'" γ羊

Ck19boo15~

CNIC-ω293

PU-0002

丘日

CHiNA NUCLEAR SCIENCE &TECHNOLOGY REPORT

放中子前后裂片碎片质量份布的换算

TRANSFORMATION BETWEEN PRE- AND

POST-NEUTRON-EMISSION "RAGMENT

MASS DISTRIBUTIONS

原子能出版社

申圃穰情报申，~

China Nuclear Inforn、ation Centre

CNIC-创帽93

pu-饵..z

放中子前后裂变碎片质量分布的换算

TRANSFORMATION BETWEEN PRE- AND

POST-NEUTRON-EMISSION FRAGMENT

MASS DISTRIBUTIONS

王福成 胡济民

Ut京大学技术物~系〉

中国核倩报中心

原子能出版社

霉事. 1....2

摘要

撞出了一个裂变中子产额分布的七点计算公式.经与从Ac到Cf革国内的裂变核章.

.u撞由自囊裂变高到45ar.v.，缸子诱量窥寰的实验比蟹，章公式幢幢好埠医峡中于分布

的主要"在.由于中于分布在产疆的提算中只是桓武耍的作用，因此可以用来换算.It中于嗣后

'量骨布.利用章公式量行换算后的厦量分布能.好地再现实量分布的平均趋势.如果将谊

会式与监中于翩襄变碎片'量分布半是量公式川联合使用，将可直接讲算.申子后的质量产

蟹，面不露，利用任何宴噩擎蟹，结出的绝时产'回画精度约为主0.5".

羹..中子产'民质量分布产'民换算

TRANSFORMATION BETWEEN PRE- AND

'POST-NEUTRON-EMISSION FRAGMENT

MASS DISTRIBUTIONS

Wang Fucheug Hu Jimin

(D啕幅rtment of Technical Physi饵. Petins University. Beijing)

ABSTRACT

A snn-point interpolati帽 f町.ala is &iyca for tbe calculation of antroll

yields as a f.actioa of frac.eat .ass for nrioas lissioni‘ I s1ste.s. Th. for­

..Ia well reprod.ces Ihe ceneral Ir.nds of npedaealal data for II wide r..Ce

of fiuioDial D.clides froa Ac to Cf with excitatioa eaercies frOID spontaDe­

oas fislion to 45 MeValpha partieln iadaeed fission. That 严rmits one to trans­

rota the 1ields betw... p~e-aeatroa-e.issioa (iam.l) aDd post-aeutroa-cmis­

sion (fiDaI).The tra.sfo~m.4 yi.lds are w.U in accord 咧th esperiments escept

fia. structures iD the lissioa of actinides. In conjuDctio圃 wilh the semi­

empirical form回la on the iailial fr吨.eat .ass dillribations liyen in an earlier

publicaUonlll • the final yields "a, be obtaiaed without an, help of empirical

data. The precilioD of the prediction is esli."ted to be 土 0.5 in the percentalc

of the ,ields.

• 1 ..

L INTRODUCTION

Th hac."l .ass 4islrib.lioas of ...rio.s Ii翩。aial 町sl..s are of ialu­

cst ..曲 t配"icallf aa4 lfalOrelicallf. II is slill i.possiltle I…ke l.eo­

nllcal pn4idioas f时 lite ial町al.4 sfsleas .itlt reASQa.ltl~ a('caney. la a

...."..s .orklll, •• Itaye 币y.. a ...i...pirinl for..la ". lhe pre-…l lVll­

..幅幅 (iailial) f吨，...1... .islribal阳s ia .町1_， fi5Siu蝇{霄e a"..4ill) .

T.Ia.ieally. it is .Ite posl-.eal l1Ml-C.iss恼，a (fi..l) rra,menl .ass .islrilHa.ioIIs

.... an of ial町回.. Eapirical "ala are. 4i"i4" beh'fta pre- ilII4 pos.-...lroa­

..i篇幅. fr吨."1 ..IS 4islri‘.lioas, with …y It'..k r~ioas. So, il is iapor­

'a.l '0 M aWe 10 'raasfor. 由e yi.14sMl.... .i.ilial a.4 fi..1 fra....l ..ss

dislri‘.Iioas so lhal .e ca. calnlale lite .ass dislrihlioas ialunled lecla.ic­

ally orωanrl lit. fiaal ell,.ri..alal .ass dislrib.lioas illlo iailial ..ass yiel..s

协 be .se4 ia co.parislo. .illa l"ories. Ho.enr , o.e aceds 10 kao. Ihc ae.­

'roa yi.14 as • f.aclio. of f,apeal .ass 10 acllline sDcb lr..dor.alions.

T Ia. ceaeral simila,ily ..oal ae.lrOD yield fuaclio.s ior lllle 10. ea.re1

lissf.».I.. 町slcas led Terrell' 1/ 10 su四csl Iltal • ...i"ersa' DeDlro. yiel. f.DC由

lioa .nisls fo, .lticla lite a...lter of ae.lroas eamed .pproach.s Zero al closed

曲ell a.clei of fifly aeelrolls or prolons ud .lIicla .Iso .ay be affedei by lhe

."laI1-1.0 .eulroa sheU. WilfriD' el al. !l1 uplaiaed 'h.l as scissioa poial slt.1I

.effects. Assu.iac lllle J $ICf(sf) 圃eulroa ,ield fuactioa deleraiaed by Bo...a

..I al. r 叫 as aa uain,ul ~sl町"吨~ ae四lro. yiel" f.aclioa , Giadler ca.,. a

me'hod of calcul.led neulron yield f .aclioa ia Ref.' S '. It is mainly dcsiCDed 10

be IIsH in conjuncliOlJ .ith suilable experi...lal dala.

Y.....olo· 1I has described a melhod. of calc回lalion II) estimale lhe a.1I1,on

11elels In fissions .ilh .edluDI-ncil.tion ener,ies. To carry 0111 lhe calculation.

oae ..sl Ke' lhe uperimealal dala of neulron yield dislribulion in lh.,DI.I-

n.ut,oll induced fission , ..er.ce lolal kinelic enerlY .s a f回nclion of f'.lmenl

.ass and yield in 10.- and lIIedi"m-eui'alion reactions. Hcnce , lhe applicaliulI~

of lhe melhod is ,alhPr IiDlited.

In presenl paper, a melhod for calculllion of aeelron yield is Kin. which

permils one 10 lr.nsform yields between initi.1 and final fraS lDenl mass dislr卜

b回lions.

2.. NEUTRON YJELD

The neulron )'ield as a funellon of frasmenl masl Is Ilself a lonl Ilor)'.

M.ny ..,erlmenll .ere done wilh ralhe, scattered rellllts. No faUsfAelur,• Z "

...utan... 由ew， ni.ts. Fie.1 silo.. •sel of ,.Wi....

,icWs. It COY町s I‘…ss r.ap f.,.. "'Ac 幅，. 'ef ..4 I.e enilaliea e.erei饵

"腼 4~ MeV. ..41 i.clnes fissioas i...cM '-, ._ll'OIIs. prolOll' ..eI .1....

，.rtid饵 as .ell •• spital…OIlS fiss郎.s. All of I.e points cnaf'町. 10 si.m.r

.....时. ,.Ucra .it. 翩翩嗣 fiN slr.c"tns. Tltere is • 4i, close I…51 …­

.... 121 .1 ..id I.e ._1.... field i. .1_1 aero for 10. ell町I.Y Jissioll. AI­

'.... all of t.. ...1108 ，隐I. f..et iollS _we I.e c帽aG. sa.怕也 .Incl.".I.e

.-pirical 崎.I.，ilia for elif阳..I Jissiolli.e srsteas are c帽plicatn ..e to I.e

..cutaiat, i. ex....i...t.1 clal. as is .‘… i. Fie.! ••• Fie.'.

..Ia口-II' of ...Iro.

•••

i抖~ ..必;二二弘弘i兰二ι:二凡.r川，I~

=重 •

•旷 .γ-. .. ..

·.,

.,6E量..0

~"ASS

Fie.' E.peri..at. of…troll ,1.lels .s bacli... of fi四H fnII...t ..SSl' -'11.AD ., ,lie f..... allow ..... ......... lin回国田W.

-.'

•.,.·"'''ad"RFZoa-2·z

·3·

••fIAGI圈IJIfT "AS.~

EI,.,imeatal al时 rOIl , i,ld eli.t rib.tio圃， of the fb.ionof '''Ra iaducld b, fa.t proto...

口.. M.Vr". 0 1:1 MIV: 配，

IUI."''咱主』

-,"

fi,.2

·.,

.·"ad-g

• III I. I" 一.

""""IIASSFi,.S £.peri....a. …'I'M ，i.'. 副.tri_，i_. .r ... fil.i.. .r ••.口 allU.25.冒 thY"阳"由恤'吨。aau.8.S IhY 啕恤'回袖Shl·: .. a咱.45 lIty画... .-rtidlllf': + u.....I..... 棚....l.·; X a:.P..I..... 翩翩翩; ''''0 as町，45

lleV 啕...回ida'n:.

0.. to lar‘e ..entai.1i回 i. experi...t.1 d.ta. it is .nfeasibl. to fiad a

-.--..,irieal for..la to acc.ratel, represetlt t‘e a..troll !ieWs frOID i...i..i....1

nssioe fr.,...ts. FI町t.llatel，. ae.troa .而"阳圃，I町S oal)' a seeo..d.r, rol. ia

".,..i.i.C tla. fi..1 .us distri_t酶as. a I"OIII Ia iatn-polation for..la.., be

..rficint for tlae ,ield tra.sfor..tioa. For tlair. ,.rposc. H Yea special ...s

阴阳. i.e. 155. 131. 12t. A./2. A./2-S. A.-13…d A叫55. arc selected.

....er. A. is the .au …bel' of CiYn fissio.I.C ..eli曲s. '121 aad ..4.1%-5 are

..pprolli..tel, poiats of .iai.u. ...d "IIi... .eutro. ,i.lds ...itla A./2 bet­

...... the_ ., 131 and A.-138 arc close to the poiats of .."i.ulD ...ss ,leW. a.d

ISS a.. A.-155 町c points at tit. flanks of tlae .ass di.tribution. Th. c翼peri­

.eDtal IIcut'OIl )'ields at thne H YeIl lDa.s points for ..，悔!IS fi..ionIA II: s,.telDs

ar. fitted .ith iI r甜IIdioa of Ihe for...

II'(A)-Cc+C...+C.E.·AIA.+C.(A.-%08) (I)

ill .hich A i. the ...凰SS fta..ber of thoH sey.n puiDts. E,· i. ncitaUon eAer~ie.

of Si...n fill阳nine 町，f....... and Ce• C.. C. alld C. are coefficiellt. to be deter­

.ia.d 1t1 fiUin~ e...pi,ic.1 dat.. .ilh I.SUItS liyn in table I.

la Eq. (I). the cit.圃Ie. of A. due to 2ftd 0' hiper chance fission at "i~h

exclt.tion en.r~ies hn. be.n nellleded. a. thc,e i. "-0 abrupt chanles of neutron

yielel functions .itb A ,.Th. t.r lD dependinc on ;, rdlcct. n帽t ，on ,ields (eature

(or different fissionill nuclid.. and different excitatioa en.rli.. of fis.ionins

nucl....

B1 Eq , (I).th. neutronyleld.althe ...en ....s point. can be calculated.One

剧。t declun the n..trun yield. from incliYiel".1 II'吨脯At bJ i饵terpolat阁1\ or

extrapolation. We n....时 Ihl. …nen-m...-point .elllOd. F岖 .4 .ho.... 四me

·喻'

aa.ples ia ..licl iaterpolatioa Dr ntnpolat iDa a曲pts lia帽r. para.lic aa.

e.t.ical cann. res~ctiyclr With the esc叩ω. of spoDtauOlls fiss iD.s. all Dr

t.c tbee C8rYn arc well ia accord wit. tlae npcri.rats. bat th ra.ical ialer­

,elation or extrapolation is to be preferrd ItrUIISC of ils smooth beha"ior.

Ta~le I The Tes.lts .r cocllici帽Is i. Eq. (I) .

A C ‘ c C , C!

•

155 !.1!l 0.405 0.0000 -0..们'

I. O.r. O.τ41 0.0翩蛐 -0......

• •• -0.3% O.τ41 O.嗣4事 -o.M57AdZ O.τz 0.5ω 0.0000 -0.01'也

A ，/:同 O.τ‘ 0.3041 -0.0441 O.四"

A ,-I3I 0.30 0._ -嘈.0533 0.0000

A ,叫" -0." o.m 0.0000 0.0311

I. FiS.4 (叶. it is sho... that three cxpcriIDeabr .-11/ o. t.e fissio圃 of lUI:

i"daced by ther.al 圃eatrons are w蕾II represcatcd '" the calc.latio. ill tile ..aia

he....III Fi&.4 (问. two n:pcriIB四ts of 1 uU fission i.claced by 45 MeV alph.

"I" ic~es '" Fraellkcl and M町It:'· ..d ~'.5 MeV alpha particles by Brill et

al. iI : I. rcspccti叫1 arc shown. As we c:hose;, yallle 叫ual to 4.:! for the

nperiment of Fraenbl and M町k. which ...as Ihe dalum KiYen in their

paper. and equal to 5.2 for the experiment of Britt eI al.. which was obtained

from Fill.。阳's paper' l' i by interpolation as inpat d.ta of E '1. (I). The nea­

tron yields are reproduc:ed ycry well by Ihe c:alculalion. One lIIa1 nole lhat

hilher ndtation enerlY for the experilllent of Fracnhl and Mayk possessed

I lIIaller nlue of ;, wbile lo..er excitation enersy for the experiment of Britt ..

al. lot larler value of ;,. We leaYe sueh c: ontridic: tio四 as it slands in order to

redace the systematic: errors of npcrimenb. The nl肘 of 内 for the experiment

of Britt el al. was Kot from systematic: form回la. so we miSdt d("ducc Ih.t the

npcriment of Fraenkcl and )i町k had larser s1sh:matic 町rors.

Fil.4 (c) s!lows that for the sponlaneous fission of ZHCm"" , the best

result are oblained wilh linear interpolalion or extrapolation. and Ihal for hilh

n c: ilalion ener(;y or l"PU fission induced by .c 5 MeV alpha parHc:le.~'!， the

differen c:es among linl.r. par.boli吃画nd c: ubical cunei becollle very small.

Fi嚣 .4(d) is the example of lI1ef ::ponlaneous fission. Only linear c: urve is in

IODd accord with expcrimen a.r…at!.

• 5 •

.•..

f " IH 117 1.~ " " "‘ '想' •• IU

• [.> r.[Ill(10)

°.4 '3." • ι -.霄~ D,"• ••

Z.UI /hf.气·e • ,,07.., ...~ __at 星萄F 飞 ..7 l'喃自， 0

.hs刨• t.·-4.w ‘~唱t~ 钮" 岳 ....‘男....-‘ "" P..

市Ca) r (c)

zskaz -

,0• ••

• •2 ...a.!!..- • ... '..l1li,0

,0

,0

• (It)

可fI

.tH ' .0

" I !~ H4 IS 101 117 IU 14. "''IAGMENT MASS

'il.. Co.pari.i... 01 .alc.la''''…tr.. , i,hl. .It. ,.,.,.…tal .a'a,c.".... i...网.tie…·惘，.............忡I -U..., -....,....., .......…a嗣I. C')"'U ,...协"a"鹏侃It， ....... ......~.-‘"， (~)"'u 'lu嗣川翩翩III ~， ..1 NeV"" 1M .. ".VI') ..... ，.，嗣楠， (I) I，吨·'翩翩翩，阳阳、刷刷刷'"IJNi帽阳曲时峙.....v 嘟u ，.阳"""， (4)......翩翩fI..阳...... e,III…I,

怡、

s. TRANSFORMATION METHOD

YieW trauf...ω…·‘"is 饵..tiall ，. tut of Tanll'sUl, i. .laicla

M抽J ..4 fi..1 cal_"u.- ,.ieNs '" f幅画. fnplelats .... RIa'"‘'1 ~.ω-·.....nJ....u.- ，.恒.. i. 由画__1"._ of t" ,...... all ........1事

'自由 _.p 曲r...p • p... y..... F... _ A. t" i.it袍J ... li..1 ca_la-

"- Aelift l ieNs an ..Ii_ as ;t]'(A) ... £" Y( ..4). .... ~A)'" ),,(Alue i.ilial

• •..r幅.....，曾Ns. I'帽pecli.，.

ne.....t面回‘ip"阳.. tile i.il恤I." fi..1 'I'咽:-hI ，.融Ns曲riN ~

T笛"幅画，

...+. ("-+w+l/!)I: Y(的- I: ，(A)+(~/.A) (.1(.. ;A» /2+·- (2.)

• •.-(%‘>

{担》

•••

"'-.-111 "'-1/1I: ),,(A) - I: ,7{..4)+ (47/.A) (.1(.,: A» /%+.-

• •i. .'ic‘ M ‘. ..4 51咿 (.7/4A).re ","'t_ .t Ae. ... (.1(..; ..4» is

...,.,.. COlI4itiDuJ Yaria.en If t耐.1 fiD_ ...t,.s ..il'" f.... c帽响-­

tary r鸣圃.tl.o-n.i.. 叫码-wr(A+叶'刑... ca. ....rit. E41.(%)" tlae fr幅

)"(..4)-( 1+.:-._~n<..4+.:J2+._U%-1β》+ [(.7/...4).-(.7/...4)_1] (.I(崎 I ..4» /2+·-

,,(..4)-( 1+..-吼 ， )Y( ..4- •.I2-.. .I2)

+[(47/· ..4).-(·7/·..4)..] (.吨.r; ..4» /2+'·· (3")

i. ..‘k ‘ t.... s.keripts -I. …. +1 ...r.r to A- I. A ..41 ..4+1 , rapecti­

.d,.. T.. secOll. t.... i. Eq. (J) ...s • s..1I "fect. 吨..1 to 0... .pprosi­

..tel" ..41 "iclll.r-or'.r t,r.s c.. be .qlect", Accor~i.Cto E41. (38) fI..1,i,I.s c.n be ob'.i." fro. i.ilial fr.C_al .... dislrihtio.s.l..阳..1，. ,accord

i.. to Eq. (3的 iam.1 ,i,ldl c.. be c.lnl.I.. froa fi..1 fr..…I...s

-411t,ia..t loas ir 1'{..4). ;.' (.吨.，'; A» .... (d7/"A) .1"‘.o"a.

If '''en il ..pe,i...tal dala of …tm , i.l..s fro. iadiYid..1 fislio. fr.,­...ts, 0.. c.n s.ooth it to r'praeal I'(..4).。如何阳. ......…..-poi."

.t'叫 lin.. ia seclion 2 ..iCbl ... .sed. Calc-I.tions of i , .nd (.,I( .rl ..4» .1"disnlHd in section 4.

J. I.. C.M of transfor..liOll fro. iamal 10 fi...1 ,ields b, Eq .(3吟， tllie

，胁.. (d7/d..4) or iam.1 ,i.ldl can direcll, ... d,d.c.d b, bo". iailial..peri­

..Ial ..Sl distrib.lions or Ih. M.i-e~，irlc.1 lor..I. ,I... ill ."..di 嚣，

Us.a, til. i.m.1 ,.peri..at.1 ...ss dislri".tioal .fler saU.ble saootlli., procel'

.0001d h.町. ..Usl.clor, to ded四c. (d7/d..4) if r.I.....t d.'. .rc .nU.ble.

, 7 •

For Ihc Ira.sf，町!pl ioIa fro. n......1 1o i.mal 1iel缸. OM -ns 10 k... I'"

i.ilial ricl.s of n剧。.i.1 srslcas 10 oblai. l lIe slopes of i.ilial ,islri"'liotts.

It is i.iliallT a"..-nt Ihal Ihe i.ili.1 1险14s. Ihc ·s1arli.c· i.ilial .ass 4islri­

"'I"s are elelrr.iaN I.). shifli.C Ihe posil i08 of fiaal .ass 'islria..l iolIs 1t1

..u iacRaeal of I"~ ..alae of ..: of Ihe fissiolli llC ~，.sle.s ..r i...n1ipl....

This ·slarlial- i.ilial .ass eislrilt.lw. is desi,a.I" by 7. .hi~h peraits I.

calc."Iioll' of lite slopes of ·slarli.,- i_ilial .ass elislri"'I.. T.a tile firsl

.ppnn: i....lion of iailial Nass yields ....e.. 71 CaD lac oblaian by Eq.(3b).

If l lIe co.-parisi拥 is salidador}" Ii) a ci..ell prnisio_. Ihc 7 , is I lIu lakea 10

lie Ihc rett.ired iailial ..ss dislribulioe. 1£ I.e co.parisioll is .asalisfadory. 由"

aaolher fUdioa of (el7/el.") is ~alCDlated .ilh s酣抽血" 7 ,. The ~OIIel ap­prosiaalioa 1o llae iailial aass dislrib.lioa 7~ is calcalalN alaia .By Ihis il",_lin acllaod llae iailial ..ss dislr山.Iioas ..dcr Ci..e. precis协. arc "deraiacd.

S1.aclri~al邸a had beller be p.1 illlo err配I for Ihe Ir..sfora.t如. from

fi..1 1o iailial yields because Ihe Ira.sforan i.ilial dislrib.lio. .町 lac ..町­

...lric.1. Ad. .or....lizaliDn must be perfor.n for Ihe Iraador配el i.ilial 町

fi..1 ..ss dislribulio.,.

4. <62(Vr, A» AND Vr

Terrell in Ref. (2] Ca Ye Ibe fDr..la

(11气 .r; A)} _,,2(r,)/z-a2(A.) (d的-dA.P/Z (4)

in whi~h '" is Ihe lolal number of neutrons emilled in a siaclc fission eve时，

.ad cr1(.,) is ils nriaacc. ,,:( A.) is 、rariance of ..4.. Ihe mass a.mber of hea.. ,.

fiss协圃 fralmenls ， and (elv,/GA.) is Ihe III ‘ erace rale of chanlc of 町 wilh A..

Ass.m·吨 (dv，/dA.) a.-prolli....lely 叫..Is zero. Ihen Eq.(4) ''«0酶'

("l("r; If» -σ1(r，)/:! (~)

So.e rese.rchers"U-: oI han already livcn sOllie esli..lions of (1(.,). Ihe rms

Y.rianc窜。f fission ncatro四 number per fission. They all assumed lhal il is

conslant for 市ariD.， fissi.，nill~ sysle...s. Howner , .e found it _lIu 10 npre­

senl ,,(.,) as • line.r function of ;1 10 fil experimenl.1 dal. in I.ble 2. The

fillinl resall is

。(.，)-0.898+0.0026;， (6)

which is beller In accord with nperimenls. The lasl snen colamns of lable 2

刷yc calculaled yalaes of 叫.，) and R(.,). where R is c!c£ined as «.,:l)_r,)/;,I ,ind~pcnd回I of the eHicicn c: y of neulron deteclion.

for the calc幅lalions of n~alron yield distribalions "(A) .nd urian c:e or

Ilssion ncgtro帽 ftamber 0'1(.,), it Is necessary I" lIno W' Ihe .alue of r,. For

Ihis purpose, Ihere arc many works on measuremeR ts. calculalions and 町s-

• ••

T.~" ~ Wi副Ita .r …UN ...", .il' ，i~.Ii.. ".. ria旧N. 趴..~.，~ ...1刷刷.."刷 111114 f., .11 ....'1…,.,咱...II Ii... r. .11 or "… ..1.... ‘.. .,.HI .X ,...,. ,. ，..翻 .1.11.. ， .X.X.fA -X....

凰捕，.1嗣副叫... c制a，.，"，.M， .'M" 剧P ，制』··，.h"M··h.w·耐，一一----~ --.-_.一-…一E呻甲

F田iMi唱町翩翩 R.f.n.... , • ' " ' • • " 且 晶'一- .....,....._-..

V 帽町 --

..... ttn CI6> 1.14' '.1町 0." -o.1N .... -,.. •.• -0.….ral -0.'11·嗣"t") ca) :.IN 1.111 0..1. 0.'" '.ID .... ..11I -0.嗣 r '.7" -0....·....C..> crr> 1.110 I.帽. 0.7t1 ....1 '.UI •••• I." ..….7" '.IM.....(1。 LII> 1.11t 1.1嗣 0.." ..,.... '.11I -0."1 I." -0.... ..ral -0....I.啪"。 C.) •.• 1.1,. 0..冒 0."1 '.'17 ..… I..... -0,_ '.7帽-.. .....thCI。 (11> I.... 1.111 ••• '.111 '.11' .... 1.111 -0 .111 '.7. -....."咽、 t.。 [!I') I.t. 1.140 D._ O.…..... ..- 1.114 -1,'11' ..,. -a..:."'Uh. fl+I.'." III> 1.401 I.llf 0.711 .... '.114 ....4 1.111 .... ..111 ...,"·U". fl........" 111I1 1.417 I.咽. o.T'. 0.'" O.'ll ..on 1.1" ..….., ..‘""IU'.. fl+O..翩.v til> t.4:'9 1.1….TIt ...幡 '.'11 ..... 10111 ..... '.111 .......U'.. I)+I..... U'l '.41回 1.101 0.114 t.….," '..1. 1.1" '.111 '..t D....‘·划U‘'. fl+O.嗣嗣.v lit) I.咽， I.….ra冒 ..ITI '.'11 ..... 1.111 ..…....‘ '."1...U,.. fl+O..翩翩' (It) '… L町， ..,.. O.IT' O.剧' ..... 1.117 ..….11' ..tSl缸IU'.- 1)+1.-''' t lO) 乱... I.ITI ..，回 ..….刷' ..... 1. 141 '.ITI •.... '.'嚣'"·U'..O+I.蝠10" (II) I.... 1.141 ..... ·唱.IIT 1.111 -'.NI 1.141 -.... ..... -I..oc. t"> Ul> t.... I.... U.Tl I ..... '.111 ..tS。 1.141 •.• ...帽 I.U"'''Cat''> till %.T:IlI 1.1….. ,.," '.Ilt I.IN 1.1" '.11' '.'11 ,,.,..<ra C"> (It) 1.1:1II ..ITI 0.'" ..….111 ..on 1..1t '.11I '.114 "..:."....1.. fI+'1Io帽d UI) ..". I.'" '.11' '嘈.tl4 '.111 -0.... 10114 -..... ',11…'..1.....'..1)+0......" (.) I.. 1.1….114 -,.., .刷I ....... 1.'11 ..... '.tI' ..楠'…"10，1)+曲..... t 属】 1.114 I. n. 0.111 …..由 '.111 -0..' I. III -0.'11 '..1. -,..,…..,.. fl+..…阳V (.1 1."1 I..M ..11晶 -0.… '.114 -咱... 101'1 '.tl4 '.tI. '.IM"....t.. I)+O......" (.) t.... I.n. 0.11' -'.on 0.'1' -..... 川' '.….111 V... 。

..IUI..0+4.…v (II> 缸III I.r.t ,.11I -o.IT' o..n -嘈.'1' 1.1'‘-0.'11 '.111 -0.……c. tor> CII) t.'" I.tll 0." -0.'" I.…...... 1."4 -I.,,' ..嗣t -D..lt'lOCI (d) <a) Uti 1.111 '.144 -0.…... -0.'" 1.141 -0.... '.144 -....,"喝. (.1) C.) t.nl I." ..Nt -O..IT ..... -o.tI' ..副" -咱.lIt '.… -1..'- ‘ I-C' (Ill (It) t." 仁"I 0."4 -0.…..11 -0."4 1.11I '.'14 ....7 0.'"Dill圃咀回国 ..... ..... '.144 .....

tematic fitting torn- lae l22•31- 3 1!. If there is not Any experiment or calculatio...

forlllula , one may deduce VI by interpolation or extrapCl lation frolll known data

。r formulae.

5 • RESULTS AND DISCUSSIONS

Neutron yield dislribulions huve some influence 011 the transformed m制S

yields. In Fig.5. several neulron yield distributions of ~a5U fis :oion induced by

thermal neutrons are emplo,ed to transform mass yields from initiaP" to final;'"

distributions. ~"utron yield experiment of Milton and FrasurJl) arter 1m∞tb is

quoted in Fig.5(a). Near fragment mass number 134 , the slope 01 neutron yields..

7D lIIl 10 .幅 1111 110 I. '40 110 I怖 ITII..四. ,

'II

lb>

e.

事，

t.

T.

S.

t.

O.

Z.

(<It ~ 7巳..

I.

I.

e.

J.

2.

O.

~.ad

E•.J.

阳丁""~丁2il1而 I." I而-丽而110

FRAGM!"T MASS

Fil.5 Mass yield trlasrormatio圃s from initial to finll yields or the fission

or u·u illduced by tbermal neut to圃s with different neutron yielddi.tributioa..

• inll/al yields'''!, 0 lill.1 yi,ldIl ' II , .lId + lIeutron yicltit by (的 Milton III .l, rIl 1. (b)Mulir It .l.ll.land(c)cilωletion. The tolid liDe reprellDb tran,formed man di.triblltion. ~

• 10 •

.aad the initial yield are all larcer. Hence , the transformed )'ield at fracmeat

mass number 134 emerg'臼 as a sharp pick wbich i!> cUDsistent with the n:peri­

menls for final yields. Near fra~ment mass Dumber 9S at which is an maximum

nlae of the neu tron Yields , the slope of ceutron ,. ields approaches zero. It-causes a sballow .tip on tbe mass yidd curve. Neutron yield given in Ref. [10]

sbow. in FiC.5{b) chanced eeatly and the distribution of the trnsformed yields

is smoother tban in FiC.5(a). The absolute standard duiation of transformed

rields from fiaal experimental malls dIstribution show in F:ie.5(吨'is 0.29铃，

rat.r,r smaller tban 由 .37惕. the absolute standard deviation by the neutron

Yields as shown in Fie. 5(b). If the i !1 ihal experimental mass yields are directly

-com阳red with final ones, we get th e- absolute standard deviation 0. 7J.. It is

-obYious that the tranlH'ormed yields is in betler acreement to final experimental

mass yields as is also evident from the (igure. The neutron yield distribution

prl'posed in the present paper is adopted in Fie.s{c) , the absolute standard devi­

-alion from final experimental yields is 0.43惕，

Combining the calculated neutron yields with the semi-empirical S-G凰ussian

formula (see ap"endix) , we can obtained the final yields as shown in Fig.S. The

.absolute standard deviation is 0.57411. The departure from final experiment is

not very much. Jt might be used for predicting final mass yield !i. The typical

precl1l1on of the prediction is about 士。.5* for absolute mass yield of actinides.

'"二 ..·』•

•..aas 且，·.·••

·"·•..~

Fil.6 Transrormation oC S-Gaunia. Cormula to Ciaal yields oC the finioa。r ,ItU ind四ced by tller.al 圃'回 t roOl "ith calculated neutron yield..

.s-Gall,..iall funclion l 川 I 0 fial 7ie1ι! "1 , + neuUOft 7ieldt b7 calω1at 1o圃. The solid linerep饵Hnts trlnsformed mass distribul1on.

Fill.7 is the example of transformalion from final to initial yieldl of I J'Uf11slon Induced by 3.9 MeV and 6.9 MeV neutron.lul with calculated neu­

tron function. Their absCllute .tandarel deviation. from the .eml-empirical 5-Gau-

• 11 •

uian formula are 0.50" and 0.39惕. respectively.

IωIn150I"1]0 la 1:10,.""'-dE '..

,,)

.•

•1...

S•

..•••

,

adMZ

••

S.

170"D.

7"

Mass yield t ra圃s(ormatioa of tole fissioa of "'U iDduc:cd by(a)3.9 MeV

aad (b) 队9 MeV ae皿ifoas fr01ll fiaal to iailial yields compared with the

5-Ga四ssiaa formu胁，

final ,ielck' IT ), 0 tb. 5-<#.田si.. ruu~iOll， ­

c.1eaI.t.d II'回trOll ,wid cliatrlbutiou.trolusr，町'回d iuitia1 distribut剧， aDd

Fi&.7

4‘

•

气h，尸

I.p.

••

•'

•••....

ad田野

aw.,,侃" 170"'

Fi&.8 Compari.ioa or tra圃.cormad mass ,i.lds from (jul to iaitial aad back

to nul with ulltrall tCorm.d fiaal ,i.ldl tor the tillioa ot UlU iaducad

by thermal aa幅tronl.

lig" rjeJds fJ • I , 0 t"".t",..d liuJ ri,JdJ, MId -+- J1eulrOll rjeld. by r.aJ.uJatiOll ••·1'·

Fic.8 proves that the method of transformation is self-consistent. Compari­

sion of the yields transformed from final to initial :o nd back to final with th.

unlraaslormed final yields Cives the absolule slalld,. rd dniation is 0.34".

10 order to illustrate that the method of transformatioD is applicable to

different fissioninl systems, we show the results of transformation from nDaI

to iamal yields with th. fission of lURa i 由dueed by 13 M.V protoas and spo.­

taaeGus fi黯ions of lltCm aad Ulef. Neutrcn rields adopt calculated fuactions.

T.eir ablolute standard deviatioas (If the traasformed yields are 0.20" , 0.53"

.nd 0.36铃， respectinly , compared with uperimental initial mass distributions

(refer to Fir;. 9).

.. .. It..电

I" 110 1211 1]0 140 I" 'IO 17.

2.

O.~70 '

5.111 '.'4.

3.

l.

O.....,J ""

7.11

•

。4国 fi.1

~ ;;, '1

::I .tl

SM-z 哺.

II.

5.

5.

Fi,.9 Compafilionl of mall yield. transform.d from liaal to initial with

u:perim.lI tl of initial dilt rib.tio四 UliDI calculat.d DIUt rOD yi.ld fuDctiO圃，• nul ,i,lds; 0 initial ,i,lds; ...川...四 .atron ,ields; .nd -t,a..lor..d dilkibatio圃. (a)…h

U..ion iadaCld b, 13 M,V prolon,' "1; (b) I..C. .ponta.,OII' n..io圃， i.itial ,ields to reler 10(I') and final ,i.lcIt to "," 10 t39J , (c) .ponlan.OII. lillon of 1.2Cf(4 01 ,

, 13 •

6. SUMMARY

W. have proposed it seven-mass-poiDt iDterpolatioD method to calculate

t!…elltroD yields as a function of fral lDent mass aDd liven the calculatioD

'oraa'a for the Deutron yields at those seven mass poiDts. which are 155. 138.

121. ~r/2. Ar/Z-5. Ar-138. and AI-ISS. The leneral treDds of aeutroD field

distribatiDs obtained by iDterpolation or extrapolation iD the fission of :a wide

raDle of nuclides from Ac to Cf with excitation enerlies from. spontan四"

白白loa to the 45 MeV alpha particles induced fission are well reproduced by this

method;

With the calculated neutron yields. the traosformation beh,een iailial aad

final fralmeat distributioos caD be performed by Terrel"s momeat method. The

tnasformed yields botb from initial to final and from final to initial are an

in accord with experiments in the fission of actinides. In prescnt work. the

calculatioas from initial to final and back ta initial or form final to initial

and back to final .re self-consistent.

CombiaiDI with the semi-empirical formala on theinitial fralment mass

distributions(see appendix). ODe could directly calculate fiDal mass yields with­

O1It aD1 reference to empirical data. The precision of prediction of tbe calcu­

..ted yields is about 土 o.s4' absolute yield ..ith elven fiaal experimental d iJtri­

butions.

The ..ork was done with the support of Chinese Nuclear Data Centre.

APPENDIXIn one of our previous worksill , which was written in Chinese. we have:

proposed a semi-empirical furmula on the pre-neutron-emlssion fralment distr•butionl in nuclear fission. The main formulae are given here for the cODvenlence

of their .pplication. The S-Gaussian (unction (ormula was

yeA. EI·) -C.G(A , A1/2 , P.o)+C.[G(A ， A.I，σ)+G(A ， Ar-A. ， σ)]

+C.[G(A ，Am ， Pmσ)+G(A ， A，-Am ，μmσ)] (AI)

In ..hich A is mall number of fragments , A, and E ,· are mass aumber and

excitation energies of the fil.loning nuclides , respectively.

G("，$，的-(σ¥'211r1np[-( t-幻Z/20Z j (A2)

is the Gaulllan functioo. and the fitted parametrrl were

• 14 •

C.(9的-O.Olesp(O.48E产}

1'.-1.4

C.( ~)-2.86(169.9-N， )+0 , 19(A ， -Z3Z.的E，·

(A3)

(A4)

(A5)

0'-5.τ-O.24(149.9-Nr)+O.12Er- (AI)

.A.- 141 .0-0.053£,- (AT)

c.(.. )-59. 3-0.213N,-O.01 7( ..4，-23号 .7)E，产 (AI)

".-1.刷-O.0094N，+O.2f'i esp[-(N,-142.5)11

+0.114 esp[-IN,-148.1I1 (At).....A.-12.3+0.2t3N ，+O.IZ， -O.03E产 (AIO)

i. wllieh N, aDd Z, are 四..tro…d protoo oumbers of fi臼io.i吨 ..elides.

rftpedinl,. The coefficjeot. of Ca.ssi.. faactioas ia Eq.(AI) mast be 1101'­

I8.liz" witb tlae factor

~== loo/(C./2+C.+C.) (All)The ablOl.te stao.ard dniatio…41 lDu:i lDum depart.re bet.eell c.lc.late.

yalaes aad experimental mass dislribalio.1 for (0. f) a.d (..圃'f) (illioa r.ac­

tio，，~ from U lTb to1"em are approximately 0.4. a.d 0.a.. I'臼pectinl ，. The

5-Ga.ssiao fuaction is in better accord .ith nperimellts of 10., eaerlY fissioD.

For (o.2a'f) reactioos .nd protoll aod alpba particle ioduced fissie.圃'. larpl'

-cluiatioas ml1Y occur. It misbt provide iailial data if the precision req田irelDeot

4Jf tbe prediction is n创刊ry hilb.

REFERENCES

( I] WaDI FDcbtal aad H. n_i. , C.i.a aAclear SCi'DU " T，础Dol咱 R.阳t. em阵OOIIJ/PU

·饵101 ， 1811.

(t] T_II , J.. 阳，...Rn'.， 127 (J96Z) 810.

IS] Wilki.. , B.D. at .1., ibid. , CI4 (J切的 IIU.

t 4] Bow.a圃. H. R. d aI.. ibid.. 1%9 (1883) 3122.{5) Gi.d1町. J. , ibid.. CI9 (J衍8) 1108.f6] V翩翩翩 Hi.. at aI., J. N.cl. Sci. Tcch.. 18 (酬的 488.

{7]酌..ak.l ， Z. aDd Ma,.k, I. , Ph,... Rn'.. CIZ (J~日 11Ot.

II J S--"lIIitt. H. W aDd K阅饵8，..旦. Ph,... i n'. Lett.. 18 忖蝴) I嗣­

(II J Apli画， V. F. et al.. Nad. Ph,..., 71 (1885) 553.(IOJ M..1i筒. E. E. at aI., Ph,... Rn'叶 184 (188η1520.

(II] 刷刷， J. C. D. and P,_. J.鼠， i. Proc. of tbe Fi,.t 5,.p. o. t" P"7'iCI a.d C..i.-t" of Fi..io.. S.lab.fI. IAEA. Vien.a. V.2. 1885. 仇39.

f!2] Dr剿. H. (;. and Whet.tODC. S. L.. J,.. Phy.. I".. 1338 (In份回3.

113J V..a皿010 ， Hilllo d .1. , J. Nud. Sci. Tec.... 18 (18'1的'(1 8.

114J s.,nett , S. C. et 此，阳". in.. C3 (/971) 20剖，

11盯Ii.hop. C. J. It .1. N.d. Ph,... AlSO (I町的 1211.

(18] T"im肘. H. et 此. ibid.. A342 (1111的 228.

tl7] Clleifllt&, Eli 'lId F,lIak.l. Zen. ,.,.. Rn. Lett ,. 21('1808) 钩，

l11J K".idt. R. and H.II..I , H. , N田:I. Pb,... A蹄。"的 211

们8J Sch.剿，日.W. 1It矶. Ph,.. Rn'.. 137B (188ω.37.

Uo] Siplfbie 圃嚣， C. et 矶， 阳，. Lltt. , 38B ( 1IrT2)ω3.

• J6 •

-.

stIl] W曲Ia. R. L. uti.峙.... J. W.. NKl.阳'1S..A%T1 (Illηla.

12%] Fill.町、 F. L..J.N圃J. Euru. 2! (I蝇的施，

In] C曲.. B. L. ct ... Playa. Ru.. IN (1956) 10f6.

1M] T，帽reU. J.. ilN.. II. (I锚η 币3.

(Z5] .恤副.. J. W. ..4 Hi.也. .1. G.. S.d. 如. E.I.. 91 (191ω.

(lIJ Lhrar也.G. ft A... llI.d E.tI'D'. 9 (191%> 1%1.

lIT] H植a.D. A. .t Plays. Rh'.. 101 (闹剧 li)l6

(21] 阳na. B. C. d ib幅.. 101 (I揭的 1012

12'] G.i.. R. ft 此. Nad. Sci. EIII.. 17 (I.的 3111.

(30) Diftl'. B. C. II 挝.. ....Wisllnl. to _ mt....a 24.

I'll S曲曲匾. M. .t 乱. J. Nad. E.erv. 23 (1911) 251.lsz) Jat1'7. A. H. ..4 Ler.er. J. L.. N.c!. "y;.. AI4Sυ97时 I.

IIJ1 日"、 R曲rt E.. Nad. Sci E鸣.. 16 (1114) I町.

(M) ..饵mi. F. ..d KouIai. V. 儿. At..比 E..咽Rn.. IG (lDi%) 13i. ,I副 U.ik. J.p. ft a1.. i. Pre=. or llae tlaird Sf.lI. .R lbe P1ayUb Ad C..istr)" of FiAiu.

lteCMSt筐. (IAEA-SIH741犁II) • V.2. Ifi3. '.19.

(-1 C..i.仙耐. J. G.. 崎町t. AERE-R-I1臼.1911.

l幻1 N岖"t. S. ft .... "fS.Rn.. CIT (IIJ1U 163.

I揭1 JU.c.f. E. ..d SCIaa恼.H. w.. 阳Js. Rn.." IT~ (I"') 1%13.

I») Fl,,,, K. F. ft a1.. ibid.. c6 (J972) 2%11.

(40) sda四u. H. W. ft .... iltid.. 141 (I.) 1146.

• 16 •

。唰A M.比LEAR 创剧岱& TECHNOLOGY REPORT

@

P.O.Box 2103

Beijing, China

书号I 15175-00293

China Nuclear Infor町、ation Centre