such a comparisoji is that at least part of the normalization is in error, i f 

the calculated и disagrees severly with the recommended value. 

TABLE III. COMPARISON OF vT VALUES 

fis s ile 

isotope Source L H 

235u 

233„ 

Walker [54] 

Meek,Rider [22] 

this work 

94.855 

94.925 

94.849 

138.650 

138.591 

138.660 

‘" r 

2.495 

2.483 

2.492 

recommended 

value[47a]a 

2.4229+.0066 

th is work 93.377 138.159 2.464 2 .4866+. 0069 

2»P u th is work 98.814 138.116 З.070 2.8799+. OO9O 

a In the 1973 evaluation the new values w ill be 

about 0.5$ lower [47b]


Apart from the fin a l normalization the present evaluation d iffe r s from 

that o f Walker [5 4 ] only in two resp ects. Due to the separation o f steps 3 

and 4 re la tiv e y ie ld s o f fis s io n products, which were only measured in one 

235 

experiment, are maintained as published. Examples fo r U are the y ie ld s 

o f °Y, 139ва and ^4^-Ce measured only by Farrar et a l. [37|38] and o f •1-35cs 

measured only by Petruska et a l. [1 0 ], but the differen ces are only slig h t, 

i f the two sets o f y ie ld s are compared in table IV. 

The second d ifferen ce is that resu lts o f individual measurements 

have been used in our evaluation rather than y ie ld s averaged by the authors. 

This has the advantage that more sets o f data are available for comparison 

and the internal consistency o f d iffere n t experiments can be 

checked. Discrepant values, which may strongly influence the average y ie ld s 

o f one experiment, can be excluded. Also a larger number o f determinations 

within one experiment can be accounted fo r . This is important, as no weighted 

averages are taken in th is evaluation. 

This d ifferen ce in procedures is re fle cte d by a comparison o f Xe y ield s 

fo r 235u in table IV. These are based on the measurements o f Lisman et al 

[ 6 ] . For the determination o f the number o f fis s io n product atoms, and thus 

for rela tiv e y ie ld s, they quote about equal accuracies for a ll samples. 

The main d ifferen ce in uncertainties among the samples arise from the determination 

o f the number o f fissio n s and is accounted for in the weighted 

average. The same trend can be observed i f the Xe y ie ld s o f Lisman et a l. 

[6 ,2 1 ] determined from the number o f fissio n s (column 6: "F iss") are 

compared to those obtained by the normalization technique (column 7 • "Norm") 

in table IV. 

6.2. Proposal o f an improved evaluation procedure 

The drawback o f a "hand" evaluation is that no weighted averages can be 

taken. During the evaluation o f “ ■'Pu thermal fis s io n y ie ld s we made the 

experience that discrepancies arise which can only be solved rather delib 

e ra te ly . Therefore we propose a computerized evaluation o f fissio n 

y ie ld s that can simultaneously take account o f a ll correla tion s. However, 

in advance to such a com puter-fitting procedure the experimental data 

serving as input have to be analyzed ca refu lly and errors have to be 

assigned in dividually. Also a p re-selection o f experimental resu lts has 

to be done. Such a computer programme could then include the follow ing 

features: 

- Relative abundanoies o f isotopes should be averaged f i r s t , 

according to step 3 in the previous section. Overall errors should 

be calculated. 

- Then the y ie ld curve could be adjusted simultaneously using isotope 

d ilu tion data, isobaric y ie ld s and measured absolute y ie ld s. 

Changes o f the rela tiv e y ie ld s , which were averaged f i r s t , should 

only be allowed for within the calculated errors. 

- I f there is disagreement among rela tiv e isotop ic y ie ld s, these can 

be included in the simultaneous fit t in g procedure to determine, which 

value is in error. However, provision has to be made within the 

whole procedure that values, where the discrepancies exceed th eir 

errors, are not just averaged. 

- Boundary conditions are: the to ta l y ie ld curve must ¿urn up to 

exactly 200f>, The s p lit between the two mass peaks, M, should be 

according to : M


My = mass o f f i s s ile isotope _ 

\j = average number o f neutrons emitted in symmetric fis s io n near M 

Д У 3 = uncertainty in U 

These boundary conditions could serve to adjust interpolated and very 

uncertain y ie ld s . In addition, charge distribu tion s could be incorporated 

into the f i t to allow a check o f experimental isobaric and independent y ie ld s. 

7. RESULTS OF THE PRESENT EVALUATION 

This paper is mainly devoted to a discussion o f evaluation procedures 

and a ju s tific a tio n o f the present evaluation method. For the sake o f 

completeness our resu lts are also included, but space does not permit 

detailed description s o f the treatment and selection o f data. These w ill be 

published la ter as SGAE reports. Here only the general information shall be 

given together with some special features. 

Our recommended y ie ld s fo r 23Û, 233U and 239Pu thermal fis s io n and 

fo r 232^h fast fis s io n are compared to other evaluations in tables IV to VII 

resp ectiv ely. The data o f Lisman et al are included fo r the reasons given 

in chapter 2. Radiochemical measurements are also shown fo r illu stra tio n . 

In some cases they are in good agreement, also with our recommended y ie ld s, 

others are highly discrepant. Thermal fis s io n y ield s for ^41pu and fa st y ield s 

fo r 2ЗЬц аре s t i i i in preparation and only preliminary resu lts available. 

Fast fis s io n y ie ld s fo r ^35u and *^9pu were not evaluated, as the complete 

set o f y ie ld s measured by Lisman et a l. [21] is presently adequate and 

further measurements in other laboratories are in progress. 

For the calcu lation o f y ie ld s other than to ta l chain y ie ld s either 

measurements o f independent y ie ld s were used as compiled for example by 

Wahl et al [48] or those calculated by Crouch [4 9 ]. The cumulative y ie ld o f 

135i was derived from the resu lts cf Hawkings et al [5 9 ]. 

235 

7 .1. Thermal fis s io n y ield s o f U 

Mass spectrom etric measurements used are those o f Lisman et al [2 1 ,5 7 ], 

Rider et al [5 ], Chu [39]* "the origin a l experiments from McMaster University 

[9-1 3, 37, 38] and y ield s o f the light mass peak reported by Steinberg and 

Glendenin [7 ]- Other measurements were not used for reasons already given 

in 4 .1 . The agreement between the selected experiments lis te d above is far 

better than that observed for mass spectrometric measurements o f 233u and 

239pu y ie ld s. 

Yields o f the ligh t and heavy mass peak were normalized a rb itra rily to 

the sum o f y ie ld s o f ^45Nd and This starting point was chosen because 

Nd isotopes were measured in most experiments and th is sum is not affected 

by in su fficie n t correction s fo r decay or neutron capture. Ce and Ba yield s 

werelinked to Nd y ield s as a group, because the isotope d ilu tion ra tios for 

Ce and Ba were not consistent with the isobaric y ie ld measurements o f Farrar 

et al [3 8 ]. For the same reason Sr (Y ), Zr and Mo y ield s were normalized 

together. Sm y ie ld s o f Lisman et al [21] were not used, as they disagree with 

low flu x measurements. 

Relative y ie ld s o f both the lig h t and the heavy mass peak were 

normalized together in such a manner that the sum o f y ie ld s in the lig h t


mass peak only was 100%. The agreement with measured absolute y ield s was 

so good ,and the sum o f y ie ld s in the heavy mass peak was in ciden tally 

100.0011, that no renormalization was considered necessary. 

233 

7 .2 . Thermal fis s io n y ie ld s o f U 

In th is case the measurements used to establish the y ie ld curve were: 

Mass spectrom etric: Lisman et al [2 1 ], Rider et al [5 ], Fleming et al [1 4 ], 

B idinosti et al [4 0 ], Anikina et al [28,30,41] 

Steinberg and Glendenin [7 ] and Melaika et al [1 3 ]. 

Ratio measurements: Gordon et al [94] and Bunney and Scadden [9 2 ], a fter 

correction for ¿35u reference y ie ld s . 

F irst a ll mass spectrom etric data were normalized to t lE sum o f Nd 

isotopes, R-values at mass numbers 143 and 144, and the consistency checked. 

The y ie ld s o f Anikina et al [28,30,41] could be corrected according to the 

233u depletion data given in [42] together with an approximate irradiation 

time and according to the decay correction s applied in the origin a l work 

and the h a lf liv e s used, as given in [3 0 ,4 1 ]. Only the isotope d ilu tion 

values o f B idin osti et al [40] were used fo r th is check. 

The ra tio s o f y ie ld s in the lig h t mass peak and o f Cs isotopes to those 

o f Nd are in reasonable agreement for the data o f Lisman [2 1 ], Rider [5 ]i 

Gordon [94] and the isotope d ilu tion values o f Anikina [30,41]- The rela tiv e 

Sr and Cs y ie ld s o f B idin osti et al are about 1C$ lower than the averages o f 

other data. As no d eta ils are given in th eir p u blication , th eir isotope 

d ilu tion values were excluded and only re la tiv e element y ie ld s used in cases, 

where no remarkable correction s were required. Yields obtained by the integral 

spectrographic method [30,43] were not used, as even re la tiv e y ie ld s d isagreed 

severely with other measurements, and sources o f error o f th is method 

are not s u ffic ie n tly known. 

As the remaining sets o f data are reasonably con sisten t, they were adjusted 

to agree in sums o f y ie ld s o f both mass peaks and the general procedure 

was follow ed as described in section 6.1. 

Special attention had to be paid to Sm y ie ld s . No mass spectrometric 

measurements were made on samples irradiated in low integrated neutron 

flu x . 147Sm y ie ld s obtained in these experiments require large correction s 

fo r neutron capture and decay and were therefore considered no more 

r e lia b le than the 147щ y ie ld s obtained from ra tio measurements. The 

outstanding high value o f Melaika et al [13] was not used. Calculated 

charge d istrib u tion s [49] indicate that independent y ie ld s o f 148pm 

and 50pm + 150gm could be 0.3$ o f ^4 jjd and °ffo o f 15®Nd resp ectively. 

Corrections fo r natural Sm contamination based on th is value fo r 148gm 

would lead to a "contamination correction " for 154gra Qf about 10 - 15% o f 

it s y ie ld . Sim ilarly, the amount o f 150gra preSent in mass spectrometric 

measurements is generally added to the 149gm y ie ld , but the calculated 

independent y ie ld s [49] o f 150pm and ! 50gm together would be about 6$ 

o f the 149sm y ie ld . As these independent y ie ld s have not yet been confirmed 

experimentally, no correction s were applied and the mass 149 y ie ld 

shown in table V has to be considered as the sum o f mass 149 cumulative 

y ie ld and 15°Pm + 15tfem independent yield. 

151 

Generally correction s fo r neutron capture in Sm are not very relia 

b le fo r high neutron flu x irradia tion s, as it e cross section depends 

strongly on the neutron spectrum. As the 235u y ie ld s measured by Bunney


T A B LE IV. 235 U FISSION YIELDS (THERMAL) 

Mass 

No. 

this 

work 

V/alker 

[44] 

Meek 

Rider 

[22] 

Croal] 

' [19] 

72 I6xl0_5 1.6xlO~5 1.6xl0-5 

73 0.0001 0.0001 0.00011 

74 0.00035 0.006° О.ООО35 0.00035 

75 0.001c 0.0012d 

76 0.003° 0. 0025a 

77 0.008 0.008 О.ОО83 О.ОО8З 

78 0.02 0.02 0.02 0.020 

79 О.О56 О.О56 О.О56 О.О56 

80 0.11° 0.11° 0.094d 

Lisman et al 

[21,57] 

а Ъ 

Fiss Norm 

radiochemical 

measurements 

81 0.22 0.22 0.18 0.22 .22+.02 [62] 

82 0.35 0.35 0. 24d 

83 О.5З2 О.5З О.52 0.55 0.526 0.529 . 56+. 04 [62] 

84 1.000 1.00 О.97 1.00 1.00 1.01 .93+.05 [62] 

85Kr 

85 

86 

87Br 

8?Rb 

0.288 

1.328 

I .97 

2.56 

0.273 

1.33 

I .96 

2.55. 

O.27I 

1.30 1.ЗО 

I .89 

2.53 

2.ОЗ 

3.2 

2.54 

0.2880 

1.32 1.33 

I .94 

2.54 

1.95 

2.57 

88 3.62 3.62 З.58 З.55 3.61 3.61 

. 273+. 004 [63] 

89 4.84 4.78 4.76 4.75 4 . 78+.O7 [64] 

90 5.91 5.88 5.83 5-55 5. 9О 5.93 4.02+.11 [65]® 

5. 61+.22 [6 6 ]f 

91 5 . 9З 5.91 5 . 9О 5.8 5.9О 5.92 5. 62+. 11[ 67] , 6 . 16[ 68] 

92 5.98 6.02 5.98 6.03 5-95 5.98 

93 6.39 6.44 6.39 6.51 6.34 6.37 

94 6.45 6.47 6.44 6. 5О 6.41 6.45 

95 6.54 6.52 6.41 6.50 6.45 6.51 6.0+.3[69] 

96 6.29 6.33 6.29 6.40 6.23 6.26 

97 6.00 6.05 6.21 5-9 5.86 5.92 5 .4 2 [64],6 .2 [69] 

98 5.81 5.78 5.86 5-9 5-77 5.83 

99 6.11 6.16 6.16 6.14 6. 14S11 6.24 6. 16+.08 [ 70]Ц 

6.03+.08 [5 9 ]g

T A B L E IV (continu ed) 

Mass 

No. 

100 

101 

102 

103 

104 

105 

106 

107 

108 

109 

110 

111 

112 

113 

114 

115 

116 

117 

118 

119 

120 

121 

122 

123 

124 

125 

126 

t h i s 

work 

6.32 

5.05 

4.19 

2.95 

1.83 

0.90 

0.387 

0. 17° 

0. 057e 

0.024 

0. 017° 

0.014 

0.010 

0.004 

0.012 

0.011 

0.011 

0.011 

0.011 

0.012 

0.013 

0.014 

0.015 

0.0164 

0.024 

0.028 

0.063 

W a lk e r 

[44] 

6.33 

5.07 

4.19 

2.85 

1.83 

О.83 

0.39 

O.19 

0. 07° 

0.03 

0.022° 

0.018 

0.016° 

0.014° 

0.012° 

0.011 

0.011° 

0.011° 

0.011° 

0.011° 

0.012° 

0.014 

0. 015° 

0.018 

0.022° 

0.029 

0.06 

Meek 

R i d e r 

[22] 

6.44 

5 .О2 

4.17 

3.0 

1.81 

O.9O 

0.39 

O.I9 

0. 07d 

0.03 

0 . 0 l 8 d 

O.OI9 

0.010 

0.016 

0.014 

0.0104 

0.018 

0.011 

0.014 

0.014 

0.014 

0.014 

0.015 

0.016 

0.018 

0.021 

0.032 


C r o a l l 

[19] 

6.50 

5.2 

4 .1 

2.85 

0.83 

0.38 

0.19 

0.03 

0.018 

0.0104 

0.015 

0.021 

L is m a n e t a l 

[21,57] 

F i s s a Norm 

6.24 

5.ОЗ 

4 .I 9 

1.82 

O.O29I 

6.30 

5 .О8 

4.21 

1.83 

0.389 

r a d i o c h e m i c a l 

m e asu rem e nts 

2 .9 2 [7 l]h, 2.97[72]h 

1 .4 [7 3 ],3 .7 [7 4 ] 

. 85+. 20 [ 7 3] 

.39¿.03 [71] 

.024+. 003 [75] 

.014+. 002 [75] 

.012+.001 [75] 

.0104[76], .0 ll8 [7 4 ] 

.010 [ 74] 

.0145+.0010[31]1 

,013+.002[77]i 

,0164+.0012 [ 31] 

.0277 '21' hj .021 [79] 

.0254 ж h 

U .036 ‘78' 

.0297 Ж Л 

.018 J 4 .


T A B L E IV (continued) 

Mass 

No. 

th is 

work 

126 Sn 0.060 

Walker 

[44] 

Meek 

Rider 

[22] 

Croall 

[19] 

Lisméin et al 

[21,57] 

F issa Norm6 

radiochemical 

measurements 

127 0.11 0.13 0.137 0.10 Sn .143+. 028"80" 

. 128+.015 !31° 

sb . 105+. 004 '31n 

.144+.020 ‘ 8 l' 

128 0.36 0.39 О.46 .36 [3 1 ]1 

12*sb 

129 j. 

0.63 

0.64 

0.90 1.0 

1.0 

1.12 

0.9 

.39+.03 [82] 

. 63+.О3 [31] 

I . 12+.28 [ 81] 

.9 + .2 [83] 

130 2.00 2.0 2.1 2.0 2.O+.5 [84] 

131 2.82 2.79 2.91 2.92 2.79 2.86 3.02[85],3.30[86] 

132 4.20 4.16 4.26 4.37 4 . I 6 4.27 4 .49[85],4.21[86] 

133 6.73 6.75 6.69 6. 6О 6.73 6.76 6.62[85], 7.48[86] 

6. 62[ 87] , 6.75 [67] 

134 7.67 7-57 7.8 0 8.03 7 .5 1 7.73 8.00 [ 85] 

135 6.55 6.51 6.43 6.41 6.37 [ 85] 

136 6.18 6.10 6.46 6.44 

137 6.26 6.24 6.20 6.20 6.28 6.32 6.13[67],6.22[88] 

6.23 + .07 [6]J 

138 6.82 6.80 6.71 7.22 6.80 6.83 

139Ba 6.55 6 .56 6.48 6.55 Ba 6. 55+.10 [ 70] 

139La 6.55 6.48 8.2 6 . 57+.02 [67] 

140 6.37 6.34 6.34 6.40 6.31 6.35 6 .36[88], 6.35[89] 

6.36L90], 6.36Î91J 

141Ce 5.85 6.10 6.0 5.50 5. 5З 

141Pr 5-85 5-84 6.10 5-65 

142 5.91 5.92 5.90 5-9 5.88 5.90 

143 5-92 5. 9З 5.91 5-9 5.90 5.92 5.67[89], 5.93 [92] 

144 5-44 5.41 5.40 5.62 5.42 5.45 

145 З.91 З.92 3.88 3.95 3.86 3.89 

146 2.96 2.97 2.95 3.05 2.95 2.97

T A B L E IV (continued) 

Mass 

No. 

147Nd 

147 sm 

th is 

work 

2.22 

2.22 

Walker 

[44] 

2.23 

2.23 

Meek 

Rider 

[ 22] 

2.19 

2.19 


Croal1 

[19] 

Lisman et al 

[21,57] 

a ,r b 

Fxss biorm 

2.24 

2. 3О 2.12 2.14 

148 1.67 1.67 1.67 1.71 I .69 1.70 

radiochemical 

measurement s 

2.23 [92] 

149 I .05 1.06 1.04 1.1 1.00 1.01 I .05 [92] 

15c 0.644 О.65 0.65 0.67 О..638 0.640 

151 0.407 0.42 0.43 0.43 0.408 0.409 

152 0.262 0.26 0.24 0.265 0.212 0.213 

153 0.163 0.164 O.158 0.15 .160 [ 92] 

154 О.О72 0.073 0.064 О.О77 О.О56З О.О564 

155 О.О32 0.032 0.031 О.ОЗЗ .031 [74] 

156 0.014 0.013 0.0134 0.014 .0138 Г92] 

.0125+^0010 [93] 

157 0.0062 0.006 0.0066 0.0061 Eu .00618 [ 92] 

.0060 + .0007 [ 83] 

158 O.OO3I О.ОО25 0.0037 0.002 .0031 +.0006 [ 93] 

159 O.OOIO5 0.001 0.00105 0.001 Gd .00101 [92] 

160 0. 00035е 0.001° О.ОООЗЗ 

161 9xl0-5 8.2xlO~5 8.7xlO-5 8.8 x 10-5 [ 92] 

a Y i e l d s c a l c u l a t e d fro m num b er o f f i s s i o n s 

b Y i e l d s o b t a i n e d b y n o r m a l i z a t i o n t e c h n iq u e ( s e e t e x t ) 

с I n t e r p o l a t e d v a l u e s 

d C a l c u l a t e d y i e l d s 

e Corrected for h a lf l i f e ( 28.5 a instead o f 19.9 a.) : 5*78 

Adjusted for reference y ie ld s : 5*85 + 0.16 

f I f a h a lf l i f e o f 28.5 a instead o f 28 a is used th is y ie ld 

becomes 5 -7 2 . 

g 99тс y ie ld determined spectrophotom etrically 

h Used for recommended y ie ld 

i Total chain y ie ld 

j Corrected fo r "У-гау in ten sity, as given in [52 ]


TABLE V. 233U FISSION YIELDS (THERMAL) 

Mass 

No. 

This 

vjork 

Rider 

et al 

[ 20] 

72 0. 0001° 9 . 9xlO-5 

73 0.00033° 0.00033° 

74 0. 0009° 0. 0009° 

75 0.0023° 0. 0023° 

Croall 

[19] 

76 0. 0068° 0. 0068° • 

Ferguson. 

O'Kelly 

[ 18] 

» d 

0.03 

Lisman et al 

[6 ,21,5 7] b 

Fiss Norm 

radiochemical 

measurements 

77 0.02 O.OI9 0.02 0.02 .0 l9 [9 6 ]g , .0 2 i[9 6 ]h 

78 0.04e 0. 10f 0. 1e 

79 0.09® 0. 19f 0.19 e 

80 0. 18е 0. 28f 0. 28e 

81 0.33 0. 46f 0.34 0.46e .33+0.04 [62] 

82 0. 60е 0. 69f 0.69e 

83 1.023 I .05 1.14 I .14 1.03 1.02 

84 

85Kr 

1.69 1.76 1.91. I .91 1.73 I .71 .77+.08 [97] (Br) 

0.507 O.512 

85 2.19 2.42 2.45 2.46 2.22 2.21 

86 2.86 2.96 3.32 3.20 2.90 2.88 

87 4.01 4-47 4.50 4.47 4.06 4.04 

88 5-54 5.37 5-36 5-36 5-57 5.56 

89 6.41 6.10 5.90 6.28 5.56[98],5.60[99] 

6 . 6 6 [ i o o ] , 6 . 5 [ 9 6 ] 

90 6.88 6.30 6.2 6.18 6.96 6.96 6.19[98], 6 .53[99] 

91Sr 6.50 5.6 6.27[97],4.82[98] 

9!y 6.52 6.0 6.37[100] (Sr) 

91Zr 6.52 6.60 6.45 6.57 6.60 6.64 3-55[98] (Y) 

92 6.65 6.63 6.60 6.63 6.69 6.69 6.76+.50[97](Sr) 

93 7.04 7.02 6. 9О 7.02 7.09 7 .О8 6.35+.50[97](Y) 

94 6.81 6.70 6. 7 О 6 .70 6.91 6.92 

95Zr 6.21 6 .13 6.10 6.22 5.01[98],6.15[99] 

9"*Mo 6.21 6 .13 6.15 6.22 6.40 6. 3О 5 . 16[ 9 8 ] (m > ) 

96 5.73 5.64 5.64 5-64 5-84 5 . 8О

T A B L E V (continued) 

Mass 

Ko. 

This 

work 

Rider 

et al 

[ 20] 

Croall 

[19] 


Ferguson 

O'Kelly 

[ 18] 

Lisman et al 

[ 6 , 2 1, 57] 

F issa Norm® 

97 5-39 5-59 5-46 5-48 5.52 5 . 4З 

98 5.14 5.25 5.20 5.25 5.22 5 . I 6 

radiochemical 

measurements 

99 4.89 5.12 4.96 4.96 5. I 6 5 .О6 4 .9 6 [1 0 l],5 .7 7 [9 7 ] 

100 4.38 4.49 4.45 4-49 4-46 4 . 4I 

101 3.19 3.10 2.90 2.84 3.27 3.24 

102 2 .4 2 2.38 2.22 2.16 2.48 2.44 

103 1.60 1.63 1.60 1.6 1 .6 [96]g ,1.78[99] 

2. 02[ 98] 

104 

105 

1.02 

0.548 

1.00 

0. 50f 

0.95 

O.I5 

О.92 

0 .5e 

I .04 1.01 

.146+. 037 [98] 

106 0.255 0.25 О.24 0.22 0.262 0.260 • 259[ 98] , . 28[ 96] g 

•23[99] 

107 0. 12e 0. 12f 0. 12e 

108 0. 065e 0. 07f 0.07e 

109 

110 

0.04 e 

о . о з 

O.O4O 

0.03f 

0.047 0.04 

О.ОЗ® 

•04[96]g 

i l l 0.021 0.023 0.021 0.03 .025[96]g ,.020[98] 

. 0187+.0002 [ 97] 

112 0.015 0.016 0.014 0.02 . 0i 25[ 97] , . 0l 6[ 96] g 

113 0. 015f 0. 02f 0. 02e 

114 0. 020e 0. 02f 0. 02e 

115 0.021 0.02 O.OI7 0.02 . 020[ 96] g , . 02l [ 96] h 

116 0. 0216 0.01f 0. 01e 

117 О.О22' 0.01f 0. 01e 

118 

119 

0. 022* 

k 

О.О23 

0. 02f 

0. 02f 

0. 02e 

0. 02e 

120 O.O2515 0. 02f 0. 02e 

121 0.027 e 0.018 0. 02e 

122 о . о з о к 0 .03f 0.03e 

123 0. 0386 0.04f 0.04e 

124 0.0501* 0. 05f 0. 05e 

121gSn .O l8[96]g



Mass This Rider Croall Ferguson, Lisman et a] 

No. work et a l. 

£ 20] 

[19] O'Kelly 

[ 18] 

[6 ,21,57] , 

Fiss Norm 

radiochemical 

measurements 

125 0. 1101 0.05 0.060 0. 1e 0.116 125sSn .050[96]g 

126 0. 18e 0.26f 0.26e 

127 0. 50e 0. 6l f 0.59 0. 61e .59 +.08 [ 98] 

128 1. 00e i . 05f 1. 05e 

f 

129 1. 56e 1 .7 0 1.7e 

f 

130 2.40e 2.33 2.33e 

131 З.54 3.46 3.55 3.41 З.51 З.50 

T "50 

2.84[98], 3 .14[99] 

3 Te 4 .57j 4.32 4.32[98],4.18[99] 

132 4.84 4.74 4.80 4.68 4.88 4.86 

133I 6.00^ 3.4 3.37[98],6.63[99] 

133Cs 6.03 5.96 5.90 5.88 6.06 6.05 

134 

TTC 

135T 

6. I 5 

• 

6.09 6.0 5-99 6.13 6.10 6.23[99] ( I ) 

4.89J 4 .78 4.84+.07[10?] 

135 6.27 5-2 6.0 5-84 I : 4. 64[99j,5 -2i [ 103] 

136 6.82 6.68 6.70 6.68 

137 6.85 6.58 6.65 6.64 6. 9З 6.94 5.39[98],6.13[104] 

138 6.00 6.3 6.4 7 .1 0 5-97 6.00 

139 6.34 6.64 5.9 6.61 6.34 [100] 

140Ba 6.35j 6.59 6.25 6 .3 7 [l0 2 ],6.01 [99] 

140La 6.45 6.70 

140., 

6.45 6.59 6 .71 6 .71 6. 5З 6.48 

141 6. 56 6.77 6.40 6.24 5.30[98],6.23[99] 

7.00[100] 

142 6. 61 6.72 6.79 6.79 6 .71 6 .61 

143 5.88 5.86 5.9 5.91 5.85 5.82 6.99 [98] 

144Ce 4.60^ 4.62 4.60 4.51 4.67 4.66 3.69[98],4.63[99] 

144Kd 4.64 4.62 4.60 4.67 4.66 

145 3.39 3.38 3.46 3.38 3.37 3.36 

146 2.53 2.54 2.60 2.58 2.53 2.52 

147 1.80 1.86 I .92 1.93 1.78 1.74


Mass 

No. 

This 

work 

Rider 

et al 

[ 20] 

Croall 

[19] 


Ferguson 

0 'K elly 

[ 18] 

Lisman et al 

[6,21,57] 

Fissa Normb 

148 1.30 I .29 1.33 1.28 1.30 1 .ЗО 

149 0.76 0.77 0.80 0.77 0.773 0.744 

150 O.5OI O.51 О.56 0.55 O.5OO 0.497 

151 О.32 0.36 0.33 9.З 5 0.365 О.364 

152 0.22 0.20 0.215 0.22 0.186 O.185 

153 O.IO7 0.12 0.13 0. I 5 

154 0.0449 0.03 0.048 0.047 О.О458 0.0445 

radiochemical 

measurements 

155 0.026 О.ОЗ О.ОЗ 

156 0. 012^ 0.0116 0.0121 0.01 Eu .0117 [ 92] 

157 О.ОО72 О.ОО635 0.00635 4 

158 0.0024® 0.0024 

159Gd O.OOO9I 0.000905 0.00091 < 0.01 

160 

l 6l„,_ 

Tb 

0.00035® 

0.000118 

0.0003 

0.00017 0.00017 ■ 

a F i s s i o n y i e l d c a l c u l a t e d fro m num b er o f f i s s i o n s 

b F i s s i o n y i e l d o b t a in e d b y n o r m a l i z a t i o n t e c h n iq u e (s e e t e x t ) 

с C a l c u l a t e d y i e l d s o f W ea ver e t a l [95] 

d E x t r a p o l a t e d y i e l d s 

e I n t e r p o l a t e d y i e l d s 

f Assumed y ield s taken from reference [ l 8] 

g Data from [9 6 ], as revised by Steinberg [7 ] 

h Data from [9 6 ], as revised by K atcoff [ 8] 

i Reference [ 6] , corrected fo r У -г а у intensity as given in [52] 

j ^3^Te, '*'33I , ^^Ba, '*'^0e and "'"'Êu are assumed to be 94. 5$i 

99-5$. 78?»i 98. 5/W 99-2% and 96. 5% o f "the tota l chain y ie ld resp ectively 

к Relative mass spectrom etric y ie ld s o f reference [61] normalized to y ield s 

o f masses 115 and 125.


T A B L E VI. 239Pu THERM AL FISSION YIELDS 

Mass 

Wo. 

th is 

work 

Meek 

Rider 

[ 22] 

Croall 

[19] 

Katс o ff 

[ 8] 

Lisman 

et a la 

[21,57] 

radiochemical 

measurements 

72 0.00011 0.00011 0.00012 0.00012 L.1x10_4[74] 

73 0 . 00025Ъ 0 . 00025е 

74 0 . 000б2Ъ 0 . 00062° 

75 0.0016Ъ 0.0014С 

76 0.0035Ъ 0 . 0031е 

77 0.0075 0.0072 0.0073 •0075[107] 

78 0.028 0.026 О.О25 ,028[107] 

79 0 . 06Ъ 0.025° 

80 о . и ъ 0 . 048е 

81 0.186 0 .178 0.182 . 186+0 . 025[ 108] 

82 0.24Ъ 0.16е 

83 0.298 0.29 О.29 О.29 0.301 B r.312[107],.31l[l08] 

84 0.482 0.47 О.47 0.47 0.487 Br .419[108] 

85кг 0.129 0.12 O .I27 0.130 .099±.004[63] 

9 1 ? 

91Zr 

85 0.566 О.56 О.54 О.5З9 0.574 

86 0.764 0.75 0.75 О.76 0 .770 

87 0.980 0.91 O.9I 2 О.92 1.00 

88 1.385 1.41 I .42 I .42 1 .3 5 

89 1.74 1.73 1.71 I . 7I 1.74+Л5[4б],1 .8 [7 4 ],1 .65[100] 

90 2.13 2.2 2.О5 2.25 2.09 2. 05+ .04[ 46] 

2.53 

2.53 

2.53 

2.42 

2.60 

2.60 

2.6 

2. 4I 

2.6 

2.43 

2.9 

2.61 2.52 

92 3.05 3.06 3.12 З.14 3.02 

93 З.92 3.89 З.94 З.97 3.95 

2.3[74],2.37[100l 

2.41+.11[46],2.8[74] 

Y 2.40[1П ]

T A B L E VI (continued) 

Mass 

No. 

th is 

work 

Meek 

Rider 

[22] 

Croall 

[19] 


K atcoff 

[8 ] 

Lisman 

et a l .a 

[21,57] 

94 4.48 4.42 4-45 4.48 4 . 5О 

95 Zr 

9 5 m o 5.07 

5.07 

5-2 

5.2 

5.06 

5.0 

5 .8 

5.03 

96 5.12 5.06 5-13 5 .17 5.12 

97~ 

5 . 61^ 

97 

' Mo 5-70 

5.3 

5.61 

5-25 

5.61 

5-5 

5.65 

98 5-93 5-84 5-84 5.89 

radiochemical 

measurements 

4.86 5.06+.33[46],5.6[74] 

5.64 5-3[74] 

99 6.33 5-9 5.86 6.10 6.59 5.61± .ЗЗГ46],6.1[74] 

5.66+.07»,6.79+.15 [l0 9 ] 

S.02+ .18[ 101] , 6. 1[ 110] 

6.17+.19L112J 

100 7 .1 6 7.05 7.0 5 7.1 0 

101 6.01 5.86 5.86 5.91 6.50 

102 6.09 5*94 5.94 5.99 6.65 

103 5.86 5*6 5-79 5.67 5.79+.37[46],5.5[74] 

104 6.03 5.88 5.88 5.93 6.61 

105 5-47 5.47 5-47 3.9 5.47±.06[46],3.7[74] 

106 4.64 4.4 4.04 4 .57 4-55 4.04+.22[46],4.7[74] 

4.52+p.23[6m]k 

107 з . з ъ 3.4° 

108 2.0b 2.6° 

109 1.13 1.2 1.13 1.40 L.13+.06[46],1.0[74] 

L .6[110],2.0[10l] 

110 0.57Ъ 0.75° 

111 0.27 0.25 0.28 0.23 . 28+ .04Г46] , ,27[74] 

. 26[ 101] , . 212[ 110] 

112 0.11 0.10 0.093 0.12 ,093+.003[46],.10[74] 

. 15[ 101] , . 11[ 110] 

Ц ? 0.065 0.072 0.065 .065[107]



Mass 

Ho. 

th is 

work 

Meek 

Rider 

[ 22] 

114 0 . 041Ъ 0 . 0550 

Croall 

[19] 

Katcoff 

[ 8] 

Lisman 

et a l . a 

[21,57] 

radiochemical 

measurements 

115 0.036 0.039 О.ОЗ6 0.041 .03 6+ .002[46] , .048[74] 

•035Ü101] 

116 0.035Ъ 0.037° 

117 0.035n 0.037° 

118 0.035n 0.035° 

119 о .о з б п 0 . 036е 

120 0 . 0 38n 0.037° 

121 0 . 041b 0.044 О.О43 

122 0.045n 0.047° 

123 0.055Ъ 

124 0.075П 

0 . 056° 

0 . 070f 

125 0.110e 0.069 0.071 0.116 

126 0.23b 

,0 

0 .1 6 

1 PI Sn .04l[74] 

127 0.55 0.46 О.55 0.39 •55+.03[46], .37[74] 

128 1 .0 Ъ 0 . 85е 

129 1 . 65Ъ 1.7° 

130 2 .6 Ъ 

с 

2.7 

131 3.73 3.69 3.8 З.78 З.60 3 . 80+ .14[ 46] , 3 . 6[ 74] 

132 5.25 5-2 5.25 5.26 5.09 5 .51±.27[46],4.9[74] 

!33x 

133 

6 .9 1 j 

6.94 

5-3 

6 .6 

5 . 5З 

6.90 

5-2 

6.91 7 .18 

134 7.43 7.31 7.47 7-47 7 .2 0 

5.53±.06[46],5.0[74] 

I 6 . 9 7 ,Xe 7.2 3 [ 105]

T A B L E VI (continu ed) 

Mass 

No. 

135j 

135 

136 

th is 

work 

6. 32^ 

7.48 

6.83 

Meek 

Rider 

[22] 

5-7 

7.21 

6.66 

Croall 

[19] 

5-97 

7 .1 7 

6.65 


K atcoff 

[8 ] 

5-7 

7 .1 7 

6.63 

Lisman 

et a la 

[21,57] 

Jl3.92 

radiochemical 

measurements 

6.041[102],6 .3 6 1[103] 

Xe 7.43 [IO 5] 

137 6.62 6.56 5.8 6.63 6.74 5.40+ .39[46],5.8[74] 

138 5-46 5 . 9I 6.28 6.31 5-40 

139 

140 

Ba 

140Ce 

л niLa 

Ce 

5.82 

5-49° 

5 . 5З 

5-24 

5.24 

5.67 

5 . 51 

5 . 51 

5.75 

5-75 

5.78 

5-47 

5.56 

5-47 

6.11 

5-87 

5-4 

5.6 5.61 

5-7 

5 .1 

142 4.97 4.87 4-97 5.01 5.04 

1/ч Се 

4.48 

Nd. 4.48 4.52 

144rP 

4 d 

3.75j 

З.76 З.79 

4.28 

4.57 

4.09 

З.84 

5 .З 

4-57 4.48 

З.79 

З.9З З.78 

5.4[74],5-87[100] 

5.47+.32[46],5.36[74] 

Ba 5.27[102] 

5.56[100],4.58[111] 

6.11+ .31Í46],4.99[1H ] 

5. l 8+ .13[ 112j 

4 .2 8 + .2 l[4 6 ],3 .9 0 [lll] 

Pr 4 .16 [111] 

4.09+.20[461,4.9[74] 

3e 3 . 85+ .09[ l l 2] 

145 З.04 2.99 3.12 З .1З 3.03 Pr 3 -4 5 [H I] 

146 2.49 2.45 2.57 2.60 2.49 

Sm 

2.09 

2.09 1 .8 7 

I .46 

2.07 

2.2 

2.07 2 .15 

148 1.68 1.68 I .70 1.73 1 .7 0 

I . 46+.08 [ 46] 

149 I .24 I .30 I .31 1 .З2 1.24 [id 1.1 1 ,Pm 1.27 [111] 

1§0 О.97 О.96 1.01 1.01 0.965 

151 О.76 О.76 0 .78 0.80 0.811 •72[111] 

152 О.58 О.57 0.59 0.62 0.581 

153 0.44 О.36 0 .37 0.37 • 39[7 4],-36[111],.4 4[Ю 6]



Mass 

N o . 

■ t h i s 

w o rk 

Meek 

R i d e r 

[ 2 2 ] 

C r o a l l 

[19] 

K a t c o f f 

[ 8 ] 

Lism a n 

e t a l a 

[ 6 , 2 1 ] 

154 О .27З O .25 O .29 O .29 0.27 

r a d i o c h e m i c a l 

m e asu rem e nts 

I 55 0.17 0.24° O .23 .166[111] 

I 56 0.12 O .O 9 0.07 0.11 .12[74],.062+.004[46] 

• 121[111], Л2[10б] 

157 0 . 080^ 0 . 076° Eu .074 [ H l ] 

158 0.045Ъ 0 . 042° 

159 0.022 0.021 0.021 0.021 •02l [ l l l ] , . 022[ 106] 

160 

b 

0.011 0 . 0098° 

161 O .O O 5I 0.0039 0.0039 0.0039 Tb .0050[111],.0050[106] 

162 0 . 0025Ъ 0.0024C 

166 0.000076 0.000068 O .O O O O68 

a Yields obtained by the normalization technique (see 4-1) 

b Interpolated value 

с Calculated y ie ld , taken from Weaver et al [95] 

d Original value corrected fo r h a lf l i f e (see 3 .2 .2 , 28.5 years instead 

o f 2 7. 4. years.) 

e Yield o f Lisman et al [6 m] corrected fo r y - -ray in ten sity, as 

given by Martin and B lich ert-T oft [5 2 ]. -jp/i 

f Cumulative y ie ld fo r stable Sn. The independent y ie ld fo r Sb 

is given as O.O88 according to Marsden and Yaffe [46] 

g Absolute measurement (fo r corrections see 7*3) 

h Relative 99jj0 y ie ld from fis s io n , (fo r correction see 7«3) 

i Relative ^35l y ie ld normalized to 6.32 fo r ^5y thermal fis s io n , 

j Cumulative y ield s o f r , ^33I , Î, 44ce and ' Eu were 

taken to be 98. 5t 99*6, 84. 5 » 99*2» 99»75 an¿ 93 percent o f tota l 

chain y ie ld . 

к Gamma spectrometric measurement by comparison with a Ru standard 

source. 

n rela tiv e mass spectrometric Sn y ield s (fu el rod) taken from reference 

[6 1 ], as rela tiv e y ield s do not change very much fo r d ifferen t types 

o f fis s io n .


and Scadden [9 2 ] are in excellent agreement with our recommended values, 

the follow in g procedure was adopted: the sum o f 151sm and 152gm y ield s 

were averaged for mass spectrom etric measurements. The 151pm y ie ld o f 

Bunney and Scadden [9 2 ], corrected fo r l^Sm independent y ie ld [4 9 ]t 

was subtracted from th is sum to calcu late the y ie ld o f 152sm> Altogether 

the Sm y ield s shown in table V are not considered to be very re lia b le 

and have to be checked by measurements on samples irradiated in low 

neutron fluxes. 

Relative y ield s o f both mass peaks were normalized to the ligh t mass 

peak only, as the sum o f interpolated and radiochemical y ie ld s was 

only 3*766%. The corresponding sum in the heavy mass peak was 6.75% with 

the main contribution (5*55%) from interpolated y ie ld s at masses 128 to 

130. Yields obtained by th is normalization were 1 - 2 % lower than absolute 

y ield s o f [5 ] and [2 1 ]. The sum o f absolute y ield s o f Lisman et al [21] 

is 98.18% including the mass 89 value from our normalization. This could 

not possibly be brought in agreement with the sum o f radiochem ically determined 

y ie ld s , and therefore the normalization was le f t unchanged. 

Relative y ie ld s in the heavy mass peak were normalized to absolute Cs 

and Nd y ie ld s o f [ 5] and [21] and the interpolated values for masses 128 

to 130 were readjusted to make the sum o f heavy mass y ie ld s 100 % . This 

can be ju s tifie d , as the ra tio o f y ie ld s in the lig h t mass peak to those 

o f Nd and Cs obtained by Lisman et al [21] were 1-3% higher than those 

o f other measurements [30, 41, 94]. 

239 

7 .3 . Thermal fis s io n y ield s o f Pu 

239 

Experimental data used fo r the evaluation o f Pu thermal fis s io n 

y ie ld s are: 

Mass spectrom etric measurements: Lisman et al [2 1 ], Rider et al [5 ], 

Pickel and Tomlinson [I 5 ]i F ritze et al [1 7 ], 

Fleming and Thode [16] and. Krizhanski et al [4 5 ]. 

Ratio measurements: Dange et a l. [105]. 

As the combined USSR measurements [28,44*45] disagreed with others, 

only some relative yields of [45] were used, as no corrections could be 

applied. 

Evaluation o f these y ield s was rather d if fic u lt because o f several 

discrepancies that could not be resolved. D etails cannot be given here 

and only the most important selection s w ill be outlined. 

Ru y ie ld s have only been measured fo r one sample by Fickel and 

Tomlinson [ 15] i and disagree severely with those reported by Lisman et al 

[21] and Dange et al [105]. However, i t was stated by Lisman et al [21] 

that Ru could not be completely recovered from sample d issolu tion . 

In addition th eir re la tiv e Ru y ie ld s (which were normalized by a ra tio 

measurement o f 106ru) are not consistent and y ie ld s in the lig h t mass 

peak sum up to 103% when normalized to the heavy mass peak. Therefore 

only the Ru y ie ld s o f Fiokel and Tomlinson [15] were selected. The mass 

99 y ie ld is an average o f the readjusted R-values o f Dange [105] and 

Lisman [6m], which are in reasonable agreement. They were adopted rather 

than c o n flic tin g radiochemical measurements also for reasons given below. 

Most d if fic u lt was the evaluation o f Cs and Xe y ie ld s and needs some 

explanation. I f the analyses o f individual samples in [5,15*16,21,105] 

are compared, the values obtained fo r the 1^3cs y ie ld are grouped around 

about 7.1% and 6.6% with no obvious systematic trends observed for 

measurements carried out at one laboratory. As a compromise a ll available 

ra tio s for th is y ie ld have been averaged. The ra tio 133xe : 54xe


T A B L E VII. 232 Th FAST FISSION YIELDS 

Mass 

No. 

This 

work 

Harvey 

et al 

[25] 

Croall 

[ 18] 

Mass 

No. 

This 

work 

77 0.010 0.014 0.015 104 0. 08a 

Harvey 

et al 

[25] 

78 0.035a 105 0.05 0.05 

79 0.08a 106 0.041 0.058 

80 0. 2a > 2. 98a 107 0.04a 

81 0 .4a 108 0.04a 

82 1. 0a I09 O.O41 ^ 0. 56a 0.052 

83 1.87 2.06 2.0 110 0.045a 

84 

«5кг 

3.44 

0.82 

3.78 3.6 111 0.045 0.07 

85 4.0 4.01 3.9 112 0.062 0.07 

86 5.66 6.21 6.0 113 0.06 0.045 

87 5-99 6.57 114 0. 06a 

88 6.32 6.92 115 O.O57 i O.O65 

89 6.72 7.14a 6.7 116 0.05a V 

90 7.40 7.4 0 7 .2 117 O.O49 0.053 

91 7.26 7.45 6.8 118 0. 05a 

92 7.49 i 6.6 119 0. 05a 

93 7.21 i 19.31a 120 0.05 

94 6.23a í 121 O.O55 

95 5.ЗО 5 . 4З 5-4 122 0.04a 

96 4 .8 a 4.97a 123 O.O3I - 3 . 0 4 a 0.029 

97 3.96 4.52 5.2 124 0.03a 

98 3.4 3.69 a 125 0.033 0.025 

99 2.76 2.86 2.80 126 0.05a 

100 1.9a 127 O.O9 0.110 

101 1.14a k 3.97a 128 0. 18a 

102 0 .5 a 129 0.36a 

юз 0.146 0.146 0.16 1ЗО 0.8a 

V 

Croall 

[19]

T A B L E VII (continued) 

Mass 

No. 

This 

work 

Harvey 

et al 

[25] 

Croall 

[18] 


Mass 

No. 

This 

work 

Harvey 

et al 

[25] 

131 I .52 I .56 1.7 144 7.66 7.20 7.9 

132 2. 7 О 2.76 2.9 145 5.78 5.52 

133 3.74 3.75 3.3 146 4-95 4.73 

134 5.06 5.18 5*4 147 2.97 3.14 3.8 

135 4.65 4 .66 5.6 148 2.18 2.08 

136 5.ЗО 5.44 5-7 149 1.44 0.88 0.9 

137 4.61 4-60 6.5 I 50 I .09 I .04 

4 

138 6.02a 5.79a 151 0.41 

139 7.38 06.99 6.8 152a O.32 

140 8.31 8.61 7-4 153 0.21 

141 7.28 7-74 7 .З 154 

_ _ , 9- 

0.06 

142 7.22a 7.27 a 155 0. 01a 4 

► 1.24a 

Croall 

[19] 

143 7.12 6.79 7.3 156 0.0026 0.003 0.003 

a Interpolated values 

y ie ld s was measured by Fleming et al [16] for two samples with good 

agreement, however, in severe c o n flic t with the Xe to Cs ra tio o f Lisman 

et al [ 2 l ] which is based on separate determinations o f these elements 

with rather large uncertainties for Xe. Therefore the ra tio o f Fleming 

was adopted fo r the normalization o f Xe to 133Cs and allowance was made 

for th eir margin o f error towards the ra tio o f Lisman et a l. This group 

o f y ie ld s is , however, very u nsatisfactory and should be reinvestigated. 

The arguments and procedure for Sm y ie ld s are sim ilar to that for 

233u, but the calcu lated independent y ie ld s o f 148pm and 150pm are only 

0.1$ and 4 o f the respective Nd y ie ld s. 

As no d irect and relia b le absolute fis s io n y ie ld measurements are 

available, absolute y ie ld s were obtained by the normalization technique. 

F inally, to support our argument not to rely on absolute fis s io n 

y ie ld measurements and to illu s tra te the uncertainty associated with such 

measurements, an example is given. Jain and Ramaniah [109] made two series 

o f measurements o f the 239pu fis s io n y ie ld o f 99m0< One is based on the 

determination o f the neutron flu x , the other one rela tiv e to the 235u 

fis s io n y ie ld o f 9 9 m o . They used the 2200 m/sec fis s io n cross sections 

and obtained the resu lts included in table VI, as well as 6.06% fo r the 

235U fis s io n y ie ld o f 9 9 m o . We recalcu lated th eir resu lts using g and s 

fa ctors from a recent survey [47Ъ] according to 

S' = 6 0 (g + rs) 

/


With г Т Т/То1 ~ 0.0022 calculated from the reported Cadmium ratio for 

Co of 200, we obtained the following resu lts: 

neutron 

temperature — > 20°C 40°C 6o°c 80°C 100°C 120°C 

d235 

6.13 6.17 6.20 6.22 6.24 6.25 

P u^^relative 6.32 6.22 6.O9 5-98 5-84 5 . 7 I 

2 39 

Pu absolute 6.29 6.22 6.12 6.03 5.92 5. 8I 

In spite of this example the data of Marsden and Yaffe were adopted 

for mass numbers not covered by the experiments liste d above. They agree 

with our adopted yield s at several mass numbers and therefore a renormalization 

was not considered necessary. 

232 

7 .4 . Fast fissio n yield s of Th 

No complete set of mass spectrometric measurements is reported for 

fast fissio n y ield s of Therefore we had to rely mainly on ratio 

measurements. The references used are: 

Mass spectrometric measurements: Kennett and Thode [113]» Harvey et al [2 5 ]; 

Renormalized ratio measurements: Iyer et al [3 6 ], Harvey et al [2 5 ], Turkevich 

and Niday [35]» 

Radiochemical measurements: Bresesti et al [ 89] , Crook and Voight [33]* 

Broom [ 11 5 ] , Ifyttenbach and von Cunten [1 14]. 

We started with the most extensive set o f yield s o f Iyer et al [ 36], 

normalized the mass spectrometrically determined Kr, Xe and Cs yield s at 

mass numbers 132 and 137 and radiochemical yield s at 140ga> Normalization 

points were selected for other data sets, which do not include those mentioned 

above. Mass spectrometric ratios were not changed and the gaaima spectrometric 

measurements o f Bresesti et al Г89] were considered superior to 

others, especially for the yield s o f ^ Ce and ■l44Cet which depend on decay 

curve resolution in measurements o f ß -spectra. Fission yield ratios 

may change, when going from a fast reactor neutron spectrum to 3 Me V fission . But 

it is assumed, that a ratio o f neighbouring mass yield s w ill not change 

apreciably and. therefore the 92gr y ield reported by Broom was calculated 

relative to the adopted ^ S r y ie ld . Other yields reported for 3 MeV 

fissio n o f 232iph, including those of Lyle et al [116,1 17], were not used. 

A ll relative yield s were fin a lly normalized to a total of 100% for 

the sum o f yield s in the heavy mass peak, as many mass numbers in the light 

mass peak are not covered by experiments. In the evaluation o f Harvey 

et al [2 5 ], shown for comparison in table VII, each mass peak was normalized 

to 100%. 

7 .5 . Uncertainties o f recommended yields 

It is d iffic u lt to assign uncertainties to values obtained by 

a normalization of relative y ield s. An attempt to derive accuracies 

o f 235U fissio n yield s from the data used w ill be discussed in detail


in a forthcoming publication. Judging from the overall agreement with 

experimentally determined absolute yield s and the consistency of the 

data used to obtain relative y ie ld s, we assign the following uncertaint 

ie s : 

23\ l: 0.7/6 - 1/i, except Kr, Xe and Sm (about 2$) 

233U: 1 . 5 $ - 2 fo , except Sm (3%) 

239 rtf 

Pu: 2 - 39», due to the unresolved inconsistencies 

232 

No comparison is possible for Th and therefore the accuracy of 

these yield s is believed to be not better than '¡¡fo . 

Ei 

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y ield . 

■90] CIUFFOLOTTI, L ., Energ. Nucleare 1¿ (1968) 272. 

"9 IJ SANTRY, D.C., YAFFE, L ., Can.J. Chem. 38 ( i 960) 464. 

92 see reference [ 68] . 

■93] DANIELS, W.R., HOFFMAN, D.C., Phys. Rev. (1966) 911. 

‘ 94] GORTON,G.E ., HARVEY, J.W ., NAKAHARA, H., Nucleonics 24 12 ( 1966) 62, 

[ 95] 

readjusted to adopted 235u reference yields and normalized to adopted 

143ce and 144ce yield s. 

WEAVER, L .E ., STROM, P .O .. KILLEEN, P .H., US Naval Radiol. Defense Lab 

report USNRDL-TR-633(1963). 

[96] STEINBERG, E .P ., SEILER, J .A ., GOLDSTEIN, A ., DUDLEY, A ., USAEC 

report MDDC-I632 ( 1948), yields as revised by Steinberg (1954) and 

quoted in reference [ 7 ] . 

[97] CHUL LEE,AMIEL, S., YELLIN, E., ISRAEL AEC report IA-1168 ( 1967), 

readjusted to adopted value o f 4 ga reference yield . 

[9 8] SANTRY,D .C., YAFFE,L ., Can. J. Chem. ¿8 ( i 960) 421. 

[99] GANAPATHY, R ., TIN MO, MEASON, J .L ., J. inorg. nucl.chem. 2£ ( 1967) 

257, readjusted to adopted value of 99jjo reference yield . 

[100] BARTHOLOMEW, R.M., MARTIN, J .S ., BAERG, A .P ., Can.J. Chem.^J 

660, readjusted to adopted value of 14°Ba ref erence y ield . 

(1959) 

[101] FORD, G .P., GILMORE, J .S ., USAEC report LA-1997 (1956). 

[102] OKAZAKI, A ., WALKER, W.H., Can. J. Phys. 43 (1965) IO36, values 

renormalized to adopted reference yield s of l3 5 i and 140ва. 

[103] NISLE, R.G. STEPAN, I .E .. Nucl. Sei. Engng. 31 (1968) 2 4 1, values 

renormalized to adopted 235U reference yield of 135l. 

ONDREJCIN, R .S ., J. inorg. nucl. chem. 28 ( 1966) I763. 

DANGE, S .P ., JAIN, M.C., MANOHAR, S .B ., SATYAPRAKASH, K ., RAMANIAH, 

M.V., RAMASWAMI, A ., RENGAN, K ., In t. Conf. Physics Chem. o f Fission 

(Proc. Sjympos. Vienna, 1969), IAEA, Vienna ( 1969) 741, readjusted to 

adopted 235u reference yields and normalized to adopted 144ce y ield . 

[106] BUNNEY, L .R ., SCADDEN, E.M., ABRIAM, J .O ., BALLOU, N .E., Int. Conf. 

peaceful Uses atom. Energy (Proc. Conf. Geneva, 1958) UN, New 

[107 ] 

York (1958)444, readjusted to adopted 235u reference yields and 

normalized to adopted 144ce y ield . 

CROALL, I . F ., WILLIS, H.H., Int. Conf. Phys. Chem. o f Fission 

(Pros. Eÿmpos. Salzburg, 1965) ¿1 IAEA, Vienna (1965) 355> readjusted 

±0 adopted 235u reference yield s and normalized to 

adopted 9'Mo y ield s. 

[108] CROALL,I.F ., WILLIS, H.H., J. inorg.nucl.chem. 2 ¿ ( 1965) 1213, 

readjusted to adopted yield s o f 99Mo and 140ва. 

[109] JAIN,H.C., RAMANIAH, M.V., Government of India AEC report 

в ARC-584 ( 19 7 1). 

[110] KIRBY, L .J ., USAEC report HW-77609 ( 1963) 3 .1 . 

[111] SKOVORODKIN, N.V ., SOROKINA, A .V ., BUGORKOV, S .S ., KRIVOKHATSKII, 

A.S. , PETRZHAK, K .A ., Radiokhimiya 12 (1970) 487, 492. 

[112] SOROKINA, A.V ., SKOVORODKIN, N .V., BUGORKOV, S .S ., KRIVOKHATSKII, 

[113] 

A.S., PETRZHAK, H.A., Atomnaya Energiya 31 (1971) 99* 

KENNETT, T.J., THODE, H.G., Can. J. Phys. 35(1957) 969* 

[114] WYTTENBACH.A., VON GUNTEN, H .R., Int. Conf. Phys.Chem. of Fission 

(Proc. sympos. Salzburg, Í965) Í , IAEA, Vienna ( 1965) 414. 

'115] BROOM, K.M., Phys. Rev. 133 (1964) В 874 

=116] LYLE, S .J ., MARTIN, G .R., RAHMAN, М., Radiochim. Acta ¿ (1968) 90. 

= 117] LYLE, S.H., SELLARS, J. , Radiochim. Acta 12 ( 1969) 43. 

‘ 118] FAHRAR, H ., CLARKE, W.B., THODE, H.G., TOMLINSON, R.H ., Can.J. Phys. 

42 ( 1964) 2063.



M iss K. W AY: Do you have any apprehensions about om itting values 

far from the average? 

M. LAM M ER: F or the m a jority o f om itted values, there w ere good 

reason s for leaving them out, for exam ple, when the nuclear data w ere out 

of date and the m easured values could not be co rre cte d . In som e ca ses 

we trusted the resu lts o f certain experim ents m ore than oth ers if we had 

the opportunity to check their reliability . On the other hand, let us take 

the ca se where three values agree and a fourth value does not: if this single 

value is in e r r o r it d istorts the average but if it is the only c o r r e c t one, 

the average w ill d iffer con sid erably from this value. N everth eless, any 

re je cte d data should be re fe rred to in an evaluation together with the reason s 

fo r not including them.

NEED OF NUCLEAR LEVEL SCHEMES 

FOR CALCULATED CROSS-SECTIONS 

OF FISSION-PRODUCT NUCLEI 

H. GRUPPELAAR 

Reactor Centrum Nederland, 

Petten, 

The Netherlands 

Abstract 


NEED OF NUCLEAR LEVEL SCHEMES FOR CALCULATED CROSS-SECTIONS OF FISSION-PRODUCT NUCLEI. 

For many fission product nuclei, no measurements of fast neutron cross-sections are available; for 

other fission-product nuclei, only a few measured points are known. Therefore, calculated cross-sections 

are needed to provide a set of data with adjustable parameters. Adjustments to cross-section data can be 

applied by using experimental data o f differential measurements from accelerators or by using results of 

integral experiments like the reactivity worths measured in the Dutch STEK reactor. In the energy range 

between 0.1 MeV and 3 MeV, which is important for fast-breeder reactors, a good knowledge o f excitation 

energies, spins and parities o f levels in the target nucleus is necessary for the calculation of both the neutron 

inelastic-scattering cross-section and the neutron absorption cross-section. In the present paper, the need of 

level-schem e information and the desirability of a compilation and/or evaluation o f these data for practical 

calculations of fission product neutron cross-sections will be discussed. 


In fast breeder reactor calculations cross sections of about 150 fission 

product nuclei in the mass range 81 < A < 164 are important. The required 

accuracy for the capture cross section at energies from about 100 eV to 10 

MeV is generally stated to be ±10% [l,2] . Since for the majority of these 

nuclei no cross section measurements have been performed in the entire 

energy range of interest, one often has to rely on evaluations primarily 

based on calculations with phenomenological nuclear models. In some cases 

cross section measurements will hardly be possible, since for many isotopes 

not enough target material is available, or because targets are highly 

radioactive. To overcome these difficulties, effective cross section measurements 

in different well-defined fast reactor spectra might be of great 

help. Experiments of this kind are being performed at Petten in the STEK 

facility [8], where the reactivity of a large number of individual isotopes, 

listed in table I, is measured in five different neutron spectra. To evaluate 

the results of these integral measurements, the application of a statistical 

adjustment technique on calculated effective cross sections is foreseen 

[8] . The cross sections depend on a limited number of parameters 

which influence the cross section in a wide energy range and a large number 

of parameters which show a more local effect, such as resonance parameters, 

and excitation energies, spins and parities of the target nucleus. 

Uncertainties in these parameters need to be known before adjustment calculations 

can be applied. In the present note some remarks will be made 

about the influence of uncertainties in the level scheme of the target 

nucleus, particularly on the capture cross section of fission product isotopes 

as a result of competitive inelastic neutron scattering. 

553

554 GRUPPELAAR 

2. PRESENT SITUATION 

TABLE I. ISOTOPES MEASURED A T S T E K a) 

9°Zr 98Mo 107pd 132Xe l^Nd i^Sm 

91Zr l°°Mo 108pd 1 34e 1ЦЗШ 15°Sm 

92Zr 99Tc UOpd 136Xe i^Nd 151s» 

« Z r lOlRu l°9 Ag * 3 3Cs l^Nd 152Sm 

9-Zr l ° 2Ru X11Cd “ Ses l « Nd IS-Sm 

96Zr ' ““Ru 128Te !3 7 Cs llt8Nd 151Eu 

92Mo l°3 Rh 13 0Te 139La !5°Nd 1 5 3Eu 

91*Mo 104pd 127J- l “ 0Ce 147Рт 156Gd 

9^Mo 105pd 129j 11,2Ce l-7Sm 157Gd 

9 7Mo 106Pd 131Xe im Pr l-SSm 15 9Tb 

Underlined isotopes are fissio n products with 

a reactivity effect of more than i% of the 

total fissio n product mixture in a typical 

fast reactor. 

Only for about one third of the isotopes listed in table I , one or more 

measured cross section points at energies above 0.1 MeV are available. 

In the energy range from 1 keV up to 10 MeV evaluations of capture 

cross sections of many fissio n products, based on the sta tistic a l model, 

have been published by Benzi et a l. [3,4] and Cook et a l. [5 ], who used the 

same cross sections in the high-energy range. Calculations of fast neutron 

capture cross sections for inclusion in the ENDF/B-III nuclear data library 

have been reported by Schenter and Schmittroth [б ]. A ll authors estimate 

a maximum error of about ±50% in the calculated cross sections. 

Information on level schemes is currently being published in the 

Nuclear Data Sheets. Unfortunately, for about 50 of the 60 nuclei listed 

in table I the most recent evaluation is more than fiv e years old. For 

nuclei in the mass range 91 £ A


For a number of nuclei ( 95Mo, 103Rh, 107Pd, 109Ag, 133Cs), with recently 

evaluated level schemes, cross section calcu lation s have been performed. 

The resu lts o f these calcu lation s were compared with ea rlier evaluations of 

Benzi et a l. [3 ,4 ]. In general deviations from 10% to 30% in the energy 

range from 0.1 to 3 MeV were found both in and a^n i . Since fo r most of 

the nuclei investigated the present level schemes s t i l l do contain many 

am biguities, uncertainties of the same order of magnitude might be expected 

even in the most up to date ca lcu lation s. 

As an example, consider the important unstable fis s io n product nucleus 

l ° 7Pd for which a recent level scheme evaluation is available |j f] . In 

table II is shown that for most excited states two J* values are p ossib le; 

the most probable one is given as the " f ir s t " p o s s ib ility . The d ifferen ce 

between the level scheme used in the 1970 cross section calcu lation [A] and 

the present one (both drawn in fig . 1) is the inclusion o f fiv e additional 

le v e ls . As a resu lt cnY decreases and cnn> increases an amount of at most 

30%, which can be seen from fig . 1. At neutron energies above 1.5 MeV the 

Weisskopf-Ewing model, which is also adopted in the FISPR0 code, was used. 

In between 0.9 MeV and about 1.5 MeV a smooth curve is drawn in order to 

match the Hauser-Feshbach and continuum calcu lation s. 

In the above mentioned example the change in cross section was mainly 

caused by an increased number of levels and did not depend very much on the 

values of J \ which was found from a ca lcu lation in which the second spin 

p o s s ib ility , lis te d in table I I , was prefered. Apparently this is due to 

the high value o f the spin o f the ground state (J71 = 5/2+) , which weakens 

the influence o f the angular momentum and parity selection rules. 

I f the spin of the ground state is low and the level density not too 

high (e .g . for even-even n u cle i), the spins and p a rities of individual 

excited states may be very important. This can be demonstrated clea rly for 

*^3Rh, where the level scheme is well known [j2 j up to 0.65 MeV: = 

1/2 , 7/2 , 9/2 , 3/2 , 5/2 , 5/2+ , 7/2 for Ex = 0, 0.040, 0.093, 0.295, 

0.358, 0.537, 0.650 MeV, resp ectiv ely . If the spin o f the excited state 

were 3/2 instead of 7 /2, the capture cross section would decrease d rastica 

lly with a maximum change o f 40% in the region between 0.05 and 1 MeV, 

due to angular momentum selection ru les. Less pronounced e ffe cts can be 

shown for a change in parity of some particular le v e ls. 

For a number o f nuclei (e .g . 93Zr, *29I , 151Sm) the level scheme is 

rather unknown, so that Hauser-Feshbach calcu lation s cannot be performed 

in the energy region above 100 keV. 

4. CONCLUSIONS AND FINAL REMARKS 

E ffects in a and anni due to missing levels in the target nucleus or 

due to unknown values can be large, with a maximum* of about 30-50% at 

energies between 0.1 and 3 MeV, which is larger than required in [j ,2] . 

In general the spin and parity of the fir s t excited state is well known, 

so that for many even-even nuclei uncertainties in the cross section do 

not occur below 0.5 MeV. 

It can be concluded that level scheme information on fis s io n product 

nuclei for excitation energies up to 3 MeV is important for accurate cross 

section evaluations. This might give additional stimulus to nuclear spec- 

troscop ists and level scheme evaluators. A convenient type of evaluation 

is that of Nuclear Data Sheets. It would be very useful i f in case of 

ambiguities the most probable value were clea rly indicated (e .g . lik e in 

table I I ) . 

E ffects in the in ela stic scattering to individual levels can be much larger.


FIG. 1. Calculated capture andinelastic-scattering cross-section for 10,Pd for two different level schemes, 

labelled with "1970" and "1972" (see Table II). Continuum calculations have been performed for excitation 

energies above 0 .9 MeV. 

Some final com m ents w ill be made on the effects o f level-sch em e uncertain 

ties on fast re a cto r param eters. F or a fast b reed er rea ctor the 

m ost im portant part o f the neutron spectrum with resp ect to capture is 

below 0. 2 MeV. In the w orst case (50% change in an), fo r En = 0. 2 to 1. 4 M eV), 

the change in the absorption reaction rate fo r an average fission product in a 

ty p ical fast b reed er rea ctor is not m ore than 4% (in the ca se o f 107Pd, F ig. 1, 

the le v e l schem e uncertainty p roduces a 1% reactivity uncertainty). The 

influence o f le v e l-sch e m e uncertainties to the breeding ratio was not investigated. 

F rom a paper subm itted to this sym posium [13] it appears 

that the contribution o f fission products to the breeding ratio cannot be 

n eglected in this energy range. E r r o r s o f le ss than 15% [13] are requ ired 

in стПу and CTnn- in the energy range where le v e l-sch e m e uncertainties might 

influence the c r o s s -s e c tio n s . This has been calculated fo r a m ixture of 

all fission -p rod u ct nuclei. F o r individual fission -p rod u ct nuclei it seem s 

that the com m only assum ed goal [1 ,2 ] of 10% in accu racy in the capture 

c r o s s -s e c tio n is som ewhat overestim ated for present rea ctor calculations 

above 0. 2 MeV.


T A B L E II. L E V E L SCHEM E O F 107Pd 

1970 a) 1972 b:> 

Ex (MeV) J* Ex (MeV) Лж 

0.0 5/2+ 0.0 (5 /2 )+ 

0. 115 l/2 + 0.3157 l/2 + 

0.210 1 1/2- 0.214 (1 1 /2 )" 

0.3028 (5/2 ,3 /2 )+ 

0.307 7/2+ 0.3122 (7 /2 ,9 /2 )+ 

0.3482°) 

0.366 (7/2 ,9 /2 )+ 

0.390 3/2+ 0.3819 (3/2 ,5 /2 )+ 

0.3924c ) 

0.412 l/2 + 

0.470 3 /2+ 0.4712 (3 /2 ,5 /2 )+ 

0.570 5/2+ 0.5677 (5 /2 ,3 /2 )+ ’ 

0.670 

+ 

CM 

•—. 

Г- 

0.6701 (5 /2 ,3 /2 )+ 

0.685 (7 /2 ") d) 

0.700 l/2 + 0.698 l/2 + 

0.770 3/2+ 0.759 (3 /2 ,5 /2 )+ 

0.781 (1 /2 ,3 /2 )" 

0 .806c ^ 

0.890 l/2 + 0.889 l/2 + 

Level scheme used in the 1970 cross section calculation [4 ]. 

^ Level scheme from [l l] . If more than two values are 

possible, the first possibility in general is more likely. 

С ) . . 

Not used m the cross section calculation shown in fig. 1. 

^ Not adopted in [l l] . 

In the last reactor core which is foreseen in the SIEK project, the 

reactivity w ill be more sensitive to the MeV range. However, the change 

in reactivity for 107Pd in the above mentioned example s t i l l is not more 

than 2.5%. In this reactor core, but also in some of the other STEK cores, 

inelastic scattering contributes significantly to the reactivity worth. 

Thus uncertainties in the level scheme w ill effect the calculated reactivity 

worth as a result of uncertainties both in (?nY and 0nni. Therefore a good 

knowledge of the level scheme of a number of fissio n product isotopes is 

important for the evaluation of results from STEK. 

557



[1] GREEBLER, P ., HUTCHINS, B .A ., COWAN, C.L. , Second Int. Conf. on 

Nuclear Data for Reactors (Proc. Conf. Helsinki, 1970), Vol. 2, 

IAEA, Vienna (1970) 17. 

[2] Renda 72, IAEA, Vienna (1972), Rep. INDC(SEC)-27/L. 

[3] BENZI, V ., D'ORAZI, R ., REFFO, G ., VACCARI, M., Fast Neutron Radiative 

Capture Cross Sections of Stable Nuclei with 29 1 A £ 79, 

Rep. CNEN-RT/FI(72)6 (1972). 

[4] BENZI, V ., PANINI, G.C., REFFO, G ., VACCARI, M., Discrete and 

Continuum Inelastic Scattering Cross Sections for Neutrons up to 10 

MeV (1970), data available via CCDN Neutron Data Compilation Centre. 

[5] COOK, J.L., Fission Product Cross Sections, Rep. AAEC/TM-549 (1970), 

and ROSE, E.K., The AAEC Fission Product Cross Section Libraries 

FISPROD.POINTXSL and FISPROD.GROUPXSL, Rep. AAEC/TM-587 (1971). 

[6] SCHENTER, R.E. , SCHMITTROTH, F. A., Cross Section Evaluations of 27 

Fission Product Isotopes for ENDF/B-III, Rep. HEDL-TME-71-143 (1971). 

[7j BASS, W.T., HOREN, D.J., EWBANK, W.B., Current Nuclear Level Schemes: 

A = 91 to 117, Rep. ORNL-4627 (1970), and 

HOREN, D.J., Current Nuclear Level Schemes: A = 118 to 139, Rep. 

0RNL-4730 (1971). 

[в] BUSTRAAN, M. et al., STEK, The Fast-Thermal Coupled F acility of RCN 

at Petten, Rep. RCN-122 (1970). 

[9] BENZI,.V., PANINI, G.C., REFFO, G ., FISPR0 I I : A Fortran IV Code for 

Fast Neutron Radiative Capture Calculations, Rep. CNEN-RT/FI(69) 44 (1969). 

[10] BENZI, V ., FABBRI, F ., ZUFFI, L ., SASSI - A Fortran Programme for t.he 

Calculation of Neutron Scattering from a Spherical Optical Potential, 

Rep. CNEN-RT/FI(71) 6 (1971). 

[11] BERTRAND, F.E., HOREN, D.J., Nucl. Data B7 (1972) 1. 

[12] AVIGNONE, F.T., FREY, G.D. , Phys. Rev. C4 (1971) 912. 

[13 USACHEV, L. N. , MANOKHIN, V. N ., these P roceed in gs. 


M. LEDERER: You have ra ised an im portant point con cern in g m easured 

versu s "estim ated b est" data. F or many le v e ls, an excellent guess of the 

spin can be m ade, although there are no data (som e such guesses would 

undoubtedly be better than "m easu red " values). This im p lies an en tirely 

different type o f com pilation. H ow ever, one would not want to supply such 

gu esses to a nuclear th eorist, who might con sid er them as confirm ation 

of his pred iction s. 

H. G RU PPELAAR: In m y paper I was not asking fo r such a com pilation. 

H ow ever, it would be v ery useful if, in the case o f two p ossib le spin values, 

the m ost probable one w ere clea rly indicated in the N uclear Data Sheets. 

Your suggestion o f a different type o f com pilation might be worthwhile for 

the purpose o f c r o s s -s e c tio n calcu lation s. H ow ever, it should not be included 

in the N uclear Data Sheets, lest it give ris e to confusion. 

C. W EITKAM P: It is obvious that the 107Pd in elastic scatterin g c r o s s - 

section goes up as you sw itch from the 1970 to the 1972 level sch em e. Is 

it also obvious that the capture c r o s s -s e c tio n goes down? 

H. G RU PPELAAR: If the num ber o f known lev els in crea ses, the capture 

c r o s s -s e c tio n w ill go down, sin ce the total width of the compound state, 

which appears in the denom inator o f the ex p ression fo r the capture c r o s s - 

section in cre a se s. The total c r o s s -s e c tio n is not v ery sensitive to level 

schem e uncertainties.

EVALUATION OF THE RANGES 

OF FISSION PRODUCTS 

F. RUSTICHELLI* 

Physics Division, Joint Research Centre, 

Euratom, Ispra, Italy 

and 

Dipartimento di Fisica, Facoltá di Ingegneria 

d ell’ Università, 

Ancona, Italy 

Abstract 

EVALUATION OF THE RANGES OF FISSION PRODUCTS. 

IAEA -SM-170/16 

In a very recent work, on the basis o f the Lindhard, Scharff and Schitftt theory and using available 

experimental data for average ranges in a few stopping elements, a com plete set o f ranges in all the natural 

elements for the median light, m edian-heavy, and overall median 235 U fission fragments was derived. A 

similar approach was used in. the present paper to derive the corresponding quantities for the thermal-neutron- 

induced 239 Pu fission. By using the Lindhard, Scharff and Schi^tt theory and the few data existing for 239 pu 

fission fragment ranges in air and A l, a com plete set o f average ranges o f 239Pu fission fragments in all the 

existing natural elements was obtained. This set includes, for each stopping element, ranges for the m edian- 

light, median-heavy, and overall median fission fragments. The method o f fission product evaluation used 

is quite general and is being extended to the other fissile nuclei o f interest. 

INTRODUCTION 

M ost of the investigations on the energy lo s s of fission fragm ents 

in m atter w ere con cern ed with individual fissio n fragm ents interacting with a 

few stopping elem ents. In this way, it was p ossib le to obtain detailed 

inform ation on the slow ing-dow n m echanism of fission fragm ents in r e la 

tion to the differen t physical param eters. H ow ever, v ery little inform ation 

exists on general quantities as the average fission product ranges which, 

in addition to present ph ysical in terest, are of p articu lar im portance in 

nuclear technology. 

T o partially ov e rcom e this lack o f inform ation on general quantities 

related to the energy lo ss of fission fragm ents, we have derived in a very 

recen t w ork [ 1] range values in all the natural elem ents fo r the m edian- 

light, m edian-heavy and overa ll m edian 235u fissio n fragm ents. The 

derivation was based on the observation that the Lindhard, Scharff, Schi^tt 

(LSS) th eory [2] is able to appropriately p red ict the relative stopping pow ers 

of different elem ents fo r the three types of 235U median fission fragm ents. 

F urtherm ore, the few available experim ental data on m edian fis s io n - 

fragm ent en ergy lo ss was u tilized in ord er to give an absolute ch aracter 

to the evaluated ranges. A sim ila r approach was used here to evaluate the 

ranges of the m edian fragm ents produced in the th erm al-n eutron-in duced 

fission of 239Pu. The task was com plicated in this case by the fact that, to 

our knowledge, no data exist on m edian fragm ents, but only on individual 

fragm ents originating in the 239Pu fission . 

Present address: Institut Laue-Langevin, B.P. 156, 38042 Grenoble Cedex, France. 

559

560 RUSTICHELLI 

H ow ever, by using the existin g experim ental data together with LSS- 

theory, it was, a lso in the case of 239Pu, p ossib le to d erive the ranges in all 

the natural elem ents for the m edian-light, m edian-heavy and overa ll median 

fission fragm ents, by means o f a m ethod to be d escrib ed in the next section. 

EVALUATION METHOD 

The proced u re used to evaluate 239Pu m edian fission fragm ent ranges 

is very sim ila r to that used in R ef. [1] to evaluate the 235u m edian fission 

fragm ent ranges. This evaluation m ethod is based on the fact that, in 

R ef. [3 ], it appeared evident that L SS-theory is able to p red ict in a sa tisfa 

ctory way the relative stopping pow ers of differen t elem ents for the 

235 U overa ll m edian fission fragm ent. The validity of L SS-theory in c o r 

re ctly predictin g relative stopping pow ers was con firm ed by a clo se 

com parison [1] with experim ental data on m edian-light and m edian-heavy 

235U fission fragm ents. 

The unified ex p ression obtained by LSS for the electron ic atom ic 

stopping pow er is [2] 

_ X â J L = g 8тг2 a --------Z lZ 2 ------------ — (1 

N dx 0 (Z 2/3+ Z 2/3)3/2 vq ' 

w here a0 and v0 are radius and v elocity of the first B ohr orbit of hydrogen, 

resp ectiv ely , v is the velocity of the p ro je ctile , N is the atom ic density of 

the stopping m aterial, e is the electron charge, Z r and Z 2 are the atom ic 

num bers of the p ro je ctile and the stopping atom , resp ectiv ely , and Ç is a 

constant " o f the ord er o f Zj^6 " [2]. The cu rves for the relative stopping 

pow ers d eferrin g to A l fo r the m edian-light and m edian-heavy 235U fission 

fragm ents w ere obtained [1, 3] from the ex p ression derived from Eq. (1): 

S Al ( Z 2 ) = ( z 2/ 3 +Zz f )3/2 ( z f + z ^ 3 ) 3/2 (2) 

with Z x assum ing the value of the 235U ligh t-fragm en t atom ic num ber 

(Z j = 37. 4) and of the 235U h eavy-fragm en t atom ic num ber (Z h = 54. 6), 

resp ectiv ely . The curve fo r the relative stopping pow ers re fe rrin g to Al 

for the overa ll m edian 236U fission fragm ent was obtained by using the 

exp ression [ 1, 3] 

0 i 0 

7^,7. 7,2/(Z 2/3 + Z2/3)3/2l [ ^ (v0/v)cIe] + zJ/6[Z hZ 2/ ( Z 2/3 + Z 2/3)3/2] 

fi 

[ J (v0/v)dE]_1 

S., (Z2) = 

6[Z 1ZM/(Z2/3+Z2'13)3/2][ j

te 

? 

0 

г 

1V) 

У 

s 

о 

3.2 

2.8 

2 .4 

2.0 

1.6 

1.2 

0.8 

0.4 ° f 

U235M EDIAN FRAGM ENT 

o, 

I A E A - S M -1 7 0 /1 6 561 

— С 

— LINDHARD, SCHARFF, SCHI0TT. 

О FULMER. 

□ ALEXANDER, GADZIK 

• SEGRÊ, WIEGAND. 

В AIELLO, MARACCI, RUSTICHELLI. 

fllllllMI 1 II ill Ml lllllllll III ill 1II lllllllll lllllllll i ii ilini liiilini iiiiliin mi Ii in 

10 20 30 40 SO 60 70 80 90 

ATOMIC NUMBER Z2 --------------О 

F IG . 1 . A t o m i c sto p p in g p ow ers r e la t iv e t o A l fo r th e o v e r a ll m e d ia n *35U fissio n fr a g m e n t as a fu n c tio n 

o f th e a t o m ic n u m b er Z 2 o f th e sto p p in g e le m e n t [ 1 ] . 

and m edian-heavy 235U fissio n fragm ents. The range in a given 

stopping elem ent for the overa ll median fission fragm ent was obtained by 

the equation rep orted in Appendix С of Ref. [3]: 

1 

 

_i_ 

2 VR{ + Rh 

w here is the m edian-ligh t fragm ent range and Rh is the m edian-heavy 

fragm ent range. 

The com p arison betw een experim ental data and L S S -th eoretical values 

of relative atom ic stopping pow er for the m edian-ligh t and m edian-heavy 

235U fissio n fragm en ts was rep orted in R ef. [1] and was quite sa tisfa ctory, 

too. On this b a sis, the assum ption was made [ 1] that L SS-theory is able 

to c o r r e c tly p red ict the relative stopping pow ers of the different elem ents 

for the m ed ia n -lig h t, m edian-heavy and overa ll median 235U fission fra g 

m ents. On the other hand, no experim ental data exist, to our knowledge, 

fo r the 239Pu m edian fragm ents, which would have allow ed us to check the 

validity of this assum ption fo r the 239Pu ca se, as it was made in F ig. 1 for 

the 235U ca se. D espite this lack o f d irect verifica tion , the presen t work 

is based on the assum ption that L SS-theory is able to co r r e c tly p red ict the 

relative stopping pow ers of the differen t natural elem ents for the three 

types of 239Pu m edian fissio n fragm ents. This assum ption is ju stified if 

one con sid ers that param eters like en ergies, atom ic num bers, m a sses of 

fissio n fragm ents do not change v ery much betw een the th erm al-n eu tron - 

induced fission s of 235U and 239Pu. 

e 

100 

(4)

562 RUSTICHELLI 

The en ergies of the two m edian fragm ents of the 239Pu fission w ere 

taken from R ef. [7] where the data of M ilton and F ra ser [8] are rep orted : 

the energy of the m edian-light fragm ent is E £ = (101. 5 i 1. 0) MeV and that 

of the m edian-heavy fragm ent is Eh = (72. 9 i 0 .7 ) M eV. In R efs [7, 8] 

the m a sses of the two m edian fragm ents b efore neutron em ission are r e 

ported, too: they are = 100. 23 _± 0. 15 for the light fragm ent and 

= 139. 77 jt 0. 15 for the heavy fragm ent. By assum ing a value of 2. 9 for 

the num ber v of neutrons em itted per 239p u therm al fission [9] and by 

using the equation1 [7] 

A , E h 

К h I 

(5) 

w here A t and Ah are the m ass num bers after neutron em ission of the light 

and the h eavy-m edian fragm ents, resp ectiv ely , the values A £ = 99. 1 and 

A h = 138 w ere obtained. The atom ic num ber Z h of the m edian-heavy 

fragm ent was obtained from the equation [12] 

z h = UCDzh = D (A h) (6) 

w here UCDZ n is the atom ic num ber obtained accord in g to the unchanged 

charge density (UCD) distribution and D (A h) is the charge deviation that, 

a ccord in g to N ören berg [1 2 ], is roughly equal to 0. 7 units for the 239 Pu 

fission fragm ent with A = 140. 

The value for UCDZ h was obtained from the equation 

Z Pu 

h A Pu 

w here Zpy and APu are the atom ic num ber (Z ^ = 94) and the m ass num ber 

(A Pu = 240), resp ectively , of the compound P u-nucleus. F rom E qs (6) 

and (7), a value Z h = 54 was obtained: the value of the atom ic num ber for 

the m edian fragm ent was then Z j =40. 

F igure 2 shows the relative atom ic stopping pow ers for the m edian- 

light, m edian-heavy and overall median 239Pu fission fragm ents, with Al 

being the re fe re n ce elem ent. The cu rves for the m edian-light and the 

m edian-heavy fragm ents w ere obtained from Eq. (2), with Z j assum ing the 

value of the light fragm ent (Z { = 40) and of the heavy fragm ent (Z h = 54), 

resp ectiv ely . The curve fo r the overa ll m edian fragm ent was obtained 

from Eq. (3). The n um erical data corresp on d in g to the three cu rves are 

rep orted in T able II. 

Once the rela tive atom ic stopping pow ers of the three median fragm ents 

are known it is sufficient to know only the absolute range value in one 

elem ent for each kind o f m edian fragm ent, in ord er to be able to derive 

the absolute ranges in all the other elem ents. In the evaluation of 235U 

fission fragm ent ranges [ 1] sev era l absolute range values for the different 

m edian fragm ents w ere available. By using all the existing experim ental 

data, an effective range in A l was obtained fo r each 235U m edian fragm ent: 

i T h e s e tw o ra tios a re n ot p r e c is e ly th e s a m e b u t, fo r th e p resen t p u rp ose, c a n b e c o n s id e r e d id e n t ic a l. 

F or d e t a ile d in fo r m a tio n s e e Refs [ 1 0 , 1 1 ] . 

(7)

IAEA - S M - 1 7 0 / 16 563 

ATOMIC NUMBER Z2 

FIG.2. Atom ic stopping powers relative to Al for the median-light, median-heavy and overall median 

239Pu fission fragments as a function o f the atom ic number Z 2 o f the stopping element. 

Ru = 3. 676 m g /c m 2 for the light fragm ent, R h = 3. 021 m g /c m 2 for the heavy 

fragm ent and = 3. 359 m g /c m fo r the overa ll m edian fragm ent. These 

range values are slightly different from the m easu red ranges in A l, but 

they are m ore appropriate in view o f the evaluation o f the ranges in all 

natural elem ents, becau se they are the resu lt of a sort of best fit, taking 

into account all the available experim ental data. 

B elow , the problem of obtaining the corresp on d in g 239Pu values for 

the three m edian fragm en ts' effectiv e ranges in A l w ill be solved. Since 

no data exist, to our knowledge, on the ranges of 239Pu m edian fragm ents, 

the proced u re used for 235U cannot be repeated exactly. H ow ever, experim 

ental data exist fo r individual 239Pu fission fragm ent ranges in air [13] 

and in A l [14], The assum ption w ill be made that the range of the light 

239pu m edian fissio n fragm ent (Ац = 100. 23) w ill be the sam e as that of 

the individual 239 Pu fragm ent having the m ass num ber A= 100, and that 

the range of the heavy 239Pu m edian heavy fragm ent (A h = 139. 77) w ill be 

the sam e as that of the individual 239Pu fragm ent having the atom ic 

num ber A - 140. 

This assum ption w ill now be ju stified. At first, it can be observed that 

the en ergies of the two 239Pu individual fragm ents under con sideration are 

equal, within a few p ercen t, to the en ergies of the corresp on d in g 239Pu 

m edian fragm ent [7]. F u rth erm ore, we shall check the validity of this 

assum ption by com paring the m easured ranges fo r individual 235U fission 

fragm ents having the sam e m ass num bers as the m edian 235U fragm ents 

(A g = 95), (Ah = 140) with the evaluated ranges [1] for the m edian-light and 

the m edian-heavy 235U fission fragm ents, resp ectively.

T A B L E I. A B SO L U T E RANGES F O R 239Pu AND 235U FISSION F R A G M E N T S IN A IR AN D A l. 

Stopp¡ng 

element 

Pu239 fission fragment 

Abso1u+e Absolu+e 

range range 

(cm) (mg/cm2) 

A = 100 

Average 

range value 

(mg/cm2) 

Pu239 fission fragment A » 140 

Absolute Absolute Average 

range range range value 

(cm) (mg/cm*) (mg/cmJ) 

Air 2.783 3.354 3.354 2.206 2.658 2.658 Katcoff, Miskel, Stanley 113| 

Al 4.046 4.046 3.210 3.210 Dange et a 1. 114| 

Stoppi ng 

e1ement 

Ai r 

Al 

2 3 5 

U median light fragment U 2 3 5 median heavy fragment 

Absolu+e 

range 

(mg/cm2) 

3.55 1 

3.02 j 

4.11 

Average 

range value 

(mg/cm2) 

3.285 

4.00 J 4.055 

R (Pu 239) 

£ = 1.021 

- R^fU 235> . 

Air 

( ^ R Â(Pu235 ) 

’ R (Pu 2 39)' 

- " > - 1.010 

Л 

R„(U 23S) 

l Al 

= 0.998 

) 

R (U 235) 

* 

Abso1ute 

range 

(mg/cm2) 

2.59 ~) 

2.29 ] 

3.45 

Average 

range value 

(mg/cm2) 

2.440 

3.03 J 3.240 

2 39 

Rh(Pu ) 

R. (U235) 

k n J 

R. (Pu2 39 ) 

r> 

R. (U2 35) 

L h 

A i r 

A l 

1.089 

= 0.991 

■ Fu 1 mer | 5 | 

< 

Author 

Author 

Alexander, Gozdik |6| 

Fulmer 15 j 

Alexander, Gozdik |б| 

2 39 

Rh (P u ) 

564 RU STICH ELLI

TABLE II. ABSOLUTE RANGES IN THE NATURAL ELEM ENTS AND THE RELATIV E STOPPING POWERS 

FOR THE M EDIAN-LIGHT, M EDIAN-HEAVY AND O V E RALL MEDIAN 239Pu FISSION FRAGMENTS 

Element Symbol 

Atomi c 

Number 

(z2 ) 

Median Light Fragment Overa 11 Med i an Fragment Median Heavy Fragment 

Re 1 at i ve 

Atomi с 

Stopp i ng 

Power 

Re 1 a ti ve 

Mass 

Stopp i ng 

Power 

Abso1ute 

Range „ 

(mg/cm ) 

Re 1 at i ve 

Atom i с 

Stopp i ng 

Power 

Re lat i ve Abso1ute 

Mass Range 2 

Stopping (mg/cm ) 

Power 

Relative 

Atomi с 

Stopp i ng 

Power 

Re 1 at i ve 

Mass 

Stopp i ng 

Hydrogen H 1 0 .1 2 2 3 .2 5 4 1.141 0 .1 1 7 3 .1 3 9 1 .0 8 4 0 .11 4 3 .0 3 9 1.034 

Hel¡um He 2 0 .2 2 7 1.531 2 .4 2 5 0 .2 2 0 1.486 2 .2 9 0 0 .2 1 5 1 .4 4 6 2 .1 7 2 

Lithium Li 3 0 .3 2 3 1.255 2 .9 6 0 0 .3 1 5 1.223 2 .78 3 0 .3 0 7 1. 195 2 .6 2 8 

Вегу 11i um Be 4 0 .41 0 1.229 3 .0 2 2 0 .4 0 2 1.202 2 .8 3 0 0. 394 1.17 9 2 .66 4 

Boron В 5 0 .4 9 2 1.228 3 .02 5 0 .4 8 3 1.2C5 2 .8 2 3 0 .4 7 5 1 .1 8 6 2 .6 5 0 

Carbon С 6 0 .56 8 1.276 2 .910 0 .5 5 9 1.257 2 .7 0 8 0. 552 1.24 0 2 .5 3 4 

Nitrogen N 7 0 .6 4 0 1.232 3 .0 1 3 0 .6 3 2 1.217 2 .7 9 6 0 .6 2 5 1 .20 3 2 .61 1 

Oxygen 0 8 0 .7 0 7 1.193 3 .1 1 2 0 .7 0 0 1. 181 2 .8 8 1 0. 694 1.171 2 .5 8 4 

Flouri ne F 9 0 .7 7 2 1.096 3 .38 8 0 .7 6 6 1 .087 3 .1 3 0 0. 760 1 .0 8 0 2 .9 0 9 

Neon Ne 10 0 .8 3 3 1.113 3 .33 5 0 .8 2 8 1. 1C7 3 .07 4 0 .8 2 4 1.101 2 .85 3 

Sod¡um Na 11 0 .8 9 1 1 .046 3.551 0 .8 8 8 1.042 3 .2 6 6 0 .8 8 5 1 .0 3 9 3 .0 2 5 

Magnes i um Mg 12 0 .9 4 7 1.051 3 .5 3 4 0 .9 4 5 1 .049 3 .2 4 5 0 .94 4 1 .0 4 7 3 .001 

A 1umi num Al 13 1.000 1 .000 3 .7 1 3 1.000 1 .00 0 3 .4 0 3 1. 000 1 .000 3 .1 4 2 

S i 1 i con Si 14 1.051 1.010 3 .6 7 7 1.053 1.012 3 .3 6 4 1 .0 5 4 1 .01 3 3 .1 0 2 

Power 

Absolute 

Range 2 

(mg/cm ) 

IA E A -S M -1 7 0 /1 6 565

T A B L E II (continu ed) 

Phosphorus P 15 

Su 1 fur S 16 

Chlori ne Cl 17 

Argon Ar 18 

Potass¡um K 19 

Ca1 с ¡um Ca 20 

Scandi um Sc 21 

T ¡+an¡um Ti 22 

Vanadi um V 23 

Chromi um Cr 24 

Manganese Mn 25 

1 ron Fe 26 

Coba 11 Со 27 

N ï eke 1 Ni 28 

Copper Cu 29 

Zinc Zn 

30 

Ga 1 1 i um Ga 31 

German i um Ge 32 

Arsenic As 33 

Seleni um Se 34 

1. 100 0 .9 5 9 3 .8 7 4 

l . 148 0 .9 6 6 3 .8 4 4 

1.193 0 .9 0 8 4 .0 8 8 

1.237 0 .8 3 6 4 .4 4 2 

1.280 0 .8 8 3 4 .2 0 4 

1.321 0 .8 8 9 4. 174 

1.361 0 .8 1 7 4 .5 4 5 

1.400 0 .7 8 9 4 .7 0 9 

1.437 0 .7 6 1 4 .8 7 7 

1.474 0 .7 6 5 4 .8 5 5 

1.509 0 .7 4 1 5 .01 0 

1.544 0 .746 4 .9 7 9 

1.577 0 .7 2 2 5 .1 4 3 

1.610 0 .7 4 0 5 .0 2 0 

1.641 0 .6 9 7 5 .3 2 8 

1.672 0 .6 9 0 5 .3 8 0 

1.702 0 .6 5 9 5 .6 3 6 

1.732 0 .6 4 4 5 .7 6 8 

1.760 0 .6 3 4 5 .8 5 6 

1.789 0 .61 1 6 .0 7 5 

1. 104 0 .9 6 2 

1 .15 3 0 .9 7 0 

1.201 0 .9 1 4 

1.247 0 .8 4 2 

1.292 0 .8 9 1 

1 .3 3 5 0. 899 

1 .37 7 0. 826 

1.418 0. 799 

1 .4 5 7 0 .7 7 2 

1 .496 C. 776 

1 .533 0 .7 5 3 

1 .570 0 .7 5 8 

1 .605 0 .7 3 5 

1 .64 0 0 .7 5 4 

1.674 0 .71 1 

1.707 0. 705 

1 .7 3 9 0 .6 7 3 

1.771 0 .6 5 8 

1.802 0 .6 4 9 

1.832 0 .6 2 6 

3 .5 3 9 1 .1 0 7 

3 .5 0 7 1. 158 

3 .7 2 3 1 .2 0 7 

4.041 1 .255 

3 .8 1 8 1.302 

3 .7 8 7 1.34 7 

4 .1 1 8 1 .39 0 

4 .2 6 2 1.433 

4 .4 0 9 1 .47 5 

4 .3 8 4 < 1 .5 1 5 

4 .5 1 9 1 .5 5 4 

4 .4 8 7 1 .5 9 3 

4 .6 3 0 1 .6 3 0 

4 .5 1 4 1 .6 6 7 

4 .7 8 7 1 .70 3 

4 .8 2 9 1.738 

5 .0 5 5 1 .77 2 

5 .1 6 9 1 .8 0 5 

5 .2 4 4 1 .83 8 

5.43 6 1 .8 7 0 

0 .9 6 4 3 .2 5 8 

0 .9 7 5 3 .2 2 4 

0 .9 1 9 3.419 

0. 848 3 .7 0 6 

0 .8 9 8 3.493 

0 .9 0 7 3 .4 6 6 

0 .8 3 5 3 .76 5 

0 .8 0 7 3 .89 2 

0.781 4 .0 2 3 

0 .7 8 6 3 .9 9 7 

0 .7 6 3 4 .1 1 6 

0 .7 7 0 4 .0 8 3 

0 .7 4 6 4 .2 1 0 

0 .7 6 6 4 .1 0 2 

0 .7 2 3 4 .3 4 6 

0 .717 4 .3 8 1 

0 .6 8 6 4 .5 8 2 

0.671 4 .6 8 3 

0 .66 2 

4 .7 4 7 

0 .6 3 9 4 .91 7 

566 RUSTIC H ELLI


Bromi ne Br 35 1.816 

Krypton Kr 36 1.843 

Rubidium Rb 37 1.869 

Stronti urn Sr 38 1.895 

Yttriurn Y 39 1.920 

Zi rcon i urn Zr 40 1.944 

N i ob i urn Nb 41 1.968 

Molybdenum Mo 42 1 .992 

Technetium Tc 43 

2 .0 1 5 

Ruthenium Ru 44 2.038 

Rhod i urn Rh 45 2 .0 6 0 

Pa 11 ad i urn Pd 46 2 .0 8 2 

Si 1 ver *9 47 2 .1 0 3 

Cadm i urn Cd 48 2 .1 2 4 

1ndi urn 1 n 49 2. 144 

Tin Sn 50 2.165 

Anti mony Sb 51 2. 185 

Te 11uri urn Te 52 2 .20 4 

lodi ne 1 53 2 .2 2 3 

Xenon Xe 54 2 .2 4 2 

0 .6 1 3 6 .0 5 6 1.862 0 .6 2 9 

0 .5 9 3 6 .2 5 8 1 .891 0 .6C 9 

0 .5 9 0 6 .2 9 3 1 .9 1 9 0. 6C6 

0 .5 8 3 6 .36 4 1 .94 7 0 .5 9 9 

0 .5 8 3 6 .3 7 3 1 .97 4 0 .5 9 9 

0 .5 7 5 6 .4 5 7 2 .00 0 0 .5 9 2 

0 .5 7 2 6 .4 9 6 2 .0 2 7 0 .5 8 9 

0 .5 6 0 6 .6 2 8 2 .05 2 

2 .0 7 7 

0 .5 7 7 

0 .5 4 4 6 .8 2 6 2. 102 0 .56 1 

0 .5 4 0 6 .8 7 5 2 .1 2 6 0 .5 5 7 

0 .5 2 8 7 .0 3 4 2 .1 5 0 0 .5 4 5 

0 .5 2 6 7 .0 5 9 2 .1 7 3 0 .5 4 4 

0 .5 1 0 7 .2 8 3 2 .1 9 6 0 .5 2 7 

0 .5 0 4 7.368 2 .2 1 9 0 .5 2 1 

0 .4 9 2 7 .5 4 5 2.241 0 .5 C 9 

0 .4 8 4 7 .66 9 2 .2 6 3 0 .5 0 1 

0 .4 6 6 7 .9 6 7 2 .2 8 4 0 .4 8 3 

0 .4 7 3 7 .85 5 2 .3 0 5 0 .4 9 0 

0 .4 6 1 8 .05 9 2 .3 2 6 0 .4 7 8 

5 .4 1 4 1.901 0 .64 2 4 .8 9 4 

5 .5 9 0 1.932 0 .6 2 2 5 .051 

5 .6 1 8 1.962 0 .6 1 9 5 .0 7 2 

5 .6 7 7 1.992 0 .6 1 3 5 .1 2 3 

5.681 2 .02 1 0 .6 1 3 5 .1 2 3 

5.751 2 .0 4 9 0 .6 0 6 5 .18 4 

5 .7 8 2 2 .0 7 7 0 .6 0 3 5.209 

5 .8 9 6 2 .1 0 5 

2 .131 

0 .5 9 2 5.30 9 

6 .0 6 5 2 .1 5 8 0 .5 7 6 5 .4 5 4 

6 .1 0 4 2. 184 0 .5 7 3 5 .4 8 7 

6 .2 4 2 2 .2 0 9 0 .5 6 0 5.60 8 

6 .2 6 0 2 .2 3 4 0 .5 5 9 5 .6 2 2 

6 .4 5 5 2 .2 5 9 0 .5 4 2 5 .7 9 4 

6 .5 2 7 2 .2 8 3 0 .5 3 7 5 .8 5 6 

6 .6 8 0 2 .3 0 7 0 .5 2 4 5 .991 

6 .7 8 6 2 .3 3 1 0 .5 1 7 6 .0 8 3 

7 .0 4 6 2 .3 5 4 0 .4 9 8 6 .3 1 3 

6 .9 4 3 2 .3 7 7 0 .5 0 5 6 .2 1 8 

7 .1 2 0 2 .3 9 9 0 .4 9 3 6 .3 7 4 

IAEA - S M - 1 7 0 /1 6 5 6 7


Ces i urn Ce 55 2.261 0 .4 5 9 8 .09 0 

Bari urn Ba 5o 2 .2 7 9 0 .4 4 8 8 .2 9 3 

Lanthanum La 57 2.297 0 .4 4 6 8 .3 2 3 

Ceri urn Ce 58 2 .3 1 4 0 .4 4 6 8 .33 1 

Praseodymi urn Pr 59 2 .3 3 2 0 .4 4 7 8 .3 1 6 

Neodyn i urn Nd 60 2 .349 0 .4 3 9 8 .45 1 

Prometb i urn Pm 61 2 .3 6 6 

Samari urn Sm 62 2 .382 0 .4 2 8 8 .68 5 

Europium Eu 63 2 .399 0 .4 2 6 8 .7 1 9 

Gadol¡ni um Gd 64 2 .415 0 .4 1 4 8 .9 6 2 

Terbium Tb 

65 2 .43 0 0 .4 1 3 8 .9 9 9 

Dysp ros i. um Dy 66 2 .44 6 0 .4 0 6 9 .1 4 2 

Holmium Ho 

67 2.461 0 .4 0 3 9 .2 2 1 

Erb i um Er 68 2 .4 7 6 0 .3 9 9 9 .2 9 4 

Thu 1 i um Tm 69 2.491 0 .3 9 8 9 .3 3 1 

Y+terbi um Yb 70 2 .50 6 0 .39 1 9 . 50 2 

Luteti um Lu 71 2.521 0 .3 8 9 9 .5 5 3 

Hafn i um Hf 72 2 .5 3 5 0 .3 8 3 9 .6 9 0 

Tanta 1i um Ta 73 2.54 9 0 .3 8 0 9 .7 6 9 

T ungsten W 74 2 .5 6 3 0 .3 7 6 9 .8 7 2 

2 .3 4 6 0 .4 7 6 7 .1 4 4 

2 .3 6 6 0 .4 6 5 7 .3 2 0 

2 .3 8 6 0 .4 6 4 7 .342 

2 .4 0 6 0 .46 3 7 .3 4 6 

2 .4 2 5 0 .4 6 4 7 .32 9 

2 .4 4 4 0.45 7 7 .4 4 4 

2 .4 6 2 

2 .43 1 0 .4 4 5 7 .64 4 

2 .4 9 9 0 .4 4 4 7 .6 7 0 

2 .5 1 7 0 .4 3 2 7.881 

2 .5 3 4 0. 430 7 .9 0 9 

2 .55 1 0.42 4 8 .03 3 

2 .5 6 9 0 .42 0 8 .0 9 9 

2 .5 8 5 0 .4 1 7 8 .1 5 9 

2 .6 0 2 0 .4 1 6 8 .1 8 9 

2 .6 1 8 0 .4 0 8 8 .3 3 5 

2 .6 3 5 0 .4 0 6 8 .3 7 6 

2 .6 5 0 0.4C1 8 .4 9 3 

2 .6 6 6 0.39 8 8 .5 6 0 

2 .6 8 2 0 .3 9 4 8 .6 4 6 

2.421 0.491 6 .3 9 3 

2 .4 4 3 0 .4 8 0 6 .5 4 7 

2 .4 6 4 0 .4 7 9 6 .5 6 5 

2 .4 8 5 0 .4 7 9 6 .5 6 6 

2. 506 0 .4 8 0 6 .54 8 

2 .5 2 6 0 .4 7 3 6 .6 4 9 

2. 547 

2 .5 6 6 0.461 6 .3 2 2 

2 .5 8 6 0 .4 5 9 6 .8 4 3 

2 .6 0 5 0 .4 4 7 7.029 

2 .6 2 4 0 .4 4 6 7 .0 5 2 

2 .6 4 3 0 .4 3 9 7.15 9 

2 .66 2 0 .4 3 5 7.216 

2 .6 8 0 0 .4 3 2 7.267 

2 .6 9 8 0.431 7 .29 1 

2 .7 1 6 0 .4 2 3 7 .4 1 9 

2 .7 3 4 0 .4 2 2 7 .4 5 4 

2. 751 0 .4 1 6 7 .55 5 

2 .7 6 8 0 .4 1 3 7 .6 1 2 

2 .7 8 5 0 .4 0 9 7.687 

568 RU STICH ELLI

T A B L E II (continued) 

Rheni um Re 75 2 .57 7 0 .3 7 3 9 .9 4 5 

Osmi urn Os 76 2.590 0 .3 6 7 10.105 

1 г i d Î urn Ir 77 2 .6 0 4 0 .3 6 5 10.159 

Platinum Pt 78 2 .61 7 0 .3 6 2 10.260 

Gold Au 79 2 .6 3 0 0 .3 6 0 10.307 

Mercury Hg 80 2 .6 4 3 0 .3 5 5 10.446 

Tha11¡um Tl 81 2 .65 5 0 .3 5 1 10.592 

Lead Pb 82 2.668 0 .3 4 7 10.688 

Bi smuth Bi 8 3 2 .6 8 0 0 .3 4 6 10.730 

Pol on i;um Po 84 2 .6 9 2 

AstatГпе At 85 2 .7 0 4 

Radon Rn 86 2. 716 

Franci urn Fr 87 2 ,7 2 8 

Rad 1 urn Ra 88 2. 740 

Acti n ¡ um Ac 89 2.751 

Thori um Th 90 2 .7 6 3 0 .32 1 11.558 

Protacti ni um Pa 91 2 .7 74 

Uran i um U 92 2 .7 8 5 0 .3 1 6 11.762 

Neptun¡um Np 93 

2. 796 

Plutonium Pu 94 2. 807 

2 .6 9 7 0.391 8 .7 0 7 

2 .7 1 2 0 .3 8 5 8 .8 4 5 

2 .7 2 7 0. 383 8 .8 8 9 

2 .7 4 2 0 .3 7 9 8 .97 4 

2 .7 5 7 0 .37 8 9 .01 2 

2 .7 7 1 0 .3 7 3 9 .1 3 0 

2. 785 Û .368 9 .2 5 5 

2 .7 9 9 0. 365 9 .3 3 5 

2 .8 1 3 0 .3 6 3 9 .3 6 9 

2 .8 2 7 

2.8 40 

2 .8 5 4 

2.867 

2 .8 8 0 

2 .8 9 3 

2 .9 0 6 0 .3 3 8 10.071 

2 .9 1 9 

2 .9 3 1 0. 332 10.242 

2 .9 4 4 

2 .9 5 6 

2 .8 0 2 0 .4 0 6 7 .7 3 9 

2 .8 1 8 0 .4 0 0 7 .85 9 

2 .8 3 5 0 .3 9 8 7 .89 5 

2 .8 5 1 0 .3 9 4 7 .96 9 

2 .8 6 7 0 .3 9 3 8.001 

2 .8 8 3 0 .3 8 8 8 .1 0 3 

2 .8 9 3 0 .38 3 8 .21 2 

2 .9 1 4 0 .3 7 9 8.28 1 

2 .9 2 9 0 .3 7 8 8.309 

2. 944 

2 .9 5 9 

2 .9 7 3 

2 .9 8 8 

3.C 02 

3 .C 1 7 

3 .03 1 0 .3 5 2 8 .91 5 

3. 045 

3 .0 5 8 0 .3 4 7 9 .06 3 

3 .C 7 2 

3.C 85 

IA E A -S M -1 7 0 /1 6 569

TABLE II (continued) 

Americî um Am 95 2.818 2.968 3. 099 

Curi um Cm 96 2.828 2.980 3.112 

Berke1i urn Bk 97 2. 839 2.992 3. 125 

Cal i form urn Cf 98 2. 84 9 3.004 3. 138 

Einstei nlurn Es 99 2. 859 3.015 3.151 

Fermi urn Fm 100 2. 869 3.027 3. 164 

570 R U STIC H E LU

I A E A - S M -1 7 0 /1 6 571 

F IG . 3 . In te g r a l ranges o f fissio n p r o d u c ts o f 235U m e a su re d b y N id a y in u ra n iu m m e t a l [ 7 , 1 5 ] . 

The ranges of 235U fission products in uranium w ere m easured by 

Niday [15] and reported in Fig. 3. It can be seen that the dependence of the 

range on the m ass num ber A j , and, as a consequence, on the atom ic 

num ber Z j of the p ro je ctile atom is quite regu lar and free from oscilla tion s 

which w ere found in som e other ca ses [16]. The range in uranium o f the 

235U fragm ent with a m ass num ber A= 95 appears to be, accord in g to F ig. 3, 

equal to 11.4 m g /cm 2 and the range of th e235U fragm ent with a m ass 

num ber A = 140 appears to be equal to 8. 8 m g /c m 2 . T hese values are in 

good agreem ent with the values obtained in R ef. [ 1] fo r the range in uranium 

of the 235U m edian-ligh t fragm ent (R { = 11. 893) and for the range of the 

235U m edian-heavy fragm ent (Rh = 8. 686). 

T able I rep orts the values of the ranges in air m easured by K atcoff, 

M iskel and Stanley [13] fo r the 239Pu fission fragm ents of m ass num ber 

A = 100 and A= 140 and the ranges in A l of the sam e fragm ents m easured 

by Dange et al. [14]. In addition, the range values in air and A l obtained 

experim en tally for the m edian-ligh t and the m edian-heavy 235U fission fra g 

m ents, d iscu ssed in R ef. [1] are rep orted . The data of R ef. [13] w ere 

obtained by using a radioch em ica l technique: the values rep orted in Fig. 3 

are deduced from the figures and not from the tables in ord er to be coherent 

with the 235и data re fe rrin g to the m axim um range. An a ir density value of 

pair = 1. 205 was used to convert the range data from cm to m g /c m 2 . The 

range values o f 239Pu fission fragm ents in A l w ere obtained by using a high- 

resolu tion gam m a -sp ectrom eter.

572 RUSTICH ELLI 

The ra tio in air and A l between Pu and U light-fragm en t ranges and 

betw een Pu and U heavy-fragm ent ranges are reported in Table I, too. 

The average values for the ratio range P u /ra n g e U is 1. 010 for the light 

fission fragm ent and 1. 040 for the heavy fission fragm ent. The effective 

ranges in A l fo r the light and heavy 239Pu median fragm ents w ere obtained 

by m ultiplying the effectiv e ranges in A l of the light and heavy 235U m edian 

fragm ents by these two experim ental ratios. The effective range in A l of 

the 239Pu m edian-ligh t fragm ent was found to be R£ = 3. 713 and of the 239Pu 

m edian-heavy fragm ent Rh = 3. 142. The 239Pu overa ll m edian-heavy fra g 

ment was obtained from R j and Rh by using Eq. 4; the value obtained is 

< R > = 3. 403. 

The absolute ranges for the three 239Pu m edian fission fragm ents r e 

ported in Table II w ere obtained by dividing the effective range in Al of each 

o f the m edian fragm ents by the th eoretical relative m ass-stop p in g pow ers 

r e fe r r e d to A l. The relative m ass stopping pow ers w ere obtained by 

m ultiplying the rela tive atom ic stopping pow ers by the atom ic weight 

ratios [1]. 

RESULTS AND DISCUSSION 

T able II rep orts the values of the relative atom ic and m a ss-stop p in g 

p ow ers, re fe rre d to A l, as calculated by L SS-theory for the m edian-light, 

m edian-heavy and overa ll m edian 239Pu fission fragm ents. Finally, the 

evaluated absolute ranges for the three types of 239Pu m edian fragm ents 

10 20 30 iO SO SO 70 BO 90 100 

ATOMIC NUMBER Z 2 ■ 

F IG .4 . A b s o lu te ra n g es in t h e n a tu ra l e le m e n ts o f th e m e d ia n -lig h t , m e d ia n -h e a v y and o v e r a ll m e d ia n 

239 pu fissio n fr a g m e n ts, as a fu n c t io n o f th e a t o m ic n u m b er Z 2 o f th e sto p p in g e le m e n t .

I A E A - S M -1 7 0 /1 6 573 

are rep orted . A d iscu ssion of the p h ysical m eaning of the range o f the 

overa ll m edian fission fragm ent was presented in Ref. [1]. In p ra ctica l 

applications, it would be p refera b le to take the corresp on d in g values for 

the m edian-light fission fragm ent instead of the overa ll m edian fis s io n - 

fragm ent ranges. The absolute ranges fo r the three types of 239Pu median 

fission fragm ents are rep orted in Pig. 4, as a function of the atom ic num ber 

Z 2 of the stopping elem ent. The resu lts obtained a re not too differen t from 

the corresp on d in g 236U values and, because of uncertainties in the approxim 

ations used, they should be con sid ered in an absolute sca le and not in 

re fe re n ce to the 235U data. 

This w ork rep resen ts only a first attempt to produce general in form a 

tion on 239Pu fissio n fragm ent ranges. The evaluation m ethod is largely 

based on the 235u experim ental data: the p re cisio n would in crea se if new 

experim ental data for 239Pu w ere available. This p roced u re o f estim ating 

absolute ranges fo r m edian fissio n fragm ents is quite general and is now 

being applied to other fis s ile nuclei of interest. 

[ 1 ] RU STICH ELLI, F ., Z . P h y s ., u n d er press. 


[ 2 ] L IN D H A R D , J . , SCH A R FF, M . , S C H I 0 T T , H . E . , K g l. D a n . V id e n s k . S e ls k . M a t .- F y s . M e d d . 33 

14 (1 9 6 3 ). 

[ 3 ] AIE LLO, V . , M A R A C C I, G . , RU STICH ELLI, F ., P hys. R e v . 4 8 (1 9 7 1 ) 3 8 1 2 . 

[ 4 ] SEGRE, E ., W IE G A N D , C . , P hys. R ev . 7 0 U 1 9 4 6 ) 8 0 8 . 

[ 5 ] FULMER, C . B . , P h ys. R e v . Ш 8 (1 9 5 7 ) 1 1 1 3 . 

[6 ] A L E X A N D E R , J . M . , G A Z D I K , M . F . , Phys. R ev . 120 (1 9 6 0 ) 8 7 4 . 

[ 7 ] H Y D E , E . K . , " T h e N u c le a r P rop erties o f th e H e a v y E le m e n ts ", 3 , C h a p te r 6 , K in e t ic E n ergy o f th e 

F ission F ra gm en ts, P r e n t ic e -H a ll, N ew Jersey < 1 9 6 4 ). 

[ 8 ] M IL T O N , J . C . D . , FRASER, J . S . , C a n . J. P hys. 4 0 (1 9 6 2 ) 1 6 2 6 ; 4 1 (1 9 6 3 ) 8 1 7 . 

[9 ] R e a cto r P h ysics C on stan ts, A N L -5 8 0 0 (S e c o n d E d ition ) (1 9 6 3 ). 

[1 0 ] TERREL, J ., P hys. R e v . 113 (1 9 5 9 ) 5 2 7 . 

[ 1 1 ] B R U N TO N , D . C . , H A N N A , G . C . , C a n . J. R es. 28A (1 9 5 0 ) 1 90. 

[ 1 2 ] NÖRENBERG, W . , P hys. R ev . 5 (1 9 7 2 ) С 2 0 2 0 . 

[1 3 ] K A T C O F F , J . , M ISK EL, J . A . , S T A N L E Y , C . W . , P h ys. R e v . 7 4 (1 9 4 8 ) 6 3 1 . 

[1 4 ] D A N G E , S . P . , JA IN , H . C . , M A N O H A R , S . B . , S A T Y A P R A K A S H , K . , R A M A N IA H , M . V . , 

R A M A S W A M I, A . , REN G AN , K . , in P h ysics a n d C h e m is try o f F ission (P r o c . S y m p . V ie n n a ), IA E A , 

V ie n n a (1 9 6 9 ) 7 4 1 , 

[1 5 ] N ID A Y , J ., P hys. R e v . 121 (1 9 6 1 ) 1 4 7 1 . 

[1 6 ] E L -H O S H Y , A . H . , GIBBONS, J .F . , Phys. R e v . 173 (1 9 6 8 ) 4 5 4 . 


N. M. SPYROU: Do you intend extending your m ethod to ca lifo rn iu m -252? 

If so you could then ch eck your range calcu lation s fo r selected elem ents 

against resu lts obtained experim en tally, e. g. b y using su rface b a rrie r 

d etectors, which are becom in g in creasin gly available. T his would be im 

portant from the m ed ical point of view. 

F. RUSTICHELLI: I am now applying the m ethod to 233 U. But, I 

agree with you that it would be in terestin g to con sid er also 252 Cf. I shall 

certain ly be doing that in the near future.

Section VII 

ACCELERATOR AND SPACE SHIELDING

Chairman 

W.W. HAVENS (USA)

I A E A - S M -17 0 /4 2 

USE OF NUCLEAR DATA IN 

DESIGNING SPACE-SCIENCE EXPERIMENTS 

B.C. CLARK, P.G. KASE, J.P. MARTIN, J.G. MORSE 

Martin Marietta Aerospace, 

Denver, C olo., 

United States of America 

Abstract 

USE OF N U CLEAR D A T A IN DESIGN ING S P A C E -S C IE N C E EXPERIM ENTS. 

S c ie n t if ic e x p e r im e n ts fo r e x p lo r a t io n o f th e p la n e ts and in te r p la n e ta ry s p a c e m ust b e d e s ig n e d to 

o p e r a te in a n u m b er o f s e v e r e e n v ir o n m e n ts , in c lu d in g th e riatural r a d ia tio n in s p a c e ( c o s m ic ra y s, solar 

fla r e s , r a d ia tio n b e lts , e t c . ). M a n -m a d e r a d ia tio n e n v ir o n m e n ts m a y b e a lso p re se n t, su ch as g a m m a and 

n eu tron e m is sio n s fr o m r a d io is o to p e t h e r m o e le c t r ic g en era tors (R T G 's ) used as s p a c e c r a ft p o w e r su p p lie s, 

a n d /o r e m is s io n s fr o m r a d ia tio n so u rces w h ic h are a pa rt o f th e s c ie n c e in stru m e n ta tio n c o m p le m e n t . 

E x a m p le s o f th e la tte r in c lu d e a lp h a , b e ta , X - r a y and r a d io is o t o p e so u r ce s, m in ia tu re X - r a y tu b e s, and 

n eu tron g e n e ra to rs o f th e D - T a c c e le r a t o r t y p e . E a ch e x p e r im e n t m ust s u r v iv e th e r a d ia tio n d a m a g e as w e ll 

as in te r fe r e n c e s d u rin g o p e r a tio n in su ch e n v ir o n m e n ts . T h e u se o f n u c le a r d a ta in d e s ig n in g se v e r a l in stru 

m en ts for e x p lo r a tio n o f M ars and V enus is d iscu ssed , w ith e x a m p le s draw n fr o m th e X - r a y flu o r e s c e n c e 

g e o c h e m i c a l a n aly ser sch e d u le d fo r la u n c h to M ars in 1 9 7 5 , p lu s an X - r a y d iffr a c t o m e t e r , a g a m m a -r a y 

s p e c t r o m e t e r , and a n eu tron a c t iv a t io n a n aly ser under stu d y fo r p o s s ib le u se o n fu tu re m ission s. C on strain ts 

u p o n o v e r a ll s p a c e c r a ft d e s ig n d u e to th e n u c le a r e n v ir o n m e n ts a re a lso d iscu sse d . T h e ty p e s o f n u c le a r 

d a ta e m p lo y e d in c lu d e r a d io is o t o p e e m is s io n c h a r a c te r is tic s , s h ie ld in g o f so u r ce s , s h ie ld in g o f c o s m ic 

rays and tra p p ed p a r t ic le s , n eu tron s c a tte r in g and a c t iv a t io n c r o s s -s e c t io n s , and g a m m a -r a y transport 

p a ra m e te rs . H igh co s ts in fu lly s im u la tin g such e n v ir o n m e n ts fo r s p a c e c r a ft - s iz e d e q u ip m e n t h a v e d ic ta te d 

h e a v y r e lia n c e u p on a n alysis rath er than e x p e r im e n ta l test in v e r ify in g s p a c e c r a ft c o m p a t ib ilit y . T h is 

g r e a tly in c r e a s e s th e e c o n o m i c v a lu e o f th e a p p lic a b le n u c le a r d a ta . 

This paper describes science experiments which will be (or could be) 

carried on spacecraft designed to explore surfaces and/or atmospheres of 

planets, such as Mars, Venus and Jupiter. It is limited to those experiments 

in which beta, gamma and X-radiations are measured in order to ascertain 

requisite physical, chemical and biological properties, and it is 

concerned with the effect of radiation background on the measurements 

themselves. 

RADIATION ENVIRONMENTS 

The radiation environments of science experiments for the exploration 

of the planets and interplanetary space include both natural and man-made 

radiation sources. 

The properties of radiation environments of the planets are influenced 

very strongly by the properties of their magnetic fields and their atmospheres. 

Planets having strong magnetic fields are likely to have belts of 

trapped proton and electron radiation, such as the well-known Van Allen 

belts of Earth. Since their discovery in 1958, the Van Allen belts have 

been extensively mapped and very detailed models of their properties are 

readily available [l, 2, 3, 4]. 

Planetary exploration so far has shown that the Moon, Venus and Mars 

have very weak magnetic fields and therefore no significant radiation belts. 

Except for atmospheric interactions, the radiation environments near these 

planets are essentially identical to the interplanetary environments. 

577

578 C LARK e t a l. 

W a r w i c k И a n d B e c k h a v e i n f e r r e d f r o m a n a l y s i s o f i t s s y n c h r o 

t r o n r a d i o n o i s e t h a t J u p i t e r h a s a s t r o n g m a g n e t i c f i e l d , a n d p r o b a b l y h a s 

e x t e n s i v e r a d i a t i o n b e l t s . U n t i l t h e P i o n e e r s p a c e c r a f t e n c o u n t e r s J u p i t e r 

i n D e c e m b e r 1 9 7 3 , p l a n n e r s o f m i s s i o n s t o J u p i t e r a r e a n t i c i p a t i n g t h a t i t s 

r a d i a t i o n b e l t s c o n t a i n t h e f l u x e s i n d i c a t e d b y F i g u r e 1 , w h i c h s h o w s t h e 

u n c e r t a i n t i e s o f c u r r e n t f o r e c a s t s o f t h e t r a p p e d p r o t o n a n d e l e c t r o n 

f l u x e s T h e p e a k f l u x e s i n t h i s m o d e l o c c u r i n t h e p l a n e o f t h e 

J u p i t e r m a g n e t i c e q u a t o r w h e r e i t i n t e r s e c t s t h e c l o u d l a y e r s v i s i b l e i n 

t h e a t m o s p h e r e . B e c a u s e t h e e l e c t r o n c o m p o n e n t o f t h i s b e l t i s d e r i v e d 

f r o m m e a s u r e m e n t s o f J u p i t e r ' s s y n c h r o t r o n r a d i a t i o n n o i s e , t h e r e i s m o r e 

c o n f i d e n c e i n t h i s p o r t i o n o f t h e m o d e l . N o m i n a l l y , t h e p e a k e l e c t r o n f l u x 

i s 2 . 0 x 1 0 ? e l e c t r o n s / c m ^ s e c ; t h e u p p e r l i m i t o f t h e e l e c t r o n f l u x i s 

6 . 0 x 1 0 ^ e l e c t r o n s / c m ^ s e c . T h e s e v a l u e s a r e c o m p a r a b l e t o t h e f l u x e s a t 

E a r t h , b u t a r e d i s t r i b u t e d t h r o u g h a c o n s i d e r a b l y l a r g e r v o l u m e s u r r o u n d i n g 

J u p i t e r . T h e p r o t o n c o m p o n e n t o f J u p i t e r ' s r a d i a t i o n b e l t i s i n f e r r e d f r o m 

t h e e l e c t r o n c o m p o n e n t , h e n c e t h e r e i s l e s s c o n f i d e n c e i n t h i s p o r t i o n o f 

t h e m o d e l . T h e p e a k p r o t o n f l u x e s a r e 3 . 3 x 1 0 ® p r o t o n s / c m ^ s e c , n o m i n a l 

Distance from Jupiter, Radii 

F IG . 1 . D is tr ib u tio n o f p roton s and e le c tr o n s in th e p la n e o f th e Jupiter m a g n e t ic e q u a to r .

I A E A - S M -17 0 /4 2 579 

a n d 6 . 0 x 1 ( ) H p r o t o n / c m ^ s e c , u p p e r l i m i t . A g a i n , t h e p e a k n o m i n a l p r o t o n 

f l u x i s c o m p a r a b l e t o t h a t a t E a r t h , b u t t h e u p p e r l i m i t f l u x i s n e a r l y 

2 0 0 0 t i m e s g r e a t e r . S p a c e c r a f t s h i e l d i n g i s i n e f f e c t i v e a t t h e p e a k f l u x 

d u e t o t h e e x t r e m e h a r d n e s s o f t h e e n e r g y s p e c t r u m 0 ] H o w e v e r , t h e e n e r 

g y s p e c t r a a r e c o n s i d e r a b l y s o f t e r a t r e m o t e d i s t a n c e s s o t h a t s h i e l d i n g m a y 

b e u s e d t o r e d u c e t h e f l u x w h e n t h e c l o s e n e s s o f a p p r o a c h i s l i m i t e d . T h e 

r a n g e o f c l o s e s t a p p r o a c h t o J u p i t e r t h a t m a y b e e x p e c t e d d u r i n g t h e M a r i n e r / 

J u p i t e r - S a t u r n m i s s i o n t o b e l a u n c h e d i n 1 9 7 7 i s a l s o s h o w n o n F i g u r e 1 . 

T h i s r a n g e , f r o m 4 . 3 t o 7 . 3 J u p i t e r r a d i i , i s b a s e d o n t w o c o n s i d e r a t i o n s — 

l i m i t a t i o n o f p e r m a n e n t d a m a g e t o e l e c t r o n i c d e v i c e s w i t h i n t h e s p a c e c r a f t 

d u e t o t h e c o n s i d e r a b l e f l u e n c e s a c c u m u l a t e d d u r i n g f l i g h t p a s t J u p i t e r , 

a n d t r a j e c t o r y c o n s t r a i n t s i m p o s e d b y t h e o b j e c t i v e o f f l y i n g p a s t S a t u r n 

l a t e r i n t h e m i s s i o n . T h e s e t r a j e c t o r y c o n s t r a i n t s a l s o f o r c e t h e s p a c e 

c r a f t t o r e m a i n c l o s e t o J u p i t e r ' s e q u a t o r i a l p l a n e . T h e f l u e n c e s e n c o u n 

t e r e d d u r i n g e q u a t o r i a l f l y - b y ' s o f J u p i t e r a r e s h o w n i n F i g u r e 2 . W h e n t h e 

r a d i u s o f c l o s e s t a p p r o a c h i s 4 . 3 J u p i t e r r a d i i , t h e n o m i n a l a n d u p p e r l i m i t 

e l e c t r o n f l u e n c e s a r e r e s p e c t i v e l y 1 . 0 x IO-*-0 a n d 4 . 2 x 1 0 ^ e l e c t r o n s / c m ^ ; 

t h e p r o t o n f l u e n c e s a r e r e s p e c t i v e l y 1 . 3 x 1 0 ^ a n d 3 . 4 x 1 0 ^ 2 p r o t o n s / c m ^ . 

1 2 3 4 5 6 7 8 9 1 0 20 

Closest Approach to Jupiter, Radii 

F IG . 2 . F lu e n c e s o f p roton s and e le c tr o n s e n c o u n te r e d d u rin g e q u a to r ia l flig h ts past Jupiter.

580 CLARK et a l. 

K a s e M h a s s h o w n t h a t t h e s e v a l u e s w o u l d b e r e d u c e d a s m u c h a s 5 0 % i f p o 

l a r f l y - b y ' s w e r e p o s s i b l e . T h e r e i s l i t t l e d i f f e r e n c e b e t w e e n t h e s e f l u 

e n c e s a n d t h o s e a c c u m u l a t e d d u r i n g d e p a r t u r e f r o m E a r t h w h e n t h e r a d i u s o f 

c l o s e s t a p p r o a c h t o J u p i t e r i s r e s t r i c t e d . T h e r a d i a t i o n e n v i r o n m e n t s o f 

p r o b e s t h a t e n t e r J u p i t e r ' s a t m o s p h e r e w o u l d b e a p p r o x i m a t e l y 1 0 0 t i m e s m o r e 

s e v e r e . 

H a f f n e r h a s i n d i c a t e d t h e p o s s i b i l i t y t h a t S a t u r n h a s r a d i a t i o n 

b e l t s . T h e s e b e l t s a r e e x p e c t e d t o h a v e 1 / 1 0 0 t h e i n t e n s i t y o f J u p i t e r ' s 

r a d i a t i o n b e l t s . T h e r e i s c u r r e n t l y n o e v i d e n c e e i t h e r f o r o r a g a i n s t o t h e r 

p l a n e t s o r a n y m o o n s o f t h e p l a n e t s h a v i n g r a d i a t i o n b e l t s . 

T h e r a d i a t i o n e n v i r o n m e n t i n i n t e r p l a n e t a r y s p a c e h a s t h r e e p r i n c i p a l 

e l e m e n t s — i n t e r g a l a c t i c c o s m i c r a d i a t i o n , t h e s o l a r w i n d , a n d s o l a r f l a r e s . 

T h e f i r s t t w o o f t h e s e e l e m e n t s a r e e s s e n t i a l l y c o n t i n u o u s , w h i l e s o l a r 

f l a r e s a r e p e r i o d i c , o r w a v e - l i k e . T h e p r o p e r t i e s o f a l l o f t h e s e s o u r c e s 

a r e s t r o n g l y i n f l u e n c e d b y t h e 1 1 - y e a r c y c l e o f s o l a r a c t i v i t y . 

G a l a c t i c c o s m i c r a d i a t i o n c o n s i s t s o f c h a r g e d p a r t i c l e s h a v i n g t h e 

f o l l o w i n g a b u n d a n c e s [ 7 , 9 j : 

R e l a t i v e A b u n d a n c e 

C h a r g e d P a r t i c l e i n t h e U n i v e r s e 

H y d r o g e n ( P r o t o n ) 1 0 0 , 0 0 0 

H e l i u m ( A l p h a ) ' 7 , 5 0 0 

L i t h i u m , B e r y l l i u m , B o r o n 3 x 1 0 " 3 

C a r b o n 1 0 

N i t r o g e n 1 5 

O x y g e n 5 0 

1 0 < Z < 3 0 3 0 

3 0 < Z 8 x 1 0 - 4 

E l e c t r o n 6 , 6 0 0 

T h e c o s m i c r a d i a t i o n a t s o l a r m i n i m u m i s a p p r o x i m a t e l y d o u b l e t h a t a t s o l a r 

m a x i m u m . T h e n e x t s o l a r m a x i m u m w i l l o c c u r e a r l y i n t h e 1 9 8 0 ' s . D i v i n e 

i n d i c a t e s t h a t t h e f l u x e s a t s o l a r m i n i m u m a r e 9 . 5 p r o t o n s / c m s e c a n d 

0 . 6 e l e c t r o n s / c m ^ s e c , a n d t h e i r m i n i m u m e n e r g y i s 1 0 0 M e V . B e c a u s e t h e s e 

p a r t i c l e s a r e e x t r e m e l y e n e r g e t i c , t y p i c a l s p a c e c r a f t s h i e l d i n g h a s v e r y 

l i t t l e e f f e c t . T h e f l u e n c e s o f p r o t o n s a n d e l e c t r o n s e n c o u n t e r e d i n t h e 

c o s m i c r a d i a t i o n e n v i r o n m e n t a r e p r o p o r t i o n a l t o t h e m i s s i o n d u r a t i o n . 

M i s s i o n s t o t h e i n n e r p l a n e t s , r e q u i r i n g o n t h e o r d e r o f a y e a r , w o u l d e n 

c o u n t e r 3 . 0 x 1 0 ® p r o t o n s / c m ^ a n d 2 . 0 x 1 0 ^ e l e c t r o n s / c m ^ . M i s s i o n s t o t h e 

o u t e r p l a n e t s e n t a i l 5 t o 1 0 y e a r s ; t h e p r e c e d i n g f l u x e s w o u l d b e m u l t i p l i e d 

a c c o r d i n g l y . 

T h e s o l a r w i n d i s a n e l e c t r i c a l l y n e u t r a l p l a s m a o f p r o t o n s , e l e c t r o n s , 

a n d o t h e r p a r t i c l e s e m i t t e d b y t h e S u n . I t i s b e l i e v e d t h a t t h e s o l a r w i n d 

e m i s s i o n i s i s o t r o p i c a n d , t h e r e f o r e , t h e p a r t i c l e f l u x i s i n v e r s e l y p r o 

p o r t i o n a l t o t h e s q u a r e o f t h e d i s t a n c e f r o m t h e S u n . M e a s u r e m e n t s a t 1 a . u . 

h a v e s h o w n t h a t t h e s o l a r w i n d v e l o c i t y i s 3 0 0 t o 8 0 0 k m / s e c ; t h e f l u x i s 

1 . 5 x 1 0 ^ t o 2 . 4 x 1 0 ® p r o t o n s a n d e l e c t r o n s / c m ^ s e c ; a n d t h e p r o t o n e n e r g y 

i s 0 . 5 t o 3 k e V . H a f f n e r [ в ] h a s s h o w n t h a t t h e v e l o c i t y o f t h e s o l a r w i n d 

i n c r e a s e s w i t h d i s t a n c e f r o m t h e S u n a n d t h a t t h e e f f e c t i v e t e m p e r a t u r e , o r 

e n e r g y d e c r e a s e s . B e c a u s e o f t h e i n v e r s e s q u a r e e f f e c t , t h e s o l a r w i n d f l u x 

w i l l v a r y c o n s i d e r a b l y b e t w e e n i n n e r a n d o u t e r p l a n e t s m i s s i o n s a n d t h e f l u 

e n c e s w i l l d e p e n d o n t h e t r a j e c t o r y h i s t o r i e s . A t V e n u s , 0 . 7 2 a . u . , t h e 

f l u x i s a p p r o x i m a t e l y t w i c e t h a t a t E a r t h . A t S a t u r n , 5 . 2 a . u . , t h e f l u x

I A E A - S M -17 0 /4 2 581 

is only 1/27 that at Earth. Diederich [10] has integrated the flux during 

year-long Viking fligh ts to Mars to obtain solar wind fluence of 3.5 x 10-*-^ 

protons/cm2 > 

Solar flares consist of protons, alpha particles and electrons emitted 

by the Sun during solar storms. The energies of these particles may range 

from 1 MeV to several thousand MeV and the duration of the event as it 

passes a given location in space may be from hours to weeks. McDonald [ l l ] 

discusses the morphology of solar flare events and indicates that a single 

event could result in a fluence at Earth of 4 .0 x 10^ protons/cm^ having 

energies greater than 30 MeV, with a maximum flux during the event of 

2 .0 x 10^ protons/cm^ sec- jhe fluxes of electrons and alpha particles are 

in general equal to or considerably less than that of protons. 

Various authors, including Modisette [1 2 ], have predicted the nature of 

the solar flare environment in future solar cycles. However, the model due 

to Diederich [10] has been adopted for this paper, which integrates the 

total fluence of a ll solar events during a year into one event measured at 

Earth. It is believed that the spatial distribution of solar flare p articles 

relative to the Sun is inversely proportional to the square of distance, 

as in the case of the solar wind. This effect is shown in Figure 3 , assuming 

that a ll of the year's events occur essen tially instantaneously in 

O.l l 10 20 

Distance from the Sun, AU 

F I G .3 . P roton flu e n c e fr o m solar fla r e s d u rin g in te r p la n e ta ry cr u is e .

582 C LARK et a l. 

the time frame of interplanetary flig h t. The fluence of solar protons with 

energies exceeding 1 MeV at Earth is 6 x 10 protons/cm^. Spacecraft 

shielding very e ffectively reduces this fluence, as shown by the figure. 

A 33 gm/cm2 aluminum shield results in a fluence of only 10° protons/cm2 

penetrating to the interior of the spacecraft. 

The atmosphere of a planet has profound effects on the radiation environment 

above and within the atmosphere and at its surface. When the 

planet has no atmosphere, as in the case of the Moon, the radiation levels 

at the surface are approximately \ those in space because of the shielding 

e ffe ct of the planet's mass. The atmosphere of Venus is so dense that probably 

no radiation from space could reach its surface. However, at some 

a ltitu d e, the cascading effect of radiation from space interacting with the 

atmosphere results in a peak of secondary p a rticles, as is observed in the 

Earth's upper atmosphere. On Mars, this increase in particle flux is e s t imated 

at 1.5 to 2.0 times the nominal value [31] The effectiveness of the 

Martian atmosphere and bulk planet in tota lly absorbing lower energy partic 

le s is as follows [1 3 ]: 

Radiation Source 

Solar Flare 

Energy > 10 MeV 

Energy > 100 MeV 

Cosmic Radiation 

Fraction of Space Value at Earth 

Penetrating to the Surface of Mars 

(6 m illibar pressure)________________ 

2 .0 x 10-3 

5 .0 x 10*2 

> 0 .4 

The preceding data are consistent with the previous observation that 

solar flare spectra are softer then cosmic ray spectra and, therefore, are 

readily shielded by even a tenuous atmosphere. 

Especially in the case of outer-planet missions, space science instruments 

may have to cope with man-made radiation sources on board the spacec 

ra ft. For instance, as the spacecraft moves away from the Sun, the amount 

of solar energy available to generate power in a solar c e ll system or to 

provide heat for thermal control diminishes. As in the case of the solar 

wind and solar fla res, solar energy is inversely proportional to the square 

of the distance from the Sun. Solar c e lls are marginally effective at Mars, 

where the solar energy available is less than h alf that at Earth, excluding 

the effect of Martian dust; at Jupiter, the solar energy available is 1/27 

that at Earth. Consequently, radioisotope thermoelectric generators (RTG) 

are to be used to power most outer-planet spacecraft, and radioisotope heating 

units (RHU) w ill provide heat in many instances. Pioneer, the Viking 

Lander and Mariner/Jupiter-Saturn a ll employ RTG's. 

The radioisotope fuel to be used in the RTG's and RHU's of outer-planet 

vehicles is plutonium oxide, 238pu 0 2. This fuel is especially desirable 

because it has an 86.8 year h a l f -li f e , provides 0.5 thermal watts of energy 

per gram, and produces low radiation emissions in comparison to other sources. 

The spontaneous emissions of this fuel are alpha p articles, neutrons, 

and gamma rays. Though 997. of this radiation is alpha p articles, these 

particles are of too low energy to penetrate the fuel container. 

Though this fuel spontaneously emits about 2100 neutrons/gram second, 

several factors a ffect the total neutron emission rate. As discussed by 

Weddell [1 4 ] these factors include reaction with the oxygen component of 

the fu e l, interactions with impurities in the fu e l, such as boron, sodium,

I A E A - S M -17 0 /4 2 583 

m a g n e s i u m , a n d a l u m i n u m , a n d m u l t i p l i c a t i o n d u e t o t h e i n t r i n s i c s i z e a n d 

p o w e r o f t h e d e v i c e . W e d d e l l s t a t e s t h a t t h e n e u t r o n e m i s s i o n r a t e c a n v a r y 

f r o m 2 0 , 0 0 0 t o 3 1 4 , 0 0 0 n e u t r o n s / g r a m s e c d u e t o t h e s e f a c t o r s , w i t h t h e e x 

p e c t e d m a x i m u m a b o u t 4 0 , 0 0 0 i n t h e c a s e o f t h e M a r i n e r / J u p i t e r - S a t u r n s p a c e 

c r a f t . T h e n e u t r o n s p e c t r u m i n c l u d e s e n e r g i e s u p t o 7 M e V . 

P l u t o n i u m o x i d e f u e l a l s o e m i t s g a m m a r a d i a t i o n . T h e n a t u r a l d e c a y o f 

p l u t o n i u m ( 2 3 8 p u ) a u g m e n t e d b y g a m m a r a d i a t i o n p r o d u c e d b y i m p u r i t i e s , 

s u c h a s 2 3 6 p U j w h i c h a r e a s s o c i a t e d w i t h t h e m a n u f a c t u r e o f t h e f u e l . I f 

1 p a r t p e r m i l l i o n o f 2 3 6 p u p r e s e n t , W e d d e l l i n d i c a t e s t h i s i m p u r i t y w i l l 

m u l t i p l y t h e t o t a l g a m m a p r o d u c t i o n r a t e b y a m a x i m u m f a c t o r o f 7 a t 1 8 y e a r s 

a f t e r i n i t i a l p u r i f i c a t i o n ; t h e n t h e r a t e w i l l d e c l i n e . N o o n [ i 5 ] s h o w s 

t h a t a g e d f u e l w i l l p r o d u c e a b o u t 2 , 0 0 0 p h o t o n s / c m ^ s e c i n t h e e n e r g y r a n g e 

1 0 0 t o 2 0 0 k e V a t a l o c a t i o n a b o u t 1 m e t e r f r o m t h e a x i s o f t h e R T G c a n i s t e r . 

T h e e n t i r e g a m m a r a d i a t i o n s p e c t r u m i n c l u d e s e n e r g i e s u p t o 7 M e V . W h e n t h e 

e m i s s i o n i s l e n g t h y , a s i n t h e c a s e o f M a r i n e r / J u p i t e r - S a t u r n , i t i s d e 

s i r a b l e t o a s s u m e t h a t t h e f u e l a g e i s 1 8 y e a r s s o t h a t t h e g a m m a r a d i a t i o n 

e n v i r o n m e n t i s n o t u n d e r e s t i m a t e d . 

T h e n e u t r o n f l u e n c e s t h a t s h o u l d b e a n t i c i p a t e d a t t h e s c i e n c e i n s t r u 

m e n t s o f t h e V i k i n g / M a r s L a n d e r a n d t h e M a r i n e r / J u p i t e r - S a t u r n o u t e r p l a n e t s 

s p a c e c r a f t a r e s h o w n i n F i g u r e 4 . T h i s f i g u r e i s b a s e d o n f l u x e s c a l c u l a t e d 

b y D i e d e r i c h [ l O ] a n d W e r t z £ l 6 ] f o r t h e r e s p e c t i v e v e h i c l e s . I n t h e c a s e 

o f t h e V i k i n g L a n d e r , t h e t w o 6 7 5 w a t t ( t h e r m a l ) R T G ' s u s e d t o p o w e r t h e 

v e h i c l e a r e e m b e d d e d i n t h e s p a c e c r a f t a n d a l l o t h e r s y s t e m s , i n c l u d i n g t h e 

s c i e n c e e x p e r i m e n t s , a r e i n c l o s e p r o x i m i t y . T h i s i s n e c e s s a r y b e c a u s e a l l 

v e h i c l e s y s t e m s m u s t b e w i t h i n t h e h e a t s h i e l d d u r i n g e n t r y a n d d e s c e n t 

t h r o u g h M a r s ' a t m o s p h e r e . T h e f l u x e s a t t h e s c i e n c e e x p e r i m e n t s c a l c u l a t e d 

b y D i e d e r i c h d o n o t i n c l u d e a t t e n u a t i o n b y t h e s p a c e c r a f t s t r u c t u r e o r 

e q u i p m e n t . T h e n e u t r o n f l u x i s 1 . 3 0 x 1 0 ^ n e u t r o n s / c m ^ s e c ; t h e g a m m a f l u x 

i s 1 . 6 5 x 1 0 4 p h o t o n s / c m ^ s e c . T h e m i s s i o n o f t h e M a r i n e r / J u p i t e r - S a t u r n 

o u t e r - p l a n e t s s p a c e c r a f t d o e s n o t i n c l u d e e n t r y o f t h e i r a t m o s p h e r e s , s o 

t h e c o n f i g u r a t i o n n e e d n o t b e c o m p a c t . T h e r e f o r e , t h e t h r e e 2 , 2 0 0 w a t t 

( t h e r m a l ) R T G ' s t h a t p o w e r t h i s v e h i c l e a r e m o u n t e d o n a b o o m , d e p l o y e d d i a 

m e t r i c a l l y o p p o s i t e t o t h e s c i e n c e i n s t r u m e n t a t i o n . A s a r e s u l t , t h o u g h 

c o n s i d e r a b l y m o r e r a d i o i s o t o p e f u e l i s t o b e c a r r i e d o n t h e M a r i n e r / J u p i t e r - 

S a t u r n s p a c e c r a f t t h a n o n V i k i n g , t h e f l u x e s a t t h e s c i e n c e e x p e r i m e n t s a r e 

s u b s t a n t i a l l y l e s s . I n c l u d i n g a t t e n u a t i o n b y t h e s p a c e c r a f t , W e r t z c a l c u 

l a t e s t h e f l u x e s t o b e 3 . 1 n e u t r o n s / c m ^ s e c a n d 3 4 p h o t o n s / c m ^ s e c . T h e 

f l u e n c e s s h o w n i n F i g u r e 4 a r e p l o t t e d a s f u n c t i o n s o f t h e t i m e o f f l i g h t 

s o t h a t t h e e f f e c t s o f s e v e r a l m i s s i o n d u r a t i o n t i m e s c o u l d b e i n d i c a t e d . 

H o w e v e r , t h e e x p o s u r e o f t h e s c i e n c e e x p e r i m e n t s a n d a s s o c i a t e d e l e c t r o n i c s 

t o t h e R T G a n d R H U r a d i a t i o n s o u r c e s a c t u a l l y c o m m e n c e s e a r l i e r d u e t o t h e 

n e c e s s i t y f o r i n t e g r a t i o n a n d c h e c k o u t o f t h e s p a c e c r a f t s y s t e m s p r i o r t o 

l a u n c h . I n t h e c a s e o f V i k i n g , t h e p r e l a u n c h e x p o s u r e i s 1 2 0 d a y s , w h e r e a s 

t h e M a r i n e r / J u p i t e r - S a t u r n e x p o s u r e w i l l b e o n l y 3 0 d a y s . T h e s e d i f f e r e n c e s 

a r e d u e n o t o n l y t o d i f f e r e n c e s i n t h e v e h i c l e s b u t a l s o t o t h e n e e d t o 

l i m i t t h e e x p o s u r e o f p e r s o n n e l a t t h e l a u n c h c o m p l e x t o t h e l a r g e r R T G ' s 

o f t h e l a t t e r s p a c e c r a f t . F i g u r e 4 i n d i c a t e s t h a t t h e t o t a l n e u t r o n f l u e n c e 

d u r i n g t h e V i k i n g m i s s i o n w i l l b e a b o u t 5 x l O ^ n e u t r o n s / c m ^ . T h e e x p o s u r e 

o f t h e s c i e n c e e x p e r i m e n t s o f t h e M a r i n e r / J u p i t e r - S a t u r n s p a c e c r a f t w i l l b e 

1 . 7 x 1 0 8 neutrons/cm2 a t J u p i t e r e n c o u n t e r a n d 3 . 5 x 1 0 ® n e u t r o n s / c m ^ a t 

S a t u r n e n c o u n t e r . I n a l l c a s e s t h e f l u e n c e s o f g a m m a r a d i a t i o n a r e a p p r o x i 

m a t e l y 1 0 t i m e s t h e n e u t r o n f l u e n c e s . 

E X P E R I M E N T S I N D E S I G N A N D D E V E L O P M E N T 

T h e V i k i n g m i s s i o n t o b e l a u n c h e d i n 1 9 7 5 , i s t h e U n i t e d S t a t e s ' n e x t 

m i s s i o n t o t h e p l a n e t M a r s . C o n s i s t i n g o f a n i n t e g r a t e d o r b i t e r a n d l a n d e r ,

5 8 4 C LARK e t a l. 

0.1 1.0 10.0 

Flight Duration, Years 

F IG .4 . N eu tron flu e n c e at s c ie n c e in stru m e n ta tio n o f in te r p la n e ta r y s p a c e c r a ft p o w e r e d b y ra d io is o to p e 

t h e r m o e le c t r ic g en e ra to rs. 

the Viking spacecraft will first go into Mars orbit and reconnoiter the 

potential landing sites before the lander is separated and allowed to enter 

the atmosphere and soft land on the Martian surface. Once landed, the radiation 

environment is a combination of the following: galactic and solar 

cosmic rays, cosmic ray interaction products (the relatively sparse Martian 

atmosphere produces a nearly maximum flux density of build-up secondaries), 

emission from the onboard RTG power supply, induced radioactivity in the 

lander body, and natural radioactivity in the Martian soil. In addition, 

planetary quarantine criteria for Mars have levied the requirement that the 

entire lander be heat sterilized just prior to launch, and this has in turn 

necessitated the use of quantities of thoriated magnesium alloy in the lander 

construction. It should be pointed out that although the RTG's and 

MgTh alloy can cause interference problems in several experiments, it is 

unrealistic to assume they can be replaced. The thoriated alloy is the 

most cost-effective means of achieving low-weight instrument housings. 

For all present and proposed Viking lander experiments studied so far, 

the RTG emissions are more serious than any other ionizing radiation environment 

by at least an order of magnitude. Clearly, any experiment for 

the Viking spacecraft system must include the RTG radiation field as a required 

design criterion (along with, for example, weight and power constraints, 

thermal range, etc.). 

Three experiments on the Viking-75 lander employ detectors of ionizing 

radiation. The first of these is an X-ray fluorescence spectrometer (XRFS)

IA E A -S M - П 0 /4 2 585 

to assay Martian soil for the concentrations of major, minor, and certain 

trace elements [l7, 18j. In operation, this instrument provides two collimated 

X-ray beams to bombard the soil surface. The resulting fluorescent 

X-ray emissions are measured with energy-dispersive analysis by four "tuned- 

response" proportional counter detectors. The two beams are the 5.9 and 

22.2 keV X-ray emissions of the radioisotopes 55pe an(j 109cd. Together, 

the four counters are sensitive over the energy range 1.0 to 25.0 keV. 

Since its inception, this spectrometer was designed with close regard for 

the interference problem. Although it is well-known that the major component 

of the counting-rate in proportional counters exposed to gamma fields 

is due to secondary electrons from the walls rather than direct gamma interactions 

in the gas, the theoretical response functions for this effect are 

apparently not yet developed. It is thus impractical to calculate proportional 

counter response to an RTG field to the accuracy desired. One consequence 

immediately applicable to design, however, is that the gamma ray 

counting rate should scale as the internal surface area of the detector. 

On the other hand, the counting rate of the fluorescent X-rays scales as the 

aperture of the thin entrance window. A large window with minimum wall area 

is therefore preferred, and a pancake detector indicated. Criteria of resolution, 

peak tailing, ruggedness and reliability rule out the pancake detector, 

and a conventional side-window cylindrical counter was selected instead. 

The counter design was then optimized for the minimum diameter and 

length (i.e., minimum internal wall area) consistent with requirements for 

adequate gas path for fluorescent X-ray absorption and uniform electric 

field geometry over the distance of the entrance window to give acceptable 

resolution. The signal-to-background ratio was then adjusted by sizing the 

radioisotope sources. In Figure 5 is presented a typical fluorescent spectrum 

overlaid by the spectrum measured in the field of a Pioneer RTG (S/N 

42), as corrected for Viking RTG fuel-loading levels. This figure is for 

the counter which is most interfered with. Of the 12 elements analyzed for 

by the XRFS, only three (mg, Al, and Si) are measurably affected by the RTG 

interference at all. Statistical analysis of these data, based upon a nominal 

operating period on*kars, has shown sensitivity and accuracy to be 

limited chiefly by the finite resolution of the counters and strength of 

the sources, rather than the RTG interference background, even for these 

three elements. 

Besides interference calculations, the XRFS experiment requires the 

best obtainable values of certain fundamental data: X-ray fluorescent 

yields, X-ray mass absorption coefficients, and X-ray mass scattering coefficients. 

These are used in a calculation from first principles of the 

element concentrations which would give rise to the observed spectra. In 

practice, we have found it necessary to employ empirical correction factors 

to the results. Better input data should allow reduction of these factors 

and a capability to accurately analyze a wider variety of sample compositions. 

Accordingly, we are presently updating our data base by replacing 

the fluorescent yield values of Fink [19] with the more recent compilations 

of Bambynek [20J and the X-ray mass interaction coefficients of Pletachy 

and Terrall [21j with those of Viegle [22j. These data are yet susceptible 

to improvement in accuracy, which would be quite welcomed for this application. 

The second and third Viking-75 experiments which are susceptible to 

RTG interference are the carbon assimilation and labeled metabolite schemes 

for detecting Martian life forms. Each employs ^ C labeled compounds and 

assays for in the gas phase. By this tracer technique, reactions char 

racteristic of metabolic processes can be detected. Sensitivity of these 

experiments in detecting life is directly related to the ability to reliably 

detect small levels of ^ C in the presence of the high RTG background.

586 C L A R K e t a l. 

F IG . 5. X -r a y flu o r e s c e n c e s p e ctra d u e to R T G -e m is s io n s and s ig n a l fr o m b a s a lt s a m p le 

(U S G e o lo g ic a l S u rvey Standard B C R -1 ). 

Realizing this, the U.S. NASA initiated studies of this problem early in 

the development phase of the biology instrument. In one study, a number of 

different detector types were evaluated for inherent efficiency for and 

energetic gamma rays £23] . The second study resulted in the development 

and test of a detection system consisting of a spherical cavity proportional 

counter for internal counting of the labeled gas at very high efficiency. 

The walls of this counter were made of scintillator with a thin 

evaporated aluminum coating to provide a cathode ground return and good 

light collection. With optimum settings of the energy windows for the 

counter and scintillator outputs, the anti-coincidence output of the counter 

correctly registers most of the beta rays while rejecting most of 

the gamma interactions f.24]. With this device, activities of 16 disintegrations 

per minute (dpm) could be detected in a one hour count with 

RTG background. This approach was not pursued, however, because of the 

significant weight penalty and a decision by the biology investigators that 

a minimum detection limit of 150 dpm would be satisfactory. On this basis, 

a theoretical, then experimental study was made which resulted in a detection 

system composed of two solid-state detectors, monitoring a pillboxshaped 

gas cavity. Nuclear data used in the study included the beta 

ray energy spectrum, electron energy-loss rate and backscattering from the

I A E A - S M -17 0 /4 2 587 

dead layer and sensitive volume of the silicon detectors, and gamma ray 

absorption coefficients for silicon. The resulting system detects 150 dpm 

with 1300 counts/minute of background when a counting period of 24 hours is 

used. This long integration time has required the development of extremely 

stable and well temperature compensated amplifying and discrimination circuitry. 

EXPERIMENTS FOR FUTURE MISSIONS 

X-ray Piffractometry - Two instruments which have been proposed for 

future Viking missions to Mars are an X-ray diffractometer and a gamma ray 

spectrometer. The purpose of the diffractometer is to measure lattice 

spacings of crystallites in the surface material to identify the minéralogie 

species present. It consists of a miniature X-ray tube and goniometer/ 

detector or position-sensitive detector. All detectors proposed to date 

are of the proportional counter type so that the considerations mentioned 

in connection with design of the XRFS apply here also. If the RTG's were 

absent, the X-ray tube would probably not be required and a radioisotope 

source such as 55pe could be used as a simpler, more stable, and more reliable 

substitute. Further work on X-ray diffraction is in progress. The 

nuclear data of concern are the X-ray coherent scattering cross-sections. 

Gamma Ray Spectrometry - A gamma ray spectrometer is needed to measure 

the concentrations of the three naturally-occurring radioactive elements in 

the soil, viz., 232'[j1) an(j 238ц# jf Martian crust can be shown to 

contain high levels of these elements (>0.1% for К and > few ppm for 

Th and U), as is the case for both the Earth and the Moon, then one can immediately 

deduce that Mars has undergone a planetary-scale geochemical 

differentiation with significant depletion of the internal K, U, and Th content. 

Otherwise, the radioactive heating would render the planet entirely 

molten. Our problem here in implementing this experiment is once again the 

RTG interference, but much more severely so than in the preceding examples. 

In Figure 6 are plotted typical gamma spectra recorded in Nal scintillator 

for two slightly different SNAP units (the fuel-holding units used for the 

RTG's) along with a typical spectrum of natural emissions from Earth crustal 

rock [25, 26, 27]. The SNAP gamma intensity even at distances of 2 and 2.7 

F IG . 6 . G a m m a sp e ctra o f R TG and Earth s o il e m is sio n s as r e c o r d e d b y N a l ( T l) s c in tilla to r in 4 m in u tes 

c o u n t t im e . S o lid c u r v e : S N A P -27 at 2 .7 m e tre s [ 2 5 ] ; d ashed c u r v e : S N A P -1 9 at 2 . 0 m etres [ 2 6 ] ; 

. d o tte d c u r v e : n a tu ra l e m is s io n w ith d e t e c t o r 1 .0 m e tre a b o v e th e ground [ 2 7 ] .

588 C L A R K e t a l. 

meters is two orders-of-magnitude or more greater than the terrestrial soil 

intensity. Since Martian soil could be only one-tenth as radioactive as 

terrestrial, it is desirable to reduce the RTG interference by at least a 

factor of 1000 from that shown in Figure 6. Shielding is out of the question 

from the weight standpoint - an adequate lead shield would weigh almost 

as much as the entire lander. Increasing the separation distance between 

spectrometer and RTG's appears to be the only practical way of reducing the 

interference to reasonable levels. To achieve the factor of 1000 would require 

removing the spectrometer to a distance of at least 60 to 80 meters 

from the lander. 

One other way of possibly reducing the interference would be to employ 

a very, high resolution gamma detector in lieu of the rather poor resolution 

scintillator and to use energy discrimination to distinguish between RTG 

gammas and soil gammas. Energy resolution provides only partial relief from 

interference, however, because although over half the RTG gammas are from 

238pUj an(j therefore do not coincide with soil gammas, there is a very significant 

fraction due to the decay of 236pu (this isotope is present only 

at the one part per million level in the SNAP fuel - its removal would be 

extremely costly). The decay of 236pu as follows: 

2.85 yr. 72 yr. (1.91 yr. total) „„„ 3 min. 

236Гц * r 232u y , 228^ r , t __ ¿ 208T1______► 208pb 

(stable) 

The most important gamma emissions are those of 208^^ > viz. 2.615 MeV (1007.), 

0.80 MeV (127o) , 0.58 MeV (867»), and 0.51 MeV (237„). Consider now the decay 

chain of the natural thorium isotope 232>jh: 

1.4x10*0 yr. 6.7 yr. 6.1 hr. 

Th--------- Ra----------- 228Ac ----- ----- * 228Th — --- - etc. 

The key point here is that the thorium decay series intersects the 23^Pu 

decay series at 228Th, with both proceeding identically thereafter. This is 

the reason we see the same peak of 2.615 MeV for all three spectra in 

Figure 6. Consequently, the RTG spectrum interferes not only from a flux 

standpoint, but also from the energy standpoint for the Th determination. 

In summary, getting the spectrometer away from the lander seems to be 

the only reasonable solution. Because of the distances required, a boom is 

out of the question. A small mini-rover, of the tethered type, could adequately 

perform this task. In addition, such a rover could possibly 

travel over a hill or behind a boulder to attenuate the RTG signal even 

further (a single boulder 0.8 meters ir. diameter would attenuate by a factor 

of 1000). 

X-RAY FLUORESCENCE OF VENUS CLOUDS 

The basic scheme used for geochemical analysis of rocks collected by a 

Mars lander can be applied to the determination of atmospheric constituents 

by a descent probe through the dense Venus atmosphere. Thus, using unstable 

nuclei which decay by capture of K, L, and M shell electrons, X-rays can be 

generated to stimulate fluorescent X-radiation from atmospheric atoms. The 

experiment therefore would use two such X-ray sources (55pe and 109cd) and 

two proportional counters mounted external to the descent probe of the Pioneer 

Venus multiprobe mission (scheduled for launch in early 1977). The 

atmosphere is analyzed directly during the descent without the need of any 

sample collection devices. Fluorescent X-rays from all elements above

I A E A - S M -1 7 0 /4 2 589 

phosphorus in the periodic table fall within the energy range of the counters. 

The host atmosphere, mostly CO? causes very little attenuation of 

the X-rays, especially the 22.2 keV x-rays. However, sensitivity of 

the experiment is greatest for heavy elements such as Hg, Br, I, Sb, and As 

which are thought to be cloud forming elements of the Venus atmosphere. The 

measurement is independent of the chemical and physical state of the fluorescing 

elements and thereby provides a complement to a mass spectrometer 

experiment which measures concentrations of gaseous components only. 

NEUTRON DETECTION 

The detection of fast neutrons in planetary atmospheres can be used as 

an effective tool in evaluating effects of cosmic radiation in the atmosphere 

and planetary surface. On Earth, such studies have been used to identify 

a mechanism for populating the inner part of the trapped radiation belt 

with protons and also to understand the production of ^ C in the atmosphere. 

Fast neutron detectors operating in the presence of other types of radiation 

must be designed to discriminate against these in favor of the more elusive 

neutrons. The method used h isto rically in many studies involved surrounding 

a pair of gas fille d proportional counters with a proton rich neutron moderator 

such as water or paraffin. The neutrons thus thermalized produced 

N-а reactions in a BF3 gas, highly enriched in Юв, in one of the proportional 

counters. The very high thermal neutron capture cross section 

thus enabled s ta tis tic a l discrimination of counts produced by other radiation 

by subtracting the counts from the other proportional counter fille d 

with BF3 gas depleted in ^ В . 

A more recent scheme for discriminating directly rather than s t a t is t ic 

a lly against other radiation uses a proton-rich scin tilla tio n p lastic or 

liquid. The neutrons are detected by observation of the ionization 

scin tilla tio n of recoil protons resulting from e la stic n-p collision s in the 

detector. The detector is made to ta lly unresponsive to protons and electrons 

entering the s cin tilla to r by surrounding it with a shell of an inorganic 

scin tilla to r such as Csl or Nal. The ionization light pulse produced 

by the charged particle in this shell is much longer than that seen in the 

organic s cin tilla to r and can readily be separated electronically to reject 

such pulses as resulting from charged particles rather than neutrons entering 

the detector. An additional scheme is added to discriminate against 

X-rays which, like neutrons, can pass by the charged particle rejection 

shell and produce characteristic electron interactions in the organic scint 

illa t o r . This involves using a special type of s cin tilla to r which results 

in a different ionization pulse shape by protons as opposed to electrons. 

Thus, recoil protons (produced by neutrons) can be separated electronically 

from Compton, photoelectric, or pair production electrons and positrons 

(produced by 7-rays) . The electronically rejected pulses in this type of 

detector can also be used to detect the protons, electrons, and 7-rays which 

enter the counter. 

NEUTRON ACTIVATION ANALYSIS 

Elemental analysis using the technique of neutron activation is a very 

sensitive method for characterizing the chemical composition of planetary 

surfaces [28]. Although the technique was proposed by a number of investigators 

in the pre-Apollo or unmanned phase of the U.S.' lunar program, it 

is as yet untried in space for compositional analysis. Developments in the 

past few years, however, in the areas of detector technology, data reduction 

and analysis, and particularly the availability of Californium-252 which 

offers extremely high neutron yields through spontaneous fission, have rekindled 

interest in using neutron activation for planetary surface analysis.

5 9 0' C LARK et a l. 

This section of the paper will treat briefly the concern of background 

radiation interferences, and their minimization, in order to obtain statistically 

valid data. 

Following absorption of neutrons, atomic nuclei generally emit gamma 

rays whose energy distribution provides "spectral signatures" which are 

characteristic of the elemental species and thus enable quantitative identification 

of the chemical elements. This radiation falls into two categories, 

namely: neutron capture gamma rays and delayed or activation gamma 

rays. In the former case, the gamma radiation is emitted in the range of 

10~14 to 10"® seconds. If the nucleus becomes radioactive, it will emit 

delayed gamma rays as it undergoes radioisotopic decay. 

A promising approach to the minimization of interfering background radiation 

was developed to aid in minerals exploration of the ocean floor [29j. 

In this environment the natural background is severe owing to the decay 

chains of the uranium and thorium present, and potassium (40r ). Prompt capture 

gamma rays have energies up to 10 MeV, whereas delayed gammas are 

emitted up to about 1.5 MeV. Measurement of the former limits the extent 

of background interference, enables simultaneous irradiation of the surface 

and measurement of the gamma response, and because of the higher energies 

emitted, the technique allows placement of the detector within the protective 

enclosure of the spacecraft. The authors proposed a mathematical 

relationship to describe the usefulness of this approach, which is S = 

10/A, where: S is defined as an index of elemental sensitivity, I is the 

number of gamma rays of a given energy emitted per 100 neutrons absorbed, 

0 is the microscopic cross section in barns. This concept required extension 

to and test of those elemental species anticipated in planetary surfaces 

. 

A basic problem here is the resolution of the complicated spectra obtained 

in capture gamma ray measurements. A solution of this problem has 

been described using both ruggedized Nal (TЦ ) detectors and the development 

of sophisticated computer-based procedures for the analysis of the 

complex pulse-height spectrum [30j. 

The evidence indicates that background radiation, arising from the 

surface itself and the environment characteristic of the planet, can be 

minimized thus enabling the return of statistically valid data and provide 

elemental analysis of the planetary surface. 

NUCLEAR DATA REQUIRED 

It is evident from the foregoing that applications of nuclear techniques 

in space science are many. Likewise, the operating environments 

often give rise to significant radiation interferences. Successful design 

of a space experiment requires careful study, both from an experimental 

and theoretical standpoint, of the response of the experiment to its intended 

signal versus the background interference. The general body of 

nuclear data has been and will continue to be of considerable importance 

to experiment design. In Table I, we list some of the types of nuclear 

data that apply to the examples discussed. In many cases, improvement in 

the fundamental data and/or radiation transport calculations would allow 

more optimal experiment design.

I A E A - S M -17 0 /4 2 591 

T A B L E I. T Y P E S O F N U C L E A R D A T A USED IN A B O V E E X A M P L E S * 

Gamma 

(20 keV to 10 MeV) 

Beta Rays 

(0 to 150 keV) 

X-rays 

(1 to 20 keV) 

Neutrons 

(thermal to 14 MeV) 

Photoelectric and pair production absorption 

coefficients 

Coherent and incoherent scattering coefficients 

Scattering direction distributions 

Scattering and energy loss in thick absorbers 

Fluorescent yields 

Photoelectric absorption coefficients 

Coherent and incoherent scattering coefficients 

Fluorescent X-ray emission energies 

Inelastic and elastic scattering cross- 

sections 

Activation cross-sections 

Radioisotope Decay Emissions of X-ray emitters and contaminants 

(lO^cd^ 65zn , etc.) and gamma ray emitters 

(neutron activation products) 

Protons, Charged Nuclei 

(1 MeV to 10 GeV) 

Energy loss rates 

Spallation and activation cross-sections 

*Because these examples cover only a limited number of cases in which 

nuclear instrumentation is used in space experiments, the breadth of 

types of nuclear data required is greater than shown here. 


fl] VETTE, J. I. et al, Models of the Trapped Radiation Environment, 

Vols. I through VII, NASA SP-3024, National Aeronautics and Space 

Administration, Washington, D. C. (1966 through 1971). 

[2] SINGLEY, G. W., VETTE, J. I., The AE-4 Model of the Outer Radiation 

Zone Electron Environment, NSSDC 72-06, National Space Science Data 

Center, Greenbelt, Maryland (August 1972). 

[3] TEAGUE, M. J., VETTE, J. I., The Inner Zone Electron Model AE-5, 

NSSDC 72-10, National Space Science Data Center, Greenbelt, Maryland, 

(November 1972). 

[4J KASE, P. G., "The radiation environments of outer-planet missions," 

IEEE Transactions on Nuclear Science, Vol. NS-19, 6.(Dec. 1972) 

141-146. 

f53 WARWICK, J. W., Particles and Fields Near Jupiter, NASA CR-1685, Jet 

Propulsion Laboratory, Pasadena, California (October 1970).

592 C L A R K e t a l. 

[6] Proceedings of the Jupiter Radiation Belt Workshop, (BECK, A. J., Ed.) 

TM 33-543, Jet Propulsion Laboratory, Pasadena, California (1 July 

1972). 

[7] DIVINE, N., The Planet Jupiter (1970), NASA SP-8069, Jet Propulsion 

Laboratory, Pasadena, California (December 1971). 

[в] HAFFNER, J. W., "Magnetospheres of Jupiter and Saturn," AIAA Journal, 

Vol. 9, No. 12 (December 1971) 2422-2427. 

[9] Satellite Environment Handbook, (JOHNSON, F. S., Ed.) Stanford Univ. 

Press, Stanford, California (1961). 

£lo] DIEDERICH, D. R., Viking Radiation Environment, TN-3770040 (Rev. A), 

Martin Marietta Aerospace, Denver, Colorado (24 April 1972). 

[11] Solar Proton Manual, (McDONALD, F. B., Ed.), NASA TRR-169, Goddard 

Space Flight Center, Greenbelt, Maryland (December 1963). 

[12] MODISETTE, J. L., VINSON, Т. M., HARDY, A. C., Model Solar Proton 

Environments for Manned Spacecraft Design, NASA TN D-2746, Manned 

Spacecraft Center, Houston, Texas (April 1965). 

[13] Mars Engineering Model, M75-125-2, NASA Langley Research Center, 

Hampton, Virginia (14 April 1972). 

[14] The Effects of Radiation on the Outer Planets Grand Tour, (WEDDELL, 

J. B., Ed.), SD71-770, North American Rockwell Corp., Downey, 

California (November 1971). 

[15] NOON, E. L., ANNO, G. H., DORE, M. A., "Nuclear radiation sources on 

board outer-planet spacecraft," NS-18, IEEE Transactions on Nuclear 

Science (October 1971). 

[16] Mariner/jupiter-Saturn 1977 Spacecraft Description, (WERTZ, C., Ed.), 

Jet Propulsion Laboratory, Pasadena, California (12 July 1972). 

[17] CLARK, В. C., X-ray Surface Sample Analyzer for Planetary Exploration," 

NASA High CR-127526 (1972), Accession No. N-72-27846. 

[18] The design and execution of the Viking Inorganic Chemistry Experiment 

is the responsibility of a team of scientists consisting of 

Professor A. K. Baird of Pomona College, Dr. B. C. Clark of Martin 

Marietta Aerospace, Professor K. Keil of the University of New 

Mexico, Dr. H. J. Rose, Jr., of the United States Geological Survey, 

and Dr. P. Toulmin, III, of the United States Geological Survey 

(Team Leader). 

[19] FINK, R. W., JOPSON, R. C., MARK, H., SWIFT, C. D., "Atomic fluorescence 

yields," Rev. Mod. Phys. 38 (1966) 513. 

[20] BAMBYNEK, W., CRASEMANN, B., FINK, R. W., FREUND, H. U., MARK, H., 

SWIFT, C. D., PRICE, R. E., RAO, P. V., "X-ray fluorescence yields, 

Auger, and Coster-Kronig transition probabilities," Rev. Mod. Phys. 

44 (1972) 716. 

[21] PLECHATY, E. F., TERRELL, J. R., Integrated System for Production of 

Neutronics and Photonics Calculational Constants - Vol. 6 Photon 

Cross Sections 1 keV to 100 MeV, UCRL-50400 (1968).

I A E A - S M -17 0 /4 2 593 

[22] VEIGLE, W. J., BRIGGS, E., BATES, L., HENRY, E. M., BRACEWELL, B., 

X-ray Cross Section Compilation from 0.1 keV to 1 MeV, DNA 2433F 

(formerly BASA 2433) (1972) available from Director, Defense Nuclear 

Agency, Washington, D. C. 20305. 

[ 23] WAINIO, K., ROGERS, W. L., An Analysis of Carbon-14 Radiation Detection 

Systems, Final Report to Contract NAS 2-5546, NASA/Ames Research 

Center (1969). 

[24] CLARK., В. C., "Carbon-14 detection in a high background radiation," 

Nucl. Instr. Math. 89 (1970) 225. 

[25] KAMINSKAS, R. A., RYAN, G. W., SMITH, C. A., RTG/Science Instrument 

Radiation Interactions for Deep Space Probes, TRW Rept. on Contract 

NAS 2-5222 with NASA/Ames Research Center (1969). 

[26] BLOCK, S., SCHMIDT, C. T., KATHREN, R. L., Radiation Dosimetry and 

Spectral Distribution of the SNAP-19 Source, UCRL-50539 (1968). 

[27] MINATO, S., KAWANO, M., "On the constitution of terrestrial gamma 

radiation," J. Geophys. Res. 7_5 (1970) 5825. 

[28] KRUGER, P., Principles of Activation Analysis, Wiley - Interscience, 

New York, N. Y., (1971) . 

[29] SENTFLE, F. E., DUFFEY, D., WIGGINS, P. F., "Mineral exploration of 

the ocean floor by in-situ neutron absorption using a Californium- 

252 source," Marine Technology Society Journal 3_, 5 (Sept.-Oct. 1969) 

9. 

[30] TR0MBKA, J. I., SENTFLE, F. E., SCHMADEBECK, R., "Neutron radiative 

capture methods for surface elemental analysis," Nuclear Instruments 

and Methods 87 (1970) 37-43. 

[31] Mars Scientific Model, Vol. 1, Jet Propulsion Laboratory Document 

No. 606-1 (1968). 


F. RUSTICHELLI: I have heard recen tly that it would be useful from 

the point o f view o f space scie n ce , p articu la rly in X -r a y investigations, 

to have sp h erica lly curved m on och rom ator cry sta ls in o rd e r to get a focu sin g 

effect. Could you com m ent on this point? I might m ention that we are 

developing this kind o f cry sta l at the Institute Max von L aue-P au l Langevin 

in G renoble in connection with neutron p h ysics experim en ts. We get the 

curvature by ch em ica l treatm ent of one of the fa ce s of silicon crysta ls. 

A fter the treatm ent the cry sta ls rem ain naturally curved, without any need 

fo r a m ech an ical o r th erm al device. This last-m en tioned ch a ra cteristic 

should be an advantage in space resea rch . 

В. C. CLARK: This developm ent is o f in terest, esp ecia lly if it resu lts 

in a greater throughput efficien cy fo r m onochrom atization o f X -r a y s . I would 

be in terested in learning m ore about this developm ent. 

R. NICKS: In your paper you m ention the p resen ce o f neutrons in the 

atm osph ere. W here do these neutrons com e from , what is their intensity 

and what is their en ergy? Can you tell us som ething about the detection 

system ?

594 C L A R K e t a l. 

В. C. CLARK: The origin o f these neutrons is nuclear reactions 

betw een incom ing charged p a rticles (co sm ic ra ys and solar flare p a rticle s) 

and the n uclei o f the constituents of the ea rth 's upper atm osphere. The 

en ergy spectrum o f this s o -c a lle d "neutron albedo" flux co v e rs a broad 

range, extending up to the en ergy of the incom ing p a rticle. Several d etection 

system s have been devised, including the BF3 - counter in a m oderator 

d escrib ed in the text. It is found that su cce ssfu l m easurem ent o f the 

neutron albedo req u ires the ability to identify and exclude the in terferen ce 

o f p rim a ry cosm ic ra y counts. T his is accom p lish ed by surrounding the 

p rim a ry d etector with a second d etector (e. g. a scin tillator shell) in sen sitive 

to neutrons and operated in a n ti-coin cid en ce with the p rim a ry d etector.

I A E A - S M -17 0 /3 5 

NUCLEAR DATA FOR SHIELDING 

AND ACTIVATION ESTIMATES FOR TRIUMF 

I.M . THORSON, W.J. WIESEHAHN 

TRIUMF Group, Simon Fraser University, 

Burnaby, B .C ., Canada 

Abstract 

NU CLEAR D A T A FO R SHIELDING A N D A C T IV A T IO N E S T IM A T E S FOR TRIU M F. 

T h e m o r e im p o r ta n t r a d ia tio n transp ort and re s id u a l a c t iv it y p r o d u c tio n e s tim a te s re q u ire d fo r th e h ig h - 

in te n s ity (1 0 0 jiA ) m e d iu m -e n e r g y (5 0 0 M e V ), H " is o ch r o n o u s c y c lo t r o n , e x te r n a l b e a m lin e s and ta rg ets o f 

TRIU M F a re e n u m e ra te d and d iscu sse d . T h e gross fe a tu re s o f th e ra d ia tio n f i e ld d istr ib u tio n d u rin g o p e r a tio n 

o f th e f a c i lit y are p r im a r ily d e p e n d e n t o n th e h a d r o n ic c a s c a d e in th e fa c i lit y c o m p o n e n ts and sh ie ld s. L a c k in g 

a d e q u a te e x p e r im e n t a l d a ta fo r th e s e c o n d a r y p a r t ic le s p e ctra and a n gu la r d istr ib u tio n s, a lm o st e x c lu s iv e 

r e lia n c e has b e e n p la c e d o n th e resu lts fr o m in tr a -n u c le a r c a s c a d e c a lc u la t io n s . T h e re s id u a l a c t iv a t io n and 

r a d ia tio n f ie ld p r o b le m s , w h ic h are m o r e c o m p a r a b le , in in te n s ity , t o th o se fo u n d at fissio n r e a cto r s than 

p r e v io u s g e n e ra tio n s o f a c c e le r a t o r f a c i lit ie s , a re c o m p lic a t e d b y th e w id e v a r ie ty o f p r o d u c t s p e c ie s fr o m 

h ig h - e n e r g y h a d ro n r e a c t io n s . T h e a v a ila b le e x p e r im e n t a l d a ta a re at b est in c o m p le t e and o ft e n fr a g m e n ta ry . 

E x te n siv e r e lia n c e fo r n u c le a r da ta r e q u ire m e n ts has b e e n p la c e d o n c o m p ila t io n s b a s ed o n R u d stam 's e m p ir ic a l 

fo r m u la ; m o r e r e c e n t ly a c t iv it y p r o d u c tio n e s tim a te s based o n S ilb e r b e r g and T s a o 's e x te n d e d e m p ir ic a l 

fo r m u la h a v e b e e n u sed . 

N u cle a r Data f o r S h ie ld in g and A c t i v a t i o n E stim a te s f o r TRIUMF 

1 . INTRODUCTION AND GENERAL DESCRIPTION OP TRIUMF 

1 .1 D e s c r ip t io n o f th e T R I -U n iv e r s ity Meson F a c i l i t y 

1 .1 . 1 TRIUMF A c c e le r a t o r : 

TRIUMF [ 1 ] c o n s i s t s o f a s i x - s e c t o r , is o c h r o n o u s c y c l o t r o n 

an d , i n i t i a l l y , tw o e x t e r n a l beam l i n e s a s shown in F ig . 1. 

H io n s a r e i n j e c t e d a t 300 keV in t o th e c y c l o t r o n and a c c e l 

e r a te d t o any e n erg y betw een 150 MeV and 500 MeV, w here th ey 

a r e s t r ip p e d t o p r o t o n s , f o r s im p le , c le a n , s im u lta n e o u s ext 

r a c t i o n in t o e i t h e r e x t e r n a l beam l i n e . The t o t a l , d e s ig n 

s p e c i f i c a t i o n beam i n t e n s i t y i s 100 (jA a t 500 MeV lim it e d by 

a c c e p t a b l e r e s id u a l r a d ia t io n f i e l d s p ro d u ce d by beam s p i l l in 

th e a c c e l e r a t o r . I f th e f i n a l beam en erg y i s red u ce d by ~ 10$ 

th e beam c u r r e n t c a p a b i l i t y o f th e a c c e l e r a t o r s h o u ld in c r e a s e 

by a f a c t o r ~ 3 , f o r th e same s p i l l . 

1 .1 . 2 E x p e rim e n ta l Beam L in e s : 

The e x p e r im e n ta l a r e a s o f th e f a c i l i t y a r e d iv id e d in t o a 

Meson A rea and a P r o to n Area a s shown in F ig . 1. In th e 

f i r s t , th e h ig h e s t i n t e n s i t y p r o t o n beams p ro d u ce m esons by 

n u c le a r r e a c t i o n s in t a r g e t s in p rim ary beam l i n e BL1. For 

i n i t i a l o p e r a t io n s tw o se co n d a ry beam l i n e s w i l l c o l l e c t p io n s 

p ro d u ce d in t a r g e t T2; o n e , a t 30° t o th e p r o t o n beam d i r e c 

t i o n , and in th e v e r t i c a l p la n e , w i l l t r a n s p o r t tt~ m esons in t o 

th e B io -M e d ic a l e x p e r im e n ta l a re a and th e o t h e r a t 135° t o th e 

595

596 TH O R SO N and W IESEH AHN 

in c id e n t p r o t o n beam, and in th e h o r i z o n t a l p la n e , w i l l c o l l e c t 

r e l a t i v e l y low en erg y p io n s o f e it h e r p o l a r i t y and t r a n s p o r t 

them th rou g h th e s h ie l d i n g t o th e m eson e x p e r im e n ta l a r e a . 

S h o r t ly a f t e r s t a r t - u p o f th e f a c i l i t y , e x p e c te d in e a r ly 1974, 

a se co n d m eson p r o d u c t io n t a r g e t , T I, w i l l be i n s t a l l e d t o 

p r o v id e e n e r g e t ic p io n s a t n ea r 0° t o th e in c id e n t p r o t o n d i 

r e c t i o n in t o a se co n d a ry beam l i n e t o th e m eson e x p e r im e n ta l 

a r e a . A t h i r d seco n d a ry beam from t a r g e t T2 and a se co n d from 

T I , n o t shown on F ig . 1 , a r e a l s o p la n n ed f o r th e n ea r fu t u r e . 

The P r o to n A rea w i l l be u sed f o r n u c le o n -n u c le o n and 

n u c le o n -n u c le u s e x p e rim e n ts . P rim ary beam l i n e BLIV i s 

s w itch e d a t th e e n tr a n c e t o th e a re a t o e i t h e r B LIV (a) o r 

B L IV (b ). P ro to n s o f v a r ia b l e en erg y in B LIV (a) w i l l be u sed 

t o p ro d u ce p o la r i z e d o r u n p o la r iz e d , m o n o -e n e r g e tic n e u tro n s 

in a l i q u i d d eu teriu m t a r g e t a n d /o r t o bombard t h in t a r g e t s 

f o r r e a c t i o n p r o d u c t s t u d ie s in an e v a cu a te d s c a t t e r i n g 

cham ber. An e x p e r im e n ta l a c t i v i t y p r o d u c t io n f a c i l i t y w ith 

th in t a r g e t s and gas t r a n s p o r t o f th e s p e c ie s r e c o i l i n g in t o 

th e gas w i l l be i n s t a l l e d im m e d ia te ly ahead o f th e beam dump 

in BLIVa. The maximum p r o t o n beam c u r r e n t co n te m p la te d f o r 

B L IV (a) i s 10 pA and th e a v e ra g e i s e x p e c te d t o be s u b s t a n t ia lly 

lo w e r . 

B LIV (b) w i l l have a p r o t o n beam c u r r e n t l i m i t o f 100 nA. 

I t w i l l fe e d p r o to n s t o o n e , o r p o s s i b l y two g e n e r a l p u rp ose 

t a r g e t p o s i t i o n s f o r ( p , n u c le u s ) r e a c t i o n s t u d ie s and t o th e 

t a r g e t f o r a h ig h r e s o l u t i o n p r o t o n s p e c tr o m e te r d e s ig n e d t o 

u t i l i z e th e in h e r e n t ly n arrow p r o t o n en erg y sp rea d u lt i m a t e l y 

e x p e c te d from th e c y c l o t r o n . 

1 . 1 . 5 P roto n Beam Dumps: 

The r e s id u a l p r o t o n beams in th e P ro to n A rea w i l l be 

dumped in t o low a c t i v a t i o n a b s o r b e r s , such a s g r a p h it e , su rrou 

n ded by i r o n - c o n c r e t e s h ie l d s t o a c h ie v e a d eq u a te d o s e - 

r a t e s in in h a b it e d a r e a s a t minumum c o s t . The beam i n t e n s i t y 

a t BLI w i l l , a t f u l l p ow er, be h ig h enough t o make a u s e f u l 

n e u tr o n s o u r c e f o r a th erm a l n e u tr o n f a c i l i t y . The r e s id u a l 

p r o t o n s w i l l be s to p p e d in a Pb o r P b /B i t a r g e t p r o d u c in g app 

r o x im a t e ly 8 n e u tron s p e r in c i d e n t 500 MeV p r o t o n . A t_100 

(jA beam c u r r e n t th e n e u tro n s o u r c e s t r e n g t h o f 5 x 1 o 15 s 1 w i l l 

p ro d u ce th e rm a l n e u tr o n f l u x e s in th e ra n ge 0 . 5 - l - 0 x l 0 13 cm 2 

s 1 in a sm a ll H20/t>20 m o d e ra to r a sse m b ly . 

T h ree tu b e s t o n e u tro n i r r a d i a t i o n s i t e s w i l l be in c lu d e d 

in th e v e r t i c a l colum n u sed f o r a c c e s s t o th e t a r g e t -m o d e r a t o r 

a s s e m b ly . Two h o r iz o n t a l tu b e s th rou g h th e ir o n c o r e s h i e l d 

in g , o f f - s e t a b ove th e p r o t o n beam p la n e , w i l l a llo w rem oval 

o f n e u tr o n beams f o r e x p e r im e n ta l p u r p o s e s . A s e p a r a te p r o t o n 

i r r a d i a t i o n f a c i l i t y f o r g r o s s a c t i v i t y p r o d u c t io n w i l l be in 

s t a l l e d im m ed ia tely ahead o f th e th erm a l n e u tr o n f a c i l i t y 

t a r g e t . 

1 .2 R a d ia t io n S o u r c e s , S h ie ld in g and A c t i v i t y P r o d u c t io n in 

TRIUMF 

1 .2 . 1 A c c e le r a t o r : 

Two beam l o s s m echanism s a r e e x p e c te d t o dom inate in th e 

a c c e l e r a t o r : c o l l i s i o n s w ith r e s id u a l gas atom s in th e c y c l o -

I A E A - S M -1 7 0 /3 5 597 

t r o n vacuum cham ber and d i s s o c i a t i o n o f th e H io n s . Both 

w i l l g e n e r a lly p ro d u ce n e u t r a l H atom s w h ich w i l l th e n be l o s t 

t a n g e n t a lly in t o th e s id e w a lls o f th e s t a i n l e s s - s t e e l vacuum 

ta n k . P resum ing no s i g n i f i c a n t p r e s s u r e g r a d ie n t s in th e 

vacuum ta n k , th e r e s id u a l gas s t r i p p i n g w i l l be u n ifo r m arou nd 

th e c ir c u m fe r e n c e and a t th e d e s ig n , n it r o g e n - e q u iv a l e n t , 

r e s id u a l p r e s s u r e o f 7 x l0 ~ e t o r r th e f r a c t i o n a l pow er l o s s 

from th e a c c e l e r a t i n g beam i s e s tim a te d t o be 3 .9 $ . The d i s 

s o c i a t i o n s p i l l i n t e n s i t y f o l l o w s th e a z im u th a l v a r i a t i o n o f 

th e m a g n etic f i e l d v a r y in g from 0 t o 2 .5 tim e s th e a v e r a g e a t 

th e vacuum ta n k w a l l. F or norm al o p e r a t io n s w ith beam e x t r a c 

t i o n a t 500 MeV, th e f r a c t i o n a l pow er l o s s t o vxB s t r i p p i n g i s 

e x p e c te d t o be 7 -6 fo, and e s s e n t i a l l y d is a p p e a r s f o r o p e r a t io n s 

a t 400 MeV o r l e s s . 

Over m ost o f th e p e r ip h e r y o f th e c y c l o t r o n th e v o id b etw 

een th e vacuum ta n k s id e w a ll and th e m ain magnet r e tu r n 

y o k e w i l l c o n t a in low a c t i v a t i o n s h i e l d i n g , t h i c k enough t o 

s to p th e s p i l l e d p rim a ry p r o t o n s . At th e gaps and t h in s e c 

t i o n s in th e m ain magnet r e t u r n y o k e s , h e a v y -c o n c r e t e b lo c k 

s h ie l d i n g arou n d th e p e r ip h e r y o f th e c y c l o t r o n w i l l red u ce 

th e r e s id u a l r a d i a t i o n l e v e l s in th e c y c l o t r o n v a u lt t o a llo w 

g e n e r a l a c c e s s w it h in h ou rs a f t e r shutdow n o f th e f a c i l i t y . 

The 5 m t h i c k c o n c r e t e s h ie l d i n g w a l ls b etw een th e c y c l o t r o n 

v a u lt and th e e x p e r im e n ta l a r e a s a r e in te n d e d t o red u ce th e 

o p e r a t in g d ose r a t e s in t h e s e a r e a s below t h a t f o r c o n tin u o u s 

o c c u p a t io n , i . e . 2 .5 mrem h- 1 . 

As o u t lin e d a b o v e , th e maximum beam i n t e n s i t y c a p a b i l i t y 

o f TRIUMF i s e x p e c te d t o be s e t by th e r e s id u a l r a d i a t i o n 

f i e l d c o n s t r a i n t s on m ain ten an ce and s e r v i c i n g o p e r a t io n s in 

and a rou n d th e c y c l o t r o n . The p r e d i c t e d r e s id u a l r a d ia t io n 

f i e l d s a t th e m id -p la n e o f th e s e r v i c e sp a ce when th e vacuum 

ta n k l i d and to p h a lv e s o f ^ h e c y c l o t r o n magnet s e c t o r s a re 

r a is e d 1 .2 m, v a r ie s from ~ 1 rem h-1 a t th e c e n t e r o f th e 

c y c l o t r o n t o ~ 5 r e m h 1 a t a p o in t o p p o s it e th e ta n k p e r i 

p h e ry . T h is e s tim a te assum es one day d eca y f o l l o w i n g a lo n g 

o p e r a t in g p e r io d a t 10 kW c o n tin u o u s s p i l l . I t i s e x p e c te d 

t h a t a t l e a s t s e m i-re m o te s e r v i c i n g o p e r a t io n s w i l l be r e q u ir e d 

b e f o r e r e s id u a l f i e l d s rea ch t h e s e l e v e l s . 

1 . 2 . 2 P r o to n Beam L in e s and T a r g e ts : 

A l l s h ie l d i n g in b oth th e P r o to n and Meson .experim e n ta l 

a r e a s a s shown in F ig . 1 w i l l be i n th e form o f d em ou n table 

b l o c k s . T h is a p p roach was a d o p te d p r im a r ily b e ca u se o f u n c e r 

t a i n t i e s in e x p e r im e n ta l s p a ce re q u ire m e n ts o v e r th e l i f e t i m e 

o f th e f a c i l i t y . I t h as th e a d d i t i o n a l a d v a n ta g e , h ow ev er, o f 

s u b s t a n t i a l l y r e d u c in g th e p r e c i s i o n re q u ire m e n ts on o p e r a t in g 

d o s e - r a t e e s tim a t e s a t th e d e s ig n s t a g e . The s h ie l d i n g shown 

f o r BLI i s b a se d on an assum ed, u n ifo rm s p i l l r a t e o f 1 nA 

m- 1 . T h is i s n o t th e l e v e l o r d i s t r i b u t i o n e x p e c te d , bu t i s 

th e t h r e s h o ld l e v e l a t w h ich r e s id u a l a c t i v a t i o n r a d ia t io n 

f i e l d s b e g in t o c o n s t r a in a c c e s s t o th e beam l i n e a f t e r sh u tdown. 

T h is s h ie l d i n g a l s o p r o v id e s a d e q u a te p r o t e c t i o n a g a in s t 

s e r io u s o v e r e x p o s u r e o f p e r s o n n e l in th e m eson e x p e r im e n ta l 

a re a in th e im p rob a b le c ir c u m s ta n c e s th a t th e e n t i r e 100 )jA 

beam i s l o s t a t a p o in t in th e tu n n e l and g o e s u n d e t e c te d f o r 

an e x te n d e d p e r io d o f tim e .


BLIVa Dump 

PROTON 

AREA 

O C LD TR O N 

33m AND 

VAULT 

FIG. 1. Plan view of TRIUMF at primary beam line elevation. 

S u b s t a n t ia l p r o t o n beam s p i l l i s , o f c o u r s e , u n a v o id a b le 

a t th e m eson and n e u tro n p r o d u c t io n t a r g e t s in th e prim a ry 

beam l i n e s . T a rg e t TI and BLI w i l l be up t o 4 g cm~s t h i c k 

o f low Z m a t e r ia l such a s H20 , С o r Be; i t w i l l rem ove up t o 

7$ o f in c i d e n t p r o to n s by e l a s t i c and n o n - e l a s t i c n u c le a r c o l 

l i s i o n s . T2 t a r g e t s w i l l be lim it e d t o 20 g cm-2 o f low o r 

medium Z m a t e r ia l (B e , Cu, e t c . ) and rem ove up t o 25$ o f th e 

in c i d e n t p r o t o n s by n u c le a r r e a c t i o n s . The Coulomb s c a t t e r i n g 

w i l l a l s o be s i g n i f i c a n t from medium Z t a r g e t s a t T2, and in 

th e u lt im a t e f a c i l i t y th e r e s id u a l p r o t o n beam w i l l be c o l 

lim a te d im m e d ia te ly a f t e r T2 f o r tr a n s m is s io n t o th e p r o t o n 

beam dump - th erm a l n e u tr o n f a c i l i t y . Up t o 25$ o f p r o to n s 

w i l l be rem oved by th e c o l l i m a t o r . 

Of th e t a r g e t s in th e p r o t o n a re a o n ly th e l i q u i d deute 

riu m t a r g e t , maximum t h ic k n e s s 1 .7 g cm 2 , w i l l rem ove subs 

t a n t i a l p r o t o n beam f r a c t i o n s , up t o The o t h e r t a r 

g e t s in B L IV (a) and B LIV (b) w i l l rem ove l e s s th a n 0 .1 $ o f th e 

in c i d e n t p r o t o n s . 

The g e n e r a l a p p roa ch a d o p te d a t TRIUMF t o accom m odate 

r e s id u a l a c t i v i t y p rob lem s r e s u l t i n g from h ig h s p i l l t a r g e t s 

i s t o im bed th e t a r g e t a s s e m b lie s in la r g e m o n o lit h ic s h i e l d 

in g b l o c k , m aking a l l vacuum and c o o l i n g c o n n e c t io n s a t th e

I A E A - S M - n O /3 5 599 

o u t s id e o f th e b lo c k . The maximum b lo c k s i z e t h a t can be 

h a n d led by th e a v a i l a b l e l i f t i n g c r a n e , 100 t o n s , a f f o r d s a 

r e d u c t io n o f ~ 1 0 -3 in th e h ig h e n e rg y n u c le o n c u r r e n t , i n t e 

g r a te d o v e r th e o u t s id e s u r f a c e , a s com pared t o a s im p le t a r 

g e t c o n t a in e r . The r e s id u a l r a d i a t i o n f i e l d a t d eca y tim e s 

s h o r t com pared t o th e o p e r a t in g p e r io d a r e th u s re d u ce d from 

th e o r d e r 10 R h-1 t o th e o r d e r 10 mR h_ 1 f o r d is t a n c e s o f 1 0 ' 

from a t h i c k t a r g e t d i s s i p a t i n g 5 kW o f beam pow er. The 

a c t u a l t a r g e t a s s e m b lie s w i l l be re m ovable th rou g h a v e r t i c a l 

a c c e s s tu b e in th e s h i e l d »b lo ck t o a s h ie l d i n g f l a s k f o r t r a n s 

f e r t o h o t - c e l l f a c i l i t i e s . 

1 . 2 . 3 P r o to n Beam Dumps: 

The m ost in t e n s e s o u r c e s o f r a d i a t i o n b o th d u rin g o p e r a t io n 

and a f t e r shutdow n a r e , o f c o u r s e , th e beam dumps, and in p a r 

t i c u l a r th e dump a t th e end o f B LI, w h ich w i l l a l s o have th e 

f u n c t io n o f a th erm a l n e u tro n f a c i l i t y , a s d is c u s s e d a b o v e . 

F or 50 kW o f p r o t o n beam pow er on th e s to p p in g P b -B i t a r g e t , 

a p p r o x im a te ly 10$ em erges from th e t a r g e t a s h ig h -e n e r g y , 

" c a s c a d e " n e u tro n s w h ich , h a v in g th e lo n g e s t r e la x a t io n 

le n g t h s , c o n t r o l th e o p e r a t in g s h ie l d r e q u ir e m e n ts . T h is 5 

kW o f c a s c a d e n e u tr o n pow er must be re d u ce d by g eom etry and 

e n e rg y a b s o r p t io n t o a r a d ia t io n i n t e n s i t y o f th e o r d e r 10-11 

W cm- 2 f o r u n r e s t r i c t e d p e r s o n n e l a c c e s s . F or d is t a n c e s o f 

10 m b etw een th e s o u r c e and f i e l d p o in t s o f i n t e r e s t , th e g e o 

m etry f a c t o r i s 10-7 cm- 2 ; th u s th e a t t e n u a t io n f a c t o r f o r 

c a s c a d e n e u tr o n e n erg y must be o f th e o r d e r 10 7 in d i r e c t i o n s 

o f a v e ra g e i n t e n s i t y . 

The r e s id u a l a c t i v i t y a ccu m u la ted i n th e P b -B i t a r g e t a f 

t e r a lo n g o p e r a t in g p e r io d a t 50 kW beam pow er i s ~ 4 0 k C i, 

o f s p e c ie s w ith l i f e t i m e s lo n g e r th a n a few m in u te s. The 

r e s id u a l r a d ia t io n f i e l d a t a d is t a n c e o f 1 0' f rom _such a 

t a r g e t a few h ou rs a f t e r sh u t-d ow n w i l l be ~ 1 0 0 R h г . 

2 . OPERATING RADIATION INTENSITY ESTIMATES. 

2 .1 H a d ron ic C ascade C a lc u la t io n s 

2 . 1 . 1 C o l l i s i o n P r o b a b i l i t y C a lc u la t io n s : 

The e s s e n t i a l p rob lem in m aking r e l i a b l e r a d i a t i o n t r a n s 

p o r t e s tim a te s f o r h ig h e n e r g y , " c a s c a d e " h a d ron s i s an a d eq 

u a te tre a tm e n t o f th e e f f e c t s o f th e h ig h ly p eak ed a n g u la r 

d i s t r i b u t i o n s o f se co n d a ry n u c le o n s from n o n - e l a s t i c n u c le a r 

r e a c t i o n s . At th e lo w -to -m e d iu m e n e r g ie s e n co u n te r e d a t 

TRIUMF o n ly n e u tro n s n eed be c o n s id e r e d in d e t a i l . The o n ly 

s i g n i f i c a n t en erg y l o s s m echanism s f o r n e u tro n s in t h i s en erg y 

r e g io n a r e n o n - e l a s t i c n u c le a r r e a c t i o n s : e l a s t i c n u c le a r 

r e a c t i o n s o c c u r w ith a p p r o x im a te ly th e same p r o b a b i l i t y but 

th e f r a c t i o n a l momentum t r a n s f e r i s so sm a ll o v e r m ost o f th e 

en erg y ra n ge o f i n t e r e s t t h a t th e y ca n , e x c e p t f o r c o l l i s i o n s 

w ith th e l i g h t e s t e le m e n ts , be ig n o r e d . That th e n e u tro n s 

w i l l dom inate a s th e v e h i c l e s f o r t r a n s p o r t o f r a d i a t i o n e n e rgy 

th rou g h m a tte r i s o b v io u s from a co m p a rison o f th e c o l l i 

s io n mean f r e e p a th s o f v a r io u s form s o f r a d ia t io n . At e n e rg 

ie s a b o v e a b ou t 100 MeV th e mean f r e e p a th betw een n on -_ 

e l a s t i c n e u tr o n c o l l i s i o n s v a r ie s sm ooth ly from ~ 7 5 g cm-2 in


FIG . 2 . C a lc u la t e d c o l li s i o n d e n s ity in ir o n o f c a s c a d e n eu tron s w ith e n e r g y g re a te r th an 1 00 M e V . 

M o n t e - C a r lo resu lts a re fo r slab s n o r m a l t o , and 0 - 3 0 ° s p h e r ic a l c o n e s e c tio n s c e n tr e d o n , th e d ir e c tio n 

o f p roton s in c id e n t at th e c e n t r e o f a 2 m c u b e . C o llis io n p r o b a b ility resu lts a re fo r p ro to n s in c id e n t n o r m a lly 

o n a 1 0 0 0 g * c m " 2 p la n e slab. 

ca r b o n t o ~ 2 0 0 g cm-2 in le a d . By com p a rison , th e mean f r e e 

p a th f o r y - r a d i a t i o n i s in th e ra n ge 10 - 25 g cm- 2 . The 

c r o s s - s e c t i o n f o r lo w e r en ergy n e u tron s a r e g e n e r a lly h ig h e r , 

a lth o u g h t h e r e a r e a few i s o l a t e d e x c e p t io n s , on e o f w h ich , 

th e sh arp d ip i n e l a s t i c s c a t t e r i n g c r o s s s e c t i o n in ir o n in 

th e r e g io n o f 26 keV , ca n be o f p r a c t i c a l s i g n i f i c a n c e . 

To e s tim a te th e r e l a x a t i o n le n g t h f o r deep p e n e t r a t io n o f 

n e u tro n s in v a r io u s m a t e r ia ls f o r th e e n erg y below 500 MeV, 

a s e r i e s o f n u m e rica l c o l l i s i o n p r o b a b i l i t y c a l c u l a t i o n s w ere 

done [ 2 ] . The c a l c u l a t i o n s w ere m o d e lle d on an i n f i n i t e p la n e 

s la b w ith n u c le o n s in c i d e n t on on e f a c e in d i s c r e t e a n g u la r 

i n t e r v a l s and en erg y g r o u p s . The c o l l i s i o n p r o b a b i l i t i e s f o r 

s u c c e s s iv e g e n e r a t io n s o f n u c le o n s f o r each e n erg y g ro u p , 

a n g u la r segm en t, and s la b s u b - i n t e r v a l , w ere com puted by 

in t e g r a t in g o v e r a l l r e le v a n t n u c le o n r e a c t i o n s in th e p r e 

v io u s g e n e r a t io n . To o b t a in th e r e s u l t s f o r th e t o t a l i n t e r - 

n u c le a r c a s c a d e , a sum m ation i s c a r r i e d o u t f o r a l l s i g n i f i 

c a n t ly c o n t r ib u t i n g g e n e r a t io n s . The e s s e n t i a l n u c le a r

I A E A - S M -17 0 /3 5 601 

r e a c t i o n d a ta req u irem e n ts a r e th e t o t a l n o n - e l a s t i c c r o s s - 

s e c t i o n v a lu e s , w h ich w ere ta k e n from e x p e r im e n ta l m easurem 

ents [3 ] , and th e se con d a ry p a r t i c l e d i s t r i b u t i o n s , w h ich 

w ere d e r iv e d from th e p a r a m e tr ic f i t s [4 ] t o B e r t i n i 's i n t r a 

n u c le a r c a s c a d e r e s u l t s [ 5 ] . 

The b ottom c u r v e o f F ig . 2 shows th e r e s u l t s o f one such 

c a l c u l a t i o n f o r 500 MeV p r o t o n s in c i d e n t on a 1000 g cm- 2 s la b 

o f c o p p e r a t n ea r n orm al in c i d e n c e . The n o n - e l a s t i c c o l l i s i o n 

d e n s it y f o r c a s c a d e n e u tro n s w ith e n e r g ie s g r e a t e r th a n 100 

MeV, i s p l o t t e d a s a f u n c t io n o f depth in th e s la b . The e f 

f e c t i v e , b roa d beam, fo rw a rd r e l a x a t i o n le n g th a t medium t o 

la r g e d e p th s in th e co p p e r s la b i s 1 5 1 g cm 2 o r 1 . 0 6 tim e s th e 

n o n - e l a s t i c mean f r e e f o r h ig h en ergy n u c le o n s . F or o th e r 

m a t e r ia ls t h i s r a t i o was e s tim a te d t o v a ry from 1 .2 1 f o r 

c a r b o n t o 0 .9 6 f o r Pb. 

The m odel u sed f o r t h e s e c a l c u l a t i o n s makes th e e s tim a te s 

a u s e f u l g u id e f o r s i t u a t i o n s w here b roa d beams a r e in c i d e n t 

on p la n e o r n e a r ly p la n e s h ie l d i n g w a l ls . Such a m odel d oes 

n o t have e x t e n s iv e a p p l i c a t i o n and i t s u s e can be j u s t i f i e d 

o n ly in th e s i m p l i f i c a t i o n i t a f f o r d s in s o lv i n g th e t r a n s 

p o r t e q u a tio n . F or th e more u s u a l s h ie l d i n g s i t u a t i o n n ea r 

p o in t r a d i a t i o n s o u r c e s , th e r e l a x a t i o n le n g th s d ed u ced from 

t h i s m odel ca n o n ly be u sed w ith s u b s t a n t ia l c o n t in g e n c y f a c 

t o r s t o a llo w f o r c o u p lin g e f f e c t s b etw een th e g e o m e t r ic a l d i 

v e r g e n c e and s e co n d a ry p a r t i c l e d i s t r i b u t i o n s from th e n u c le a r 

r e a c t i o n s . More e la b o r a t e c a l c u l a t i o n s have b een u n d erta k en 

r e c e n t l y t o e s tim a te th e r e l a x a t i o n n ea r p o in t o r l i n e s o u r c e s 

w ith more r e a l i s t i c m o d e ls , a s d e s c r ib e d in th e n e x t s e c t i o n . 

2 . 1 . 2 Monte C a rlo C a lc u la t io n s 

In p r i n c i p l e th e Monte C a rlo m ethod i s p o t e n t i a l l y e x a c t 

in s o lv i n g v a r io u s p rob lem s in r a d i a t i o n t r a n s p o r t , and th e 

u s u a l a p p l i c a t i o n s a r e in s tu d y in g c o m p lic a t e d system s th a t 

ca n n ot be s o lv e d by l e s s g e n e r a l m eth od s. T h ere a r e s e v e r e 

l i m i t a t i o n s on i t s a p p l i c a t i o n t o p ro b le m s in v o lv i n g low 

p r o b a b i l i t y b e ca u s e o f s t a t i s t i c a l a c c u r a c y p ro b le m s . Deep 

s h ie l d p e n e t r a t i o n o f r a d ia t io n arou n d h ig h i n t e n s i t y f a c i l i 

t i e s i s a p a r t i c u l a r a c u te exam p le. W h ile s p e c i a l w e ig h tin g 

t e c h n iq u e s ca n be u sed th e y a r e t e d io u s and r e q u ir e c a r e f u l 

t e s t i n g f o r m ost a p p l i c a t i o n s . 

The Monte C a rlo c o d e NMT [ 6 ] w h ich was d e v e lo p e d a t Oak 

R id g e f o r n u cle o n -m e so n t r a n s p o r t s t u d ie s , h as b een u sed t o 

e s tim a te th e c a s c a d e p a r t i c l e f l u x e s arou n d a few h ig h in t e n 

s i t y p o in t s in TRIUMF. The co d e u s e s Monte C a rlo te c h n iq u e s 

f o r g e n e r a t in g th e i n t r a - a s w e l l a s th e in t e r - n u c l e a r c a s ca d e 

s im u la tio n , th u s r e d u c in g th e in p u t d a ta req u ire m e n ts t o a 

minumum. The NMT c o d e g e n e r a te s a s e r i e s o f p a r t i c l e h i s t o r i e s 

and s t o r e s t h e s e , u s u a lly on m a g n etic t a p e , f o r su b seq u en t anal 

y s i s by s e p a r a te c o d e s . S e v e r a l such a n a ly s is c o d e s have been 

w r i t t e n a t TRIUMF t o c o m p ile c o l l i s i o n d e n s i t i e s and f l u x e s 

(C0LLD ), p a r t i c l e c u r r e n t s (ANNE), r e c o i l e n erg y d i s t r i b u t i o n s 

(RECOIL), r e s id u a l p r o d u c t d i s t r i b u t i o n s (PROD) and d e t e c t o r 

s p e c t r a l r e s p o n s e (DECT). 

The two u p p er c u r v e s o f F ig . 2 show th e ca sca d e n e u tron 

c o l l i s i o n d e n s i t i e s in a 2 m cu b e o f i r o n when 500 MeV p r o 

to n s a r e in c id e n t a t th e c e n t e r . The to p c u rv e shows th e c o l -


l i s i o n d e n s it y s o r t e d in t o s la b s p e r p e n d ic u la r t o th e in c id e n t 

d i r e c t i o n , a s a f u n c t io n o f s la b d ep th from th e p o in t o f i n c i 

d e n ce . I t i s th u s e s s e n t i a l l y e q u iv a le n t t o th e c o l l i s i o n 

p r o b a b i l i t y c a l c u l a t i o n d e s c r ib e d a b o v e , and th e s lo p e o f th e 

c u r v e g iv e s a r e l a x a t i o n le n g th o f 154 g cm’ 2 in g ood a g r e e 

m ent. The o t h e r c u r v e i s th e c o l l i s i o n d e n s it y f o r ca s c a d e 

n e u tro n s a b ove ~ io o M e V in th e fo rw a rd 0 - 30° c o n e , from th e 

same NMT r e s u l t s . _The s lo p e o f th e cu rv e g iv e s a r e l a x a t i o n 

le n g th o f 16 8 g cm 2 f o r t h i s " p o i n t " s o u r c e g eom etry . 

3 . RESIDUAL ACTIVATION ESTIMATES 

3 -1 E x p e rim e n ta l Data 

The d ata req u irem e n ts f o r m aking r e l i a b l e r e s id u a l a c t i v a 

t i o n e s tim a te s f o r medium and h ig h en erg y p r o t o n a c c e l e r a t o r s 

a r e much g r e a t e r th a n f o r e it h e r f i s s i o n r e a c t o r s o r lo w e r 

en ergy a c c e l e r a t o r s . In p r i n c i p l e , th e re q u ire m e n ts f o r medium 

and h ig h e n erg y e l e c t r o n a c c e l e r a t o r s a r e a s b roa d as th o s e 

f o r p r o t o n m a ch in es, but f o r th e same pow er d i s s i p a t i o n n e u tro n 

p r o d u c t io n and r e s id u a l a c t i v a t i o n by e l e c t r o n s i s a f a c t o r 

10 2 t o 10-3 l e s s th a n f o r p r o t o n s . F or h ig h en erg y h adron 

r e a c t i o n s a w id e v a r i e t y o f p r o d u c t s , a s fou n d i n f i s s i o n r e a c 

t i o n s , i s com bined w ith th e u n iv e r s a l t a r g e t p o s s i b i l i t i e s , as 

in n e u tr o n c a p tu r e r e a c t i o n s . The s i t u a t i o n i s s u b s t a n t ia l ly 

r e l i e v e d , h ow ever, by th e much sm ooth er v a r i a t i o n in p r o d u c t io n 

c r o s s - s e c t i o n a s a fu n c t io n o f r e s id u a l s p e c i e s , t a r g e t n u c le u s 

and h a d ron e n e r g y , a s com pared t o th e n e u tr o n c a p tu r e c a s e . 

T h is h as le d t o th e v e r y v a lu a b le d evelop m en t o f e m p ir ic a l 

fo rm u la e Í7, 8 ] f o r r e p r o d u c in g e x p e r im e n ta lly known c r o s s - 

s e c t i o n s and e s t im a t in g unknown o n e s , as d is c u s s e d in th e f o l 

lo w in g s e c t i o n s . 

The e x p e r im e n ta l d ata a v a i l a b l e t o 1964 has b een c o m p ile d 

by B ru n in x in CERN r e p o r t s [9 1 T h is c o m p ila t io n , and an 

in t e r n a l C halk R iv e r c o m p ila t io n [1(3 made in c o n n e c t io n w ith 

th e ING p r o j e c t , have b een u sed e x t e n s iv e l y f o r e s t im a t in g 

r e s id u a l a c t i v i t y p r o d u c t io n a t TRIUMF, e s p e c i a l l y f o r low - 

to-m ediu m mass t a r g e t s w here th e e x p e r im e n ta l d ata a r e r e l a 

t i v e l y much more c o m p le te . F or n e u tro n s i n th e en erg y r e g io n 

b elow ~ 2 5 MeV th e sta n d a rd d ata c o m p ila t io n s o u r c e f o r e s t i 

m ates a t TRIUMF h a s , o f c o u r s e , b een BNL-325 [H ]. 

3 -2 E m p ir ic a l A c t i v i t y P r o d u c t io n E stim a te s 

E m p ir ic a l fo rm u la e d e f i n i n g th e d i s t r i b u t i o n o f r e s id u a l 

s p e c ie s f o l l o w i n g h ig h en erg y n u c le o n -n u c le a r c o l l i s i o n s 

have b een u sed e x t e n s iv e l y in m aking r e s id u a l a c t i v i t y e s t i 

m ates a t TRIUMF. The o r i g i n a l fo r m u la t io n , due t o Rudstam 

[ 7 ] , has a l s o b een u sed by B a r b ie r and C ooper [1 2 ] in t h e i r 

v e r y u s e f u l t a b u la t io n o f s o u r c e s tr e n g t h s and r a d i a t i o n f i e l d s 

f o r a w id e v a r i e t y o f t a r g e t e le m e n ts , in c id e n t n u c le o n e n e rg 

i e s and d eca y p e r io d s . To p r o v id e e s tim a te s o f r e s id u a l 

a c t i v i t y f o r in d iv i d u a l is o t o p e s and th e s p e c i f i c c o n d it i o n s 

a t TRIUMF, a c o d e , ACTA, and a d eca y d ata bank, s im il a r t o 

bu t more e x t e n s iv e th a n th a t u sed o r i g i n a l l y by B a r b ie r and 

C o o p e r, w ere c o m p ile d . The co d e u sed a s u b r o u t in e , RUDSTAM,

I A E A - S M -17 0 /3 5 603 

F IG .3 . C a lc u la t e d r e s id u a l r a d ia tio n f i e ld d e c a y cu r v e s fo r v a r io u s e le m e n ts u sin g th e e m p ir ic a l fo r m u la e 

o f S ilb e r b e ig and T s a o (S IL T ) and R udstam (a s e s tim a te d b y B a rb ier). 

f o r th e a c t i v i t y p r o d u c t io n e s tim a te s w h ich was b a sed on a 

3 / s pow er e x p o n e n t ia l r a t h e r th a n G a u ssia n shape f o r th e r e s i 

d u a l ch a rg e d i s t r i b u t i o n . 

A more r e c e n t e m p ir ic a l d e s c r i p t i o n o f r e s id u a l s p e c ie s 

d i s t r i b u t i o n s , s im ila r t o Rudstam , b u t e x te n d e d in ra n ge o f 

t a r g e t s and r e s id u a l s p e c ie s has b een p u t fo rw a rd by S il b e r b e r g 

and T sao [ 8 ] . By th e u s e o f m u lt ip le s e t s o f p a ra m eters f o r 

d i f f e r e n t ra n g e s o f n u c le o n e n e r g y , t a r g e t and r e s id u a l i s o 

t o p e , f a i r l y g ood agreem en t w ith th e a v a i l a b l e e x p e rim e n ta l 

d ata h as b een a c h ie v e d f o r a lm o st a l l t a r g e t n u c l e i and r e a c 

t i o n p r o d u c t s . In p a r t i c u l a r th e y in c lu d e " p e r i p h e r a l " r e a c 

t i o n s su ch a s ( p , 2p) and ( p , p n ) , h ig h e x c i t a t i o n f i s s i o n , 

w h ich i s im p o rta n t f o r h ig h mass t a r g e t s , and "b r e a k -u p " o f 

low mass t a r g e t s a s w e l l a s th e u s u a l s p a l l a t i o n and e v a p o ra 

t i o n p r o c e s s e s . 

A s u b r o u t in e , SILT, has b een w r i t t e n w h ich u s e s S ilb e r b e r g 

and T s a o 's form u la and p a ra m eters t o e s tim a te th e p r o d u c t io n 

c r o s s - s e c t i o n s in th e r e s id u a l a c t i v a t i o n c o d e . F ig . 3 shows 

th e r e s u l t s f o r 600 MeV p r o to n s on alum inum , ir o n and n ic k e l 

from t h i s co d e and s u b r o u t in e . The d o t t e d c u rv e a t F ig . 3 i s 

B a r b i e r 's r e s u l t f o r i r o n u s in g R u d sta m 's fo r m u la e ; B a r b i e r 's 

r e s u l t f o r n i c k e l i s n e a r ly i d e n t i c a l t o h is i r o n c u r v e . The 

new er r e s u l t s i n d i c a t e t h a t n i c k e l i s s u b s t a n t i a l l y w orse 

th a n i r o n f o r r e s id u a l a c t i v a t i o n , and t h a t a f t e r lo n g o p e r a 

t i n g and d eca y p e r io d s aluminum i s a l s o w orse th a n i r o n , in 

agreem en t w ith an o b s e r v a t io n by W a lla ce [13 ]. F ig . 4 shows 

th e SILT r e s u l t s f o r s t a i n l e s s s t e e l , c o n c r e t e and lim e s t o n e , 

a l l m a teria ls o f p r a c t i c a l im p o rta n ce a t TRIUMF.

604 TH O R SO N and WIESEHAHN 

C ooling P e rio d , days 

F IG .4 . C a lc u la t e d re s id u a l r a d ia tio n f i e ld d e c a y cu r v e s fo r v a r io u s c o n s tr u c tio n m a te r ia ls as e s tim a te d b y th e 

e m p ir ic a l fo r m u la e o f S ilb e r b e r g and T s a o (S IL T ) and R udstam (B a rb ie r). 

4 . SUMMARY OF FUTURE DATA REQUIREMENTS 

4 .1 R a d ia t io n T ra n s p o rt E stim a te s 

The m ost im p o rta n t u n c e r t a i n t i e s in r a d i a t i o n t r a n s p o r t 

arou n d m edium -en ergy p r o t o n a c c e l e r a t o r f a c i l i t i e s l i k e TRIUMF 

a r e in th e a n g u la r d e p e n d e n c ie s , r e l a t i v e t o th e. in c id e n t 

momentum, o f th e deep p e n e t r a t io n r e l a x a t i o n le n g th s f o r th e 

h ig h en erg y n e u t r o n s , th e dom inant en erg y c a r r y in g com pon en t. 

The g e n e r a l s o lu t i o n s t o t h e s e p ro b le m s r e q u ir e b oth r e l i a b l e 

n u c le a r r e a c t i o n d a ta and e la b o r a t e co m p u ta tio n a l te c h n iq u e s 

a n d /o r f a c i l i t i e s . Any s i g n i f i c a n t m ism a tch in g o f t h e s e two 

com pon en ts c a n n o t, o f c o u r s e , be e x p e c te d t o y i e l d optimum 

r e s u l t s . The Monte C a r lo r e s u l t s f o r b oth i n t r a - and i n t e r - 

n u c le a r c a s c a d e s , a s em p loyed , f o r exam p le, in th e NMT c o d e , 

p r o v id e th e m ost u s e f u l and r e l i a b l e e s tim a te s f o r s i t u a t i o n s 

in v o lv i n g a t t e n u a t io n f a c t o r s up t o 10 3 . 

When TRIUMF and o t h e r f a c i l i t i e s in th e same in t e n s i t y 

ran ge becom e o p e r a t i o n a l th e m ost r e l i a b l e m ethods o f m aking 

deep p e n e t r a t io n r a d i a t i o n t r a n s p o r t e s tim a te s w i l l l i k e l y be 

by i n t e r p o l a t i o n and e x t r a p o la t io n o f th e d i r e c t l y m easured 

i n t e n s i t i e s . In th e s h o r t term them , th e i n c e n t i v e f o r th e 

a c q u i s i t i o n o f th e e x t e n s iv e seco n d a ry p a r t i c l e d i s t r i b u t i o n 

d a ta s p e c i f i c a l l y f o r deep p e n e t r a t io n s h ie l d i n g c a l c u l a t i o n s 

i s u n l i k e l y t o in c r e a s e . In th e lo n g e r term th e n u c le a r d ata 

re q u ire m e n ts f o r s h ie l d i n g p r o t e c t i o n w i l l be d ep en d en t on 

th e in t r o d u c t i o n o f m ach in es o f s i g n i f i c a n t l y h ig h e r i n t e n s i t y 

th a n t h o s e now com ing in t o s e r v i c e . A s u b s t a n t ia l bod y o f 

n u c le a r r e a c t i o n d a ta w i l l be g e n e r a te d by f a c i l i t i e s l i k e 

TRIUMF from fu n d am en tal e x p e rim e n ta l p rogra m s. At th e o u t s e t , 

a t l e a s t , th e e f f o r t i s l i k e l y t o be c o n c e n t r a t e d on s im p le

I A E A - S M - n O /3 5 605 

s y s te m s , i . e . , l i g h t n u c l e i , and w i l l p r o b a b ly n o t w a r r a n t, o r 

r e q u ir e , much e x p l i c i t e f f o r t f o r co m p re h en siv e c o m p ila t io n , 

a t l e a s t f o r s e co n d a ry p a r t i c l e d i s t r i b u t i o n d a ta . 

An im p o rta n t o p e r a t i o n a l p rob lem fou n d arou n d medium and 

h ig h en erg y a c c e l e r a t o r s i s th e v a r i a t i o n in r a d ia t io n le a k a g e 

a d m ix tu re and s p e c t r a . T h is p rob lem i s im p o rta n t b e ca u se o f 

in a d e q u a c ie s in th e a v a i l a b l e p e r s o n n e l d o s im e try te c h n iq u e s 

w h ich a r e u s u a lly a l l e v i a t e d by m aking co m p re h e n siv e d ose 

a n d /o r d o s e - e q u iv a le n t m easurem ents a t " r e p r e s e n t a t i v e p o in t s " 

in th e f a c i l i t y and r e l a t i n g t h e s e t o p a r t i c u l a r com pon en ts 

t h a t a r e m easured on p e r s o n n e l d o s im e te r s . W h ile th e le a k a g e 

s p e c t r a and a d m ix tu re ca n , in p r i n c i p l e , be d eterm in ed e n t i r e l y 

by e x p e rim e n t, r e c o u r s e i s u s u a lly i n d i c a t e d , a t l e a s t a s a 

su p p lem en t, t o r a d i a t i o n t r a n s p o r t c a l c u l a t i o n s . I n c r e a s in g 

a t t e n t i o n w i l l be r e q u ir e d f o r such e s tim a te s a t TRIUMF. 

The d ata req u irem e n ts f o r t h e s e e s t im a t e s , w h ile th e same in 

p r i n c i p l e a s t h o s e f o r th e deep p e n e t r a t io n c a l c u l a t i o n s , a re 

c o n c e n t r a t e d more a t th e lo w e r , f i s s i o n r e a c t o r e n erg y ra n g e , 

w here th e d a ta a r e f a i r l y c o m p le te , th a n a t th e h ig h e r e n e r g ie s 

w here r e c o u r s e must be made t o th e i n t r a - n u c l e a r c a s c a d e r e 

s u l t s . 

4 .2 R e s id u a l A c t i v i t y E s tim a te s 

As d is c u s s e d a b ove in s e c t i o n 3 - 3 j th e r e s id u a l a c t i v i t y 

p r o d u c t io n by h ig h en erg y r e a c t i o n s h as been e s tim a te d a t 

TRIUMF from e x p e r im e n ta l and e m p ir ic a l d eterm in ed c r o s s - s e c t i o n 

v a lu e s . No s t r o n g i n c e n t i v e i s f o r s e e n a t t h i s tim e t o embark 

on c r o s s - s e c t i o n m easurem ents e x p l i c i t l y f o r r e s id u a l a c t i v a 

t i o n e s t im a t e s . F a ir l y e x t e n s iv e , fu n d am en ta l p h y s ic s p r o 

grams a t TRIUMF and o th e r h ig h i n t e n s i t y f a c i l i t i e s a r e exp 

e c t e d t o y i e l d s u b s t a n t i a l l y more d a ta in t h i s a re a o v e r th e 

n e x t few y e a r s . T hese d a ta s h o u ld be a sse m b le d a s soon as 

p o s s i b l e a f t e r p u b l i c a t i o n in t o f r e e l y a v a i l a b l e c o m p ila t io n s , 

p r e f e r a b l e in c o n ju n c t io n w ith c o n t in u in g r e fin e m e n t s o f th e 

e m p ir ic a l p r o d u c t io n c r o s s - s e c t i o n fo r m u la t io n s . 


[ 1 ] TRIUMF P r o p o s a l and C ost E s tim a te , E. W. V ogt and J. J. 

B u r g e r jo n , E d i t o r s , N ov. 1966. 

TRIUMF A nnual R e p o r t s , E d ite d by J. J. B u r g e r jo n ( 1 9 6 8 ) , 

N. B r e a r le y ( 1 9 6 9 j 1970, 1 9 7 1 ), E. W. V ogt and A. S tr a th d e e 

( 1 9 7 2 ) . 

[ 2 ] I . M. T h o rs o n , S h ie ld in g and A c t i v a t i o n in a 500 MeV 

C y c lo t r o n F a c i l i t y , TRIUMF R e p o rt T R I-6 8 -4 ( 1 9 6 8 ) . 

[ 3 ] R. G. P. V oss and R. W ils o n , P r o c . R oy. S o c. (L on don) A2 36 

41 ( 1 9 5 6 ) . 

M. H. M acG regor, e t a l . , P hys. R ev. I l l 1 1 5 5 (1 9 5 8 ). 

T. C o o r, e t a l . , P hys. R ev. 98 1 3 6 9 П -9 5 5 )■ 

F. Chen, e t a l . , P hys. R ev. 99 857 (1 9 5 5 ) . 

W. P. B a l l , N u cle a r S c a t t e r in g o f 300 MeV N e u tro n s, R ep ort 

UCRL-I9 38 ( 1 9 5 2 ) .


[ 4 ] R. G. A i s m i l l e r , M. L e im d o rfe r and J. B a r is h , A n a l y t ic a l 

R e p r e s e n t a t io n o f N o n - e l a s t i c C r o s s -S e c t io n s and P a r t i c l e 

E m issio n S p e c tr a from N u c le o n -N u c leus C o l l i s i o n s in th e 

Energy Range 25 t o 400 MeV, R ep ort 0RNL-4046 ( A p r i l I 9 6 7 ) . 

[ 5 ] H. W. B e r t i n i , P hys. R ev. 131 1801 ( 1 9 6 3 ) and P hys. R e v ., 

AB2 ( 1 9 6 5 ) . 

[ 6 ] W. A. Colem an and T. W. A rm stron g, The N u cleon -M eson T ra n sp 

o r t Code NMTC, R e p o rt 0RNL-4606 (1 9 7 0 ). 

[ 7 ] G. Rudstam.j P h i l. Mag. k6_ 344 (1 9 5 5 ) and 

G. Rudstam , Z. N a tu r fo r s c h 21a 7 (1 9 6 6 ). 

[ 8 ] R. S i l b e r b e rg and C. H. T sa o , P a r t i a l C r o s s -S e c t io n s in 

High E nergy N u clea r R e a c t io n s f o r T a r g e ts w ith Z s 2 8 , 

( P r e - p r i n t , t o be p u b lis h e d , 1972) and P a r t ia l C r o s s - 

S e c t io n s in H igh E nergy N u cle a r R e a c tio n s f o r T a r g e ts 

H e a v ie r th a n N ic k e l, ( P r e - p r i n t , t o be p u b lis h e d , 1 9 7 2 ). 

[ 9 ] E. B ru n in x , High E nergy N u cle a r R e a c t io n C r o s s - S e c t io n s , 

R e p o rts CERNÖ1-1 ( 1 9 6 1 ) , CERN 6 2 -9 ( 1 9 6 2 ) and CERN 6 4 -1 7 

(1 9 6 4 ). 

[1 0 ] T. A. E astw ood and D. C. S a n tr y , P r iv a t e C om m unication 

( 1 9 6 3 ) . 

[1 1 ] N eu tron C r o s s - S e c t io n s , 2nd E d i t io n , BNL-325 (1 9 5 6 ) and 

S u pplem en ts. 

[1 2 ] M. B a r b ie r and A. C o o p e r, E stim a te s o f In d u ced R a d i o a c t iv i t y 

in A c c e l e r a t o r s , R e p o rt CERN-65-34 ( 1 9 6 5 )* 

[ 1 3 ] R. W a lla c e , N u cl. I n s t , and M eth. 1 8 , 19 405 ( 1 9 6 2 ) .

TRANSPORT OF NEUTRONS 

INDUCED BY 8 0 0 -MeV PROTONS* 

R.G. FLUHARTY, P.A . SEEGER, D.R. HARRIS, 

J.J. KOELLING, O.L. DEUTSCH? 

University o f California, 

Los Alamos Scientific Laboratory, 

Los Alamos, N. M e x ., 

United States o f America 

Abstract 

T R A N SPO R T OF NEUTRONS IN D U C E D BY 8 0 0 - M e V P R O TO N S. 

I A E A - S M -17 0 /4 5 

N eu tron transport c a lc u la t io n s are p re se n te d fo r a p u lse d n eu tron and p ro to n re s e a r ch (W e a p o n s N eu tron 

R e s e a rch , W N R ) f a c i lit y . Pulses o f 8 0 0 -M e V p roton s are o b ta in e d fr o m th e Los A la m o s M e s o n P h ysics F a c ilit y 

(L A M P F ) o f 5 to 10 ps d u ra tion or 1 t o 2°}o o f th e f u l l LAM PF b e a m , y ie ld in g a m a x im u m a v e r a g e n eu tron 

s o u r c e stren gth o f 1 - 2 x 1 0 15 n e u tro n s /s . T h e c a lc u la t e d s h ie ld re q u ire d to r e d u c e th is s o u r c e t o ~ 1 m r a d /h 

co n s is ts o f 2 .6 m o f s te e l p lu s 0 .4 m o f m a g n e tite c o n c r e t e and b o ro n glass fr it. T h e v e r t ic a l p r o to n b e a m 

and ta rg e t re q u ire s p e c ia l c o n s id e r a tio n o f th e u n d ergrou n d s h ie ld in g t o r e d u c e flo o r d o s a g e . 

N eu tron s o u r c e , e n e r g y d e p o s itio n , and a c t iv a t io n c a lc u la t io n s are based o n tw o c o n tin u o u s -e n e r g y 

M o n t e - C a r lo c o d e s , N M T C and M C N , a d a p te d t o C D C 6 6 0 0 and C D C 7 6 0 0 co m p u te r s . T h e N M T C c o d e c o n 

ta in s t h e d e t a ile d M o n t e - C a r lo in tr a n u c ie a r -c a s c a d e c a lc u la t io n s o f B ertin i. T o m a in ta in a d e q u a te s ta tis tic a l 

a c c u r a c y fo r d e e p p e n e tr a tio n , a series o f p r o b le m s is run in w h ic h le a k a g e n eu tron s fr o m th e p r e v io u s 

p r o b le m are w e ig h te d and sp lit as a s o u r cé fo r th e n ew p r o b le m c o n ta in in g a d d ed m a te r ia l. T h e lo w - e n e r g y 

M C N c a lc u la t io n s , w h ic h use standard c r o s s -s e c t io n sets fo r e n e r g ie s b e lo w 20 M e V , are in c lu d e d in th e last 

1 .2 m o f th ick n e s s. 

T o p r o v id e m o r e e f f ic i e n t c a lc u la t io n a l m e th o d s , a p a r a lle l e ffo r t has b e e n u n d erta k en t o g e n e r a te 

m u ltig r o u p c r o s s - s e c t io n sets u sin g th e in tr a n u c ie a r -c a s c a d e m o d e l. A n a d v a n ta g e o f th is m e th o d is th at 

e x p e r im e n t a l v a lu e s c a n a lso b e in c o r p o r a t e d . A lib r a r y has b e e n so co n s tru c te d fo r ir o n and n in e o th e r 

e le m e n t s , in a fo r m a t fo r c o m b in a t io n w ith ENDF lib ra rie s , fo r te n e n e r g y g rou p s fr o m 20 t o 8 00 M e V . 

C o m p a r is o n tests h a v e b e e n m a d e o n a s p h e r ic a l p r o b le m w ith a 1 - m v o id fo llo w e d b y 2 m o f ir o n . T h e 

m u ltig r o u p M o n t e - C a r lo p r o g r a m A N D Y -M G C R , w ith s o u r ce w e ig h tin g and s u r fa ce s p littin g , agrees w ith th e 

SN transp ort c o d e D T F -I V ; h o w e v e r , th e D T F resu lts are o n ly Q0°joof th e resu lts o f th e N M T C m e th o d 

d e s c r ib e d a b o v e . S in c e th e d iff e r e n c e is a r e la x a t io n - le n g t h e f f e c t , it p r o b a b ly r e f le c ts th e in a d e q u a c y 

o f th e P3 c r o s s - s e c t io n e x p a n sio n te s te d t o d a t e . In a d d itio n t o te stin g w ith h ig h e r -o r d e r c r o s s -s e c t io n sets, 

p la n s in c lu d e e x p e r im e n t a l tests o f t h ic k ir o n sh ie ld s. 


The Weapons Neutron Research (WNR) facility is being designed for neutron 

spectroscopy by means of neutron time of flight. The pulsed neutron source 

is to be produced by impinging pulses of 800-MeV protons from the Los Alamos 

Meson Physics Facility (LAMPF) on various thick targets. Pulses are to be obtained 

by separately switching the proton injector beam of LAMPF to produce 

pulses from 5-nsec to 5- or 10-ysec long while a pulsed switching magnet is 

activated. After the short pulse operation, the switching magnet is to be 

turned off and the normal 490-ysec pulse from the source is provided for the 

many other uses for the accelerator.Ш Thus, 1 to 2% of the LAMPF output (8 

to 16 kW of target power) will be provided. A summary of the pulsed characteristics 

of LAMPF and WNR is given in Table I. 

o f A m e r ic a . 

* W ork p e r fo r m e d under th e a u s p ice s o f th e U n ite d States A t o m ic E n ergy C o m m is s io n . 

t P resent address: M a ssach u setts In stitu te o f T e c h n o lo g y , C a m b r id g e , M ass. 0 2 1 3 9 , U n ite d States 

607

)U Ö F LU H A R TY e t a l. 

TABLE I. LAM PF AND WNR CHARACTERISTICS 

LAMPF WNR 

Voltage (MeV) 800 800 

Average Current (mA) 1 0.01-0.02 

Macropulse Width (usee) 500 0.008 to 5-10 

Pulses per sec 120 120-240 

Peak Macropulse Current (mA) 17 17 

Micropulse Width (nsec) 0.08 0.3 

W E A PO N S NEUTRON RESEARCH F A C ILIT Y 

FIG . 1. S c h e m a t ic sh ow in g h ow a short in je c t o r p u lse o f p roton s is d e f le c t e d south b y a p u lse d sw itc h in g 

m a g n e t in to th e W N R transport s y ste m , th rou g h 9 0 °, and o n to th e ta rg ets t o p r o d u c e n eu tron s. N eu tron b e a m s 

a re re p re se n te d u sin g t im e o f flig h t fo r th e e n e r g y -d e p e n d e n t resp on se o f a d e t e c t o r . T h e m a jo r p o r tio n o f 

th e LAM PF b e a m is u t iliz e d e ls e w h e r e b y tu rn in g th e sw itc h in g m a g n e t o f f . 

The LAMPF machine is a linear accelerator consisting of three types of 

accelerators. The 750-keV beam from a Cockcroft-Walton injector is accelerated 

to ~100 MeV in a 200-MHz Alvarez section, and then to 800 MeV in the 805 

MHz side-coupled cavity system. At the end Of the accelerator, the pulsed proton 

beam is transported to the WNR experimental area. First, the beam is deflected 

90°, translated downward, and transported underground 150 to 200 m to 

the WNR experimental areas. This transport process is shown schematically in 

Fig. 1. 

An isometric view of the WNR experimental area is given in Fig. 2, showing 

two principal target areas. In the first target, the beam is deflected 

90° to point into the ground. Before it enters the ground, it impinges upon

MAIN BEAM UNE 

IAEA-SM-17 0 /4 5 609 

F IG . 2 . A v is u a l re p re se n ta tio n o f th e W N R ta rg e t a re a . T h e h ig h - p o w e r ta rg et is lo c a t e d in a v e r t ic a l 

b e a m , a llo w in g a b s o rp tio n o f th e forw a rd h ig h - e n e r g y n eu tron s in th e e a rth . T h is h ig h - p o w e r ta rg e t has 11 

n e u tro n b e a m ports and re q u ire s a m a s s iv e s h ie ld . T h e lo w - p o w e r ta rg e t a re a p r o v id e s fo r lo w n eu tron return 

fr o m th e w a lls . 

2*zo 

a JOU target of 4-cm diam. by 20-cm long to produce ~20 neutrons per proton. 

This target will absorb 8 to 16 kW from protons and 3 to 6 kW from fission 

(the rest of the proton energy is removed by fast neutrons). It is surrounded by 

a cylindrical void ~2-m diam. and 2-m high, and then by an iron-concrete shield 

~3.7-m thick. There are to be 11 horizontal neutron beams penetrating to the 

experimental areas outside. One 200 m evacuated flight path (beam path) will 

have an illumination of 1.82-m diam. at the end. Other flight paths (5, 35, 

50, 100 m) will have smaller apertures. 

The second target area is shown in the foreground of Fig. 2; it is a 

large room where the central target position is at least 6 m from any wall, 

floor, or ceiling to reduce the back-scattered neutrons. This target area 

can be utilized for a horizontal target with il% of the intensity of the first 

target or for a neutron scattering chamber utilizing a neutron beam from the 

first target. This second target area has great versatility for spectrum 

measurements, spectrum tailoring, and scattering measurements. 

2. NEUTRON AND PROTON TRANSPORT 

2.1 NMTC-MCN 

A continuous energy Monte Carlo calculational system, NMTC-MCN, ^ 

has been developed for use at the Los Alamos Scientific Laboratory for neutron, 

proton, and meson transport from 0 to 3.5 GeV, by P. A. Seeger. The system 

can be used on the CDC-6600 or CDC-7600 computers, and has options for MCN

610 F LU H A R TY et a l. 

geometry and time-dependence. Outputs are on tapes which contain complete in 

dividual p a rticle records as requested fo r reaction events or surface crossings. 

Analysis programs fo r sorting and counting o f the taped events provide 

tabular and graphic displays o f the integrated information. 

One code used, NMTC, is that developed at Oak Ridge National Laboratory 

fo r medium energy p a rticle transport between about 15 MeV to 3.5 GeV. The 

nuclear portion by B ertini M assumes known input tota l reaction cross sections 

(e la s tic scattering is neglected) and calculates the reaction products by Monte 

Carlo assuming a cascade inside the nucleus pictured as a Fermi gas. This 

intranuclear cascade is terminated when the cascading p a rticles have either 

escaped from the nucleus or have not enough energy to escape. Account is then 

taken o f the residual nuclear energy by p a rticle evaporation (mostly neutron). 

Escaping p a rticles that have energies above an arbitrary cu to ff are transported 

by Monte Carlo u n til another nuclear reaction occurs, a problem boundary is 

crossed, or (in the case o f charged p a rticle s) they reach the cu to ff energy. 

As NMTC was adapted to the CDC-6600 by H. I. Isra el, l^] very d eta iled , in dividual 

p article-even ts (outside the nucleus) are recorded on a magnetic tape f i l e . 

This very general tape also may include ion ization losses, pion and muon production, 

etc. 

Neutron transport for energies below the NMTC cu to ff energy is continued 

with the continuous Los Alamos Monte Carlo code MCN, using the tape output o f 

NMTC as the source. A cross-section library is maintained fo r th is code, and 

the geometry routine is very general. The MCN geometry is now available as an 

option to the NMTC portion o f the code, permitting a sin gle geometrical descrip 

tion o f the problem. A more concise optional tape format has been developed, 

su itable fo r both NMTC and MCN. Only the energy, p o sitio n , v e lo c ity , 

time, s ta t is t ic a l weight, and p a rticle type fo r each p a rticle are buffered and 

recorded, avoiding m ultiple tape re e ls. The high-energy output p a rticles 

(p, n, if* ', and it- ) from NMTC and the low-energy neutrons from' MCN may be 

w ritten on a sin gle tape. 

2.2 Multigroup Cross Sections 

In a p ara llel e ff o r t , the B ertini intranuclear cascade has been used 

to generate 41-energy group-average cross-section sets fo r ten elements 

(H, C, 0, S i, A l, Fe, Ca, Mo, W, and Pb) in the ENDF/B format. This multigroup 

set provides access to faster running multigroup Monte Carlo and d iscrete 

ordinate transport programs. Currently, these cross sections are being used 

with the programs ANDY-MGCRÍ^] and DTF-IV.1^1 The average cross-section approach 

allows ready adjustment to experimental cross-section evaluations. 

Currently, the cross sections are available with Pq, Pj , P2, and Pj Legendre 

c o e ffic ie n ts fo r 20 to 800 MeV. 

3. SOURCES 

Neutron source optim ization and source spectral adjustment are important 

objectives fo r the f a c i lit y , so source studies are continuing. The NMTC-MCN 

system has been used to generate both primary and secondary sources, and output 

tapes can be used as sources fo r subsequent problems fo r both the NMTC-MCN 

and the multigroup systems. Examples where sources are used further involve 

shielding and moderator optim ization fo r tim e -o f-flig h t sources. In a previous 

stu d y ,И emphasis was placed on the generation o f variable spectra 

sources and high neutron y ie ld per proton.

I A E A - S M -17 0 /4 5 611 

F I G .3 . T h e a n gu la r d istr ib u tio n at 1 m o f n eu tron s e m it t e d fr o m a 4 - c m - d i a m . b y 1 5 - c m - l o n g ta rg e t o f 

2S8U is show n fo r 4 e n e r g y g rou p s. N o te th e stron g forw a rd d istr ib u tio n fo r n eu tron s h a v in g e n e r g ie s a b o v e 

1 00 M e V . 

F IG . 4 . T h e n eu tron s p e ctra o f 9 0 “ (a v e r a g e d o v e r ± 1 0 e) fo r ta rg ets o f 23BU w ith d im e n s io n s o f 3 - c m d ia m . 

b y 1 5 - c m lo n g and 6 - c m d ia m . b y 1 5 - c m lo n g are sh ow n . T h e a d d e d th ic k n e s s c o n v e r ts th e n eu tron s t o a 

90e 

s o fte r s p e c tr u m w ith m o r e n eu tron s. A b o v e 2 0 M e V , th e tw o cu r v e s a re n o t s t a t is tic a lly d iffe r e n t and h a v e 

b e e n a v e r a g e d to g e th e r .

612 FLU H A R TY e t a l. 

A characteristic of the spallation source is the markedly forward component 

of the high-energy neutrons (>100 MeV). The anisotropy of this component 

is illustrated in Fig. 3, which shows the neutron current at 1 m produced by 

800-MeV protons impinging along the axis of a 4-cm-diam. by 15-cm-long 238jj 

target. Below 20 MeV, the neutrons are emitted in a nearly isotropic pattern. 

Because the forward high-energy neutrons are poorly attenuated, the applied 

beams requiring lower neutron energies are taken off at angles of 90° or 

greater to the proton beam direction. For the first (high-power) target, the 

multiple beam ports are at 90° to the vertical proton beam. 

Below 20 MeV, the calculated spectra can be characterized as evaporation 

spectra. Assuming a spectral shape used for fission spectra, the NMTC evaporation 

spectra from 2^°u contain ~75% neutrons at 3-MeV temperature and 25% 

at 1-MeV temperature. Plots of the spectra at 90° from different 23Û targets 

are shown in Fig. 4. The targets are both 15-cm long and have diameters 

of 3 cm and 6 cm. It is seen that the additional radial thickness serves as 

a spectral converter wherein neutron inelastic scattering in the 238jj produces 

a new spectrum characteristic of a lower neutron temperature. Some portion of 

this conversion is also present in the smaller diameter target. 

To a first rough approximation, the thick sources studied have one high- 

energy neutron per proton (between 20 and 800 MeV), and for neutron energies 

below 20 MeV, the number of neutrons is one-tenth the atomic number (A/10). 

Increased yields result from fission and (n,2n)(n,xn) processes as the neutrons 

are transported out of the target. I J Experimental measurements, by Mady et 

al. [9] with 750-MeV protons yield ~30% more fast neutrons at 30 and 150° than 

predicted by NMTC. Because of their importance to accelerator shielding, these 

results need verification. Here the predictions of the code are utilized, but 

safety factors are included to allow for the experimental uncertainty. 

4. SHIELDING 

Monte Carlo calculations for deep penetration or large attenuations of 

radiation require weighting techniques—even with the fastest computers. 

Here, the principal method used is that of surface splitting, although exponential 

weighting should be better in theory. Secondarily, source weighting, 

Russian roulette, and variable energy cutoff as a function of position are resorted 

to. The success of this approach is based on the physical property 

that the penetration is propagated by the high-energy neutrons (above 100 MeV) 

where the lowest cross sections are encountered. The exception to this generalization 

involves the "windows"--particularly in Fe, where essentially zero 

cross sections are observed because of interference between s-wave resonances 

and potential scattering in spin-zero targets. To avoid this exception, a 

cardinal rule of neutron shielding is followed; namely, always construct 

shields of mixtures of elements. Thus, sufficient cross section is provided 

in the windows to avoid a "trapped" component, allowing neutrons to "stream" 

through the shield. 

A major design study has been made on the shield for Target 1, which 

produces ~10l5 neutrons/sec. A vertical cut of this shield is shown in Fig. 

5; the target is located in a 6-ft by 6-ft cylindrical void surrounded by 

~9 ft of steel plus 3 ft of heavy concrete. The external 1 ft of concrete 

will also contain boron glass to limit neutron-capture gamma rays to the relatively 

soft 476-keV boron component. 

Calculations for the design of the Target 1 shield to reduce neutron 

dosages below 1 mrem/h were performed using the NMTC-MCN system. The procedure 

followed for these calculations was as follows:

(a) A cy lin d rica l geometry was used. 

I A E A - S M -П О /4 5 613 

(b) A series o f problems were calculated in which successive 

layers were added to the previous calcu lation s using NMTC 

only (Ejj>20 MeV). 

(c) The leakage neutrons from the previous problem were used 

as a source fo r the next problem with added thickness. 

(d) The p a rticle s from each source tape, representing the output 

o f the previous problem, were run three times to provide 

sp littin g given by the expected attenuation fa ctor. 

(e) Low-energy output tapes from NMTC for the last four th icknesses 

o f shield were used as a source for MCN runs to c a lculate 

the leakage o f low-energy neutrons. 

(f) Neutron dosages are based on integrated or to ta l neutrons 

or currents leaking from surfaces. This is considered to 

be a conservative estimate, compared with the more r e a lis 

t i c fluxes (integral o f p a rticle s/co s in e o f angle with 

respect to the surface normal). 

Plots o f the dosage as a function o f v e rtica l distance are presented in 

Fig. 6, fo r various ra d ii corresponding to the t i c marks on the neutron beam 

axis in Fig. 5. The sig n ifica n t feature to be noted in Fig. 6 is the large 

leakage near and under the flo o r or in the forward d irection to the beam. 

Special care and tedious study were required to reduce the dosage at flo o r 

F IG . 5. A v e r t ic a l c r o s s - s e c t io n o f th e h ig h -p o w e r ta rg e t s h ie ld in g , as stu d ied fo r s h ie ld d e s ig n . It has 

b e e n d e te r m in e d th a t a su p erior s h ie ld resu lts fr o m s o lid ir o n o r le a d sh ie ld in g b e lo w th e c e n tr e c a v it y 

in ste a d o f th e h o l e in to th e grou n d . T i c m arks o n th e n eu tron b e a m a x is rep resen t r a d ia l p o s itio n s fo r w h ic h 

d o s a g e is p lo t t e d in F ig . 6 .

6 1 4 F LU H A R TY e t a l. 

F IG . 6 . R a d ia tio n d o s a g e as a fu n c tio n o f v e r t ic a l d is ta n c e fr o m th e n eu tron b e a m p o r t le v e l , at d iffe r e n t 

r a d ii fr o m th e c e n t r e o f th e p r o to n b e a m . T h e p o s it iv e v e r t ic a l d ir e c t io n is in th e p r o to n b e a m d ir e c t io n 

(d o w n w a rd ). N o t e th e h ig h d o s a g e le v e ls in th e grou n d w h ic h c a u s e h ig h d o s a g e s at th e flo o r l e v e l o f th e 

e x p e r im e n t a l r o o m . T h is fig u r e is s c a le d t o F ig . 5.

I A E A - S M -17 0 /4 5 

F IG . 7 . T h e le a k a g e n e u t r o n s /c m 2 (m e a su r e d fr o m th e p r o to n d ir e c t io n ) o n th e o u ts id e o f a 2 - m - t h i c k 

s p h e r ic a l ir o n s h e ll, as a fu n c tio n o f a n gu la r p o s itio n . T h e in n er radiu s o f th e s h e ll is 1 m ; th e so u r ce 

neu tron s e n te r in g t h e s h e ll a re show n in F ig . 3 . N o te th a t th e d o s a g e p a ttern fo r a ll n eu tron e n e r g ie s is 

e q u iv a le n t t o t h e a n gu la r d istrib u tio n o f th e n eu tron s p e ctru m c o m p o n e n t a b o v e 1 00 M e V . 

DISTANCE (cm) 

F IG . 8 . A c o m p a r is o n o f t h e a v e r a g e d o s a g e o v e r th e s u r fa ce o f th e s p h e r ic a l ir o n s h e l l p r o b le m o f 

F i g .7 , fo r th r e e d iffe r e n t c a lc u la t io n a l m e th o d s . N M T C -M C N is a co n tin u o u s e n e r g y M o n t e - C a r lo sy ste m , 

A N D Y -M G C R is a m u ltig ro u p M o n t e - C a r lp s y s te m , and D T F -I V is a d is c r e te o rd in a te m e th o d . T h e a g r e e 

m e n t is e x c e l le n t , but F i g . 7 in d ic a t e s th at p o s it io n in fo r m a tio n is a lso n e e d e d to c o m p a r e th e m e th o d s . 

615

616 FLU H A R TY et a l. 

levels where neutrons leak through the ground and up through the flo o r ; underground 

shielding was found necessary to reduce these levels. More recent 

studies reveal that a solid shield at the bottom o f the void is preferable to 

the voided hole in to the ground shown in Fig. 5. 

To emphasis the importance o f the angular d istribu tion o f the source, 

resu lts from a calcu lation with a spherical iron sh ell are shown in Fig. 7. 

The same neutron source as shown in Fig. 3 was used, surrounded by a 1-m-radius 

void and then 2-m o f iron. The resu lts presented are the surface neutron leakage 

as a function o f angular p ositio n , with respect to the proton beam d irection 

. It is observed, from comparison with Fig. 3, that the surface dose in 

a ll energy bins essen tia lly follow s the angular distribu tion o f the 100 to 800- 

MeV component o f the source. 

The same spherical iron problem has been also calculated by ANDY-MGCR and 

DTF-IV using average multigroup cross section s. A comparison o f the dosage 

fo r high-energy neutrons averaged over the spherical surfaces as a function o f 

radius is shown in Fig. 8. The agreement is considered sa tisfa ctory for such 

ca lcu la tion s, since the relaxation length by NMTC is only 1.3% higher than by 

using the average cross section s. Higher order polynomial expansion o f the 

cross sections is being tested as a possible explanation. Some 15 to 20% o f 

the d ifferen ce may be explained by those protons which continue through the 

target in to the iron sh ield. These are not considered in the multigroup trea tments 

and are included in NMTC. Note that the same physical quantities fo r the 

dosage are present only at the outside surface fo r th is problem. The NMTC approach 

tru ly calcu lates surface leakage as a function o f sphere s iz e , but the 

other calcu lation methods include m ultiply re fle cte d neutrons across internal 

surfaces because only one calcu lation has been performed. 

5. DISCUSSION 

Despite early intentions to obtain general resu lts which allow sim plified 

methods to follow , the major e ffo r t has been on s p e c ific design problems. To 

accomplish th is , considerable computer resources have been required which are 

not generally available. It is not our intention to imply that the techniques 

used here should n ecessarily be follow ed, because simpler techniques are clea rly 

desirable. 

The spherical iron problem can serve as a comparison standard; simple 

cy lin d rica l problems, using earth and concrete, are being carried out. The 

discrete-ordin ate methods (DTF-IV) and NMTC-MCN approach agree reasonably w ell, 

but the multigroup ANDY-MGCR-Monte Carlo approach is not completely understood. 

Although the spherical iron agreement is good, thick cylinders o f earth curren 

tly present problems. Further testin g o f the multigroup cross-section sets 

are needed, and clean experimental comparisons are v it a lly needed. To carry 

out the spherical iron problem with NMTC-MCN, two to three hours o f CDC-7600 

time was required, and a fa ctor o f fiv e more using the CDC-6600. In comparison 

the multigroup ANDY-MGCR required ~5 min. (5 problems), and DTF ~30 sec (is o 

trop ic) . 

The resu lts to date demonstrate the promise that point kernel and removal 

cross-section methods can be evolved. The major problem w ill be to account 

properly fo r source anisotropy in the high-energy region. The value o f the com 

putational system being developed for WNR has already been demonstrated in the 

understanding o f the physics o f the problems and in the design o f the fa c ilit y .

I A E A - S M -17 0 /4 5 

REFERENCES 

[1] NAGLE, D. E., KNAPP, E. A., in Yale University Conference on Linear 

Accelerators, 1963 (Yale Univ. Press, New Haven, 1964), p. 171; in 

Proceedings of the Fifth International Conference on^High Energy 

Accelerators, Frascati, Italy, 1965 (Comitíto Nazionále Energía Nucleáre, 

Rome, 1966), p. 403; IEEE Trans. Nucl. Sei. 12 623 (1965). 

[2] COLEMAN, W. A., ARMSTRONG, T. W., "The Nucleon-Meson Transport Code, 

NMTC," ORNL-4606 (1970). 

[3] CASHWELL, E. D., NEERGARD, J. R., TAYLOR, W. M., TURNER, G. D., "MCN: A 

Neutron Monte Carlo Code," Los Alamos Scientific Laboratory report 

LA-4751 (1972). 

[4] BERTINI, H. W., Phys. Rev. 131 1801 (1963) and erratum Phys. Rev. 138 

AB2 (1963). 

[5] ISRAEL, H. I., COCHRAN, D. F., "DTF Shielding Calculations at 800-MeV 

LAMPF," Second International Conference on Accelerator Dosimetry and 

Experience, Stanford Linear Accelerator Center, Stanford, California 

(1969). 

[6] HARRIS, D. R., "ANDYMG3, the Basic Program of a Series of Monte Carlo 

Programs for Time-Dependent Transport of Particles and Photons," Los 

Alamos Scientific Laboratory report LA-4539 (1970); HARRIS, D. R., 

FLUHARTY, R. G., KOELLING, J. J., WHITTEMORE, N. L., "Medium- and 

Low-Energy Cross Section Library," Trans. Am. Nucl. Soc. 15 962 (1972). 

[7] LATHROP, K. D., "DTF-IV, A FORTRAN IV Program for Solving the Multi- 

Group Transport Equation with Anisotropic Scattering," Los Alamos 

Scientific Laboratory report LA-3373 (1965). 

[8] FULLWOOD, R. R., CRAMER, J. D., HAARMAN, R. A., FORREST, R. P., Jr., 

SCHRANDT, R. G., "Neutron Production by Medium-Energy Protons on 

Heavy Metal Targets," Los Alamos Scientific Laboratory report LA-4789 

(1972). 

[9] MADEY, R., WATERMAN, F. M., submitted for publication, Kent State 

University, Kent, Ohio; see also Ref. [8], above. 

D I S C U S S IO N 

I. M. THORSON: In F ig. 8 showing calculated relaxation o f neutron 

flux in the sp h erica l sh ields, what angle is the resu lt fo r , o r is it integrated 

over a ll outgoing d irection s? 

R .G . FLU HARTY: It is integrated fo r all d irection s. 

W . B. LEWIS: What is the d ifferen ce between R ussian Roulette and 

Monte C arlo? 

R. G. FLU HARTY: I would p refer that an expert answer your questions 

about R ussian R oulette, but m y v ersion is as follow s: to avoid spending tim e 

on neutrons travellin g back through the su rface (inw ards), the p a rticles are 

random ly "k ille d " but they are accounted fo r by weighting m ethods. 

617

618 F LU H A R TY e t a l. 

W. B. LEWIS: In sections 4 and 5 of the paper there is referen ce to 

windows in iron shielding fo r certain neutron en erg ies. What would you 

use instead o f iron or in addition to it? 

R. G. FLUHARTY: B ecause o f cost con sid eration s, iron is still the 

p re fe rre d shield m aterial in spite o f the windows. Hydrogen with 1. 5 atom %, 

is con sid ered adequate to elim inate window effects. M ore p re cis e ly , the 

optim um m ixture is 1. 5 atom % hydrogen. 

R. NICKS: Y our d iscu ssion is lim ited to neutron attenuation. What 

about photon production and propagation. Neutron capture and in elastic 

scatterin g w ill probably rep resen t im portant gamma sou rces. Did you 

reso lv e the p roblem o f photon propagation? 

R . G. FLUHARTY: No, we did not calculate the gam m as. H ow ever, 

this question has not been com p letely ignored because the gamma p rod u ction 

w ill follow the penetrating h igh -en ergy neutrons and because the gamma 

attenuation is m uch m ore rapid than fo r these neutrons. M oreover, the 

outer 15-18 inches of the shield con sists o f m agnetite aggregate con crete 

with a boron frit o r glass. The hydrogen m oderation and capture in boron 

la rg ely elim inates the iron capture gam m as. The 476-kW boron gammas 

can be ea sily shielded. Gamma production and transport options are a v a ilable 

fo r the m ultigroup m ethods we are using. 

R . NICKS: In calculating the neutron transport in the shield, you make 

use of D TF IV. I do not think that a code o f this kind is adapted to handling 

the strong flux an isotrop ies. What was the o rd er o f the Sn-approxim ation? 

R . G. FLUHARTY: I do not wish to state the ord e r o f the Sn approxim ation 

becau se I have forgotten the value. 

H. RIEF: What is the cost estim ate for the spallation target and the 

proton deflection fa cility ? How long w ill it take to construct this facility? 

R. G. FLUHARTY: The beam channel cost is estim ated to be 

US $ 1 m illion and the budget fo r the whole WNR fa cility is $4. 4 m illion . 

C om pletion is expected in two years. 

G. A . KOLSTAD: A ll three speakers in this session have d escribed 

v e ry in terestin g applications — in space scien ce, a ccelera tor shielding, 

beam tran sport and beam tailorin g. A ll have indicated that their ca lcu la 

tions requ ired nuclear data which are insufficient for their needs. Yet 

none o f them listed the nuclear data needed, giving the bom barding energy, 

p a rticle and resolu tion requ ired. 

Would it be p ossib le fo r any o f them to sp ecify the requ ired inform ation 

in the form of request lists so that m ea su rers o f nuclear data can be 

stim ulated to make the m easurem ents which might m eet their needs or 

future needs o f a sim ilar nature? Such tabulations could be included in the 

p roceed in gs o f this con feren ce. 

R . G. FLU HARTY: The B ertini approach is not expected to provide 

good answ ers fo r Be, C, N and O, so these have first p rio ritie s for angular 

dependent in elastic scatterin g c r o s s -s e c tio n m easurem ents, i .e . (p; n '(E ), 0), 

(n; n '(E ), 0), (n; p(E ), 0) [including xn ', xp' produ cts as w ell] for en ergies 

from 20 MeV up to 3 GeV. This should co v e r the applied a cce le ra to r field 

and space applications. Angular effects fo r isotop es spaced through the 

chart o f A values are needed to con firm B ertini calculations. It would be 

u seful to test the assum ption that A l and Si have the sam e c r o s s -s e c tio n s . 

Data are needed on high en ergy fission c r o s s -s e c tio n s (heat production 

as w ell as neutron), and the delayed neutron fraction s are a vital question 

fo r p ossib le booster expansion o f the sou rce capability. T his latter question

I A E A - S M -17 0 /4 5 619 

is o f sufficient in terest to have made us decide to m easu re the delayed 

neutrons o u rselv es. 

Deep penetration m easurem ents are needed because the c r o s s -s e c tio n 

a ccu ra cy requ ired can be obtained only in this m anner. 

W .W . HAVENS, J r. (Chairm an): I am afraid that we shall have to get 

these fa cilitie s operating and do som e experim ents with them b efore there 

w ill be adequate data in this en ergy range to get the inform ation which is 

n e ce ssa ry fo r checking the calcu lation s.

CHAIRMEN OF SESSIONS 

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S ection II W .B . LEWIS Canada 

Section III O. J. EDER A ustria 

Section IV A. H. W. ATEN CCE 

Section V K. H. LIESER F ederal R epublic o f Germ any 

Section VI G. B. YANKOV USSR 

Section VII W. W. HAVENS USA 

Section VIII Yu. F. CHERNILIN IAEA 

Section IX R .L . JOLY France 

Section X B. GRINBERG F rance 

Section XI P. A LB ERT F rance 

Section XII G. A. BARTHOLOMEW Canada 

Section XIII A. H. W APSTRA Netherlands 

Section XIV A. T .G . FERGUSON UK 

Section XV H. P. M ÜNZEL F ed eral R epublic of Germ any 

Section XVI D .J . HOREN USA 

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