,

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-. (!9●LA-3169

ClC-l 4 REPORT COLLECTIONREPRODUCTION

COPY

I-DS ALAMOS SCIENTIFIC LABORATORYOF THE UNIVERSITY OF CALIFORNIAo LOSALAMOS NEWMEXICO

IJ

A METHOD FOR ESTIMATING FRACTIONAL YIELDS

FROM LOW- AND MEDIUM-ENERGY NEUTRON

INDUCED FISSION

—. --r - ,

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—’

,

LEGAL NOTICE

This report was prepared as an account of Govern-ment sponsored work. Neither the United States, nor theCommission, nor any person acting on behalf of the Com-mission:

A. Makes any warranty or representation, expressedor implied, with respect to the accuracy, completeness, orusefulness of the information contained in this report, orthat the use of any information, apparatus, method, or pro-cess dtsclosed in this report may not infringe privatelyowned rights; or

B. Assumes any liabilities with respect to the useof, or for damages resulting from the use of any informa-tion, apparatus, method, or process disclosed in this re-port.

As used in the above, “person acting on behalf of theCommission” includes any employee or contractor of theCommission, or employee of such contractor, to the extentthat such employee or contractor of the Commission, oremployee of such contractor prepares, disseminates, orprovides access to, any information pursuant to his em-ployment or contract with the Commission, or his employ-ment with such contractor.

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LA-3169UC-4, CHEMISTRYTID-4500 (35th Ed.)

Il)S ALAMOS SCIENTIFIC LABORATORYOF THEUNIVERSITYOF CALIFORNIA LOSALAMOS NEW MEXICO

REPORT WRITTEN September 1964

REPORT DISTRIBUTED: January 12, 1965

A METHOD FOR ESTIMATING FRACTIONAL YIELDS

FROM LOW- AND MEDIUM-ENERGY NEUTRON

INDUCED FISSION

by

Kurt Wolfsberg

TMS report expresses the opinions of the author orauthors and does not necessarily reflect the opinionsor views of the Los Alamos Scientific Laboratory.

Contract W-?405-ENG. 36 with the U. S. Atomic Energy Commission

1

ABS!IRACT

Amethd is givenfor estimatingfractional.yieldsof productsfrom

low- and medium-energyneutroninducedfission. The methodis based on

experimentalmeasurementsof somefractionalindependentand cumulative

yields,and involvesthe assumptionthatyieldsof productsslongbeta-

decaychainsare describedby a Gaussianfunctionwith the samewidth

(a)for sM. mass nwnbers.

Equationsare givenfor estimating%, “themost probablecharge. ”

Fractionalyieldsmsy be obtainedfrom a tablewhichlistsfractional

yieldsas a functionof Z - %“

3

.

,

.

.

.

Althoughcumulativeyieldsof many long-lived,latemembersof

fissionproductchainsare knownfor a nwiberof fissionpxmcessesfzwm

experimentalmeasurements,theyieldsof most of the short-lived,earlier

medbers

themnaJ.

fission

purpose

havenot been meas~. Themeasuredfractional.yieldsfor

neutronfissionof IF=s,IF35, and Pu2Seand for 14-M3Vneutm.m

of ~5 and @98 are summarizedin references 1 and 2. The

of this ?xqyx?tis to presentthe necessaryequationssnd tables

for ma.kLngrapidpredictionsof fractionalyteldsfxxm low- and mediun-

energyneutzxminducedfission. !Ibmakesucha predictionbythe method

givenhere,one firstestimatesavalue of ~, thevslue of Z for the

maximunof the independentyieldversusZ curve,for the mass nuuiberof

the fissionprocessof interest. A chargedispersioncurveis then used

to estimatethe fractionalyieldof element Z for thatmass nuniber.

The readerslxxd.dconsultrefezxmces1 - 4 for discussionand derivation

of the methoddescribedbelow. .

zj?va3uesfor thermalneutronfissionof ~5 are used as reference

vsluesfor givenmass nmbers, and adjustmentsare made for otherfission

pzvcesses. For high-yieldmass nmbers,

a~mtitdbyz 2,3

~ f = 0.4237A- 2.19 (for82<

and

ref%?

, the reference!+ is

A < 100)

ref5 =0.433U - 6.06 (forA > 135) (1)

where A is the mass number. Not enoughmeasurementshavebeen made for

5

.low-yieldmass nmbers to make suchgeneralizations.

- followingequationsare then used to adjust~f for a different

fissionpzmcess:4

&+ =().5 (~-g@ -0.21(+-236) +0.19 (vT -2.@) (2)

and

(3)

where ~ is the chargeof the fissioningnucleus,~ is the initialmass

of the canpoundnucleus(i.e., tha mass of the targetnucleusplus one),

end VT is the averagenumber

obtainedfmm equation4:5

VT = ;(thexmsl)+ kE

in which E

are givenin

is the incident

TableI.

.

of neutronsper fission. valuesof VT are

(4)

neutronenergy. Valuesof the constants

!MBLEI

Constantsfor Equationha

Rwcess -zUB?!lQ — k

~s(n,F)

~’(n,F)

@38(n,F)

Pu=s(n,F)

%rcauxwference5.

2.9 0.1.15

2.43 0.135

2.41 0.138

2.87 0.111

●

.

. !LWle II listsvalus of A% for some commonfissionprocesses;

otherscanbe calculatedeasily.

TABLEII

vaUlasof%

Pzmcess A%

~%th, @ 0.43

Puas(nth, ‘) 0.25

~5(~4e6, F) 0.37

@s6(~4,6, @ -0.25

Zhe fractionsll.cwnulativeyieldof a nuclidewith charge Z is

givenby the Gaussianequation:

{ -%+0.5)/%.]=0.5 +0.5 (z

in whichf(Y) is the errorfunction,definedby the expression

Y

sf(Y) =* o exp (- t2) dt

(5)

(6)

6which canbe nmdlly evaluatedon a computer. A valueof a of 0.59?

0.06 is assunedto applyfor aXl mass nunbersfromlow- and mediun-energy

1-3 Wble III listsvaluesof fractionalinde-neutroninducedfission.

pendentand cumulativeyieldsas a functionof (Z - ZJ for vsluesof

7

~ of 0.59, 0.53, md 0.65.

!lbestimatea

1. Calculate

2. Dete?mine

3. Detemine

4.

5.

For

14.o-M!ev

A=

fractionalyield,perfontithe followingsteps:

~=f fromequation1.

UT from equation4 snd TableI.

A+ frcau !lkibleII or frcm equation2.

throughequation3.

Look up the fractionalyieldsfor the propervalueof (Z - Zp)

in TableIII for eachof the threea’s.

exsmple,let us estimatethe fractionalyieldsof Ba142frcm

neutronfissionof WS8:

142, z = 56,~=P, E=14.0, ~=239

lhxxnequation1: 5‘f = 55.44

From equation4 and TableI: VT

From equation2: As=- 0.27

m equation3: ~ = 55.17

z-~= 0.8>

From l%ble111:

= 4.34

Fractional

{ }

0.276 fora=O.59

independentyield= 0.261for a =0.53 i.e.,o.276~ ~“~1~

0.285for a = 0.65 .

Fractional.

{ }

0.g88foru=O.59 + 00006cwnulativeyield

= O.* foru =0.53 i.e.,0.988- 0 0080.g80fora =0.65 ●

Thesetwo fractionalyieldswith theiruncertaintiesrepresentthe

fractionof the chainformed(afterprompt

and the fractionof the chainfoxxnedw to

tivelye

I

neutronemission)at z = 56

and incltiingz = 56, res~c-.

4

8

A few womlsof cautionin the use of thismethodare in o~er. The

value of a of 0.59 t 0.06 has been detexmlnedfor themnalneutronfission

of @ss fez? mass nunbers91 - 95 a 139 - 143;1$3 the valueis also

consistentwith three

assunedthatthe same

the fissionptmcesses

mass nmbers from

Gaussiancurveis

consldem?d.This

2otherfissionprocesses. It iS

validfor sM. mass nmbers for

assumptionwas made in obtaining

equation1 frmn e~rlmental data and is againmade in estimatinga yield

frcm TableIII. In reference2 it is slwwnthat the methodof this report

predictsmost valuesof Z@ whichhavebeen inferredfrommeasurements

of fractionalyields,fairlysuccesslhilly

the predictedZ$ts franthe measured!$?~s

ever,the ~’s predictedfor mass rnmibers

with the averagedeviationof

beingO.I1 chargeunit. How-

89- 95 frau themnalneutron

fissionof

averageof

-s are consistentlyhigher than thosemeasuredby an

0.17 chargeunit.

1. A. C. Walil.,R. L. Ferguson,D. R. Nethawsy,D. E. l%outner,and K.Wolfsberg,Phys.Rev. , 1.112(1962).

2. K. Wolfsberg,to be ptilishedin Phys.Rev.,1965.

3. A. C. Wahl,A. E. Norris,and R. L. Fergwon”(privateccssmunication),19; and A. E. Norris,PhD Thesis,WashingtonUniversi&, 1963,Universi& Mi.crofilms(AnnArbor,Mich.), L. c. CardNo. Mc-6A.-2325.

4. C. D. Oorgell,M. Khplan,and R. D. Fink,Can.J. Chem.~, 646 (1$61).

5. ArgonneNationalL~oratory ReportANL-5800,2nd M., 1X3 (unpublished).

6. C. Hastings,Jr.,Approximationsfor Digita3Computers,p. 169,PrincetonUhiversi@ - Sill,Princeton,1955.

9

.

.

TABLE!111

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