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ABOUT THIS REPORT

This official electronic version was created by scanning the best available paper or microfiche copy of the original report at a 300 dpi resolution. Original color illustrations appear as black and white images. For additional information or comments, contact: Library Without Walls Project Los Alamos National Laboratory Research Library Los Alamos, NM 87544 Phone: (505)667-4448 E-mail: [email protected]

C O

ABSTRACT.......................................................................1

I T HA E V AO N UC S E....................

ABc

D

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A v eF uC rS ef P oP A p.R - MA n ao R e ai t 4 S .............

C o mF o k kT ro S lD D t SC h a r g eE lS c a..................................4H a u s eP a rS tf N ia O CSection Calculations.................................................6E v a lo N e u tR eo I ...............C a l co n +C S eu t N E o20 MeV..............................................................1n + zE v af R e2 o E N................C rS e cC a lU M i ca O L eModels..............................................................2A d do G a mP r oD t t E N1Evaluation..........................................................34C o nM a ta L C oC r oD .........C a l co E x c iC S ef 1 ........C a l co E x c iC S ef A N .C o u p lC a lf n + Z S c........I n iC a l co P rF iN eS a ~ ft N e u t rF i s2 3......... . . . . .....

I N U CC R O SP R OA T E.......................

A T i m e -P hS pf F io 2 a 2 3. . .

B New Version of NJOY.................................................5c I AP r oC C o m...........................D

...E n e r g yo U n r e sC S e.........

E N N o nC a pi A .............................

I IF I SP R OA A C TY ID D D EABUILDUP..................................................................61

A S u mF i s s ia A cD a..................B Delayed Neutron Data and Spectra....................................61c Fission-ProductYield Status........................................62D D e v eo C IL if S pP C a.E D e v eo t S OC a D L f t C

o N eS oa S pf ( R eS pF i sand $ Delayed Neutrons.....................................65

I N E U TF C AL MC C OD E...........

REFERENCES....................................................................78

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F i3 6D i r ei n e l ac r os e cf t s c a to n ebi t a r gs t a ti d e n tt t ho F 3 N t t a bo t hc o u p l e d - c ho p t ip o t eu si t c a l ci ow i sc o n t i n ua n e u te n e ro 6 a 9 M

1

pp

4

2S

5azoz

i~

F i3 7n e u t r o

4 Uy I I 1 I I 1 I # I

,

,

*,,,

b‘ ; ,+ n c o mn uc r3 S a,‘‘ — G rs t‘ ‘ - - - - - - F‘‘3

2 -

/

s e

s e

. Lo 1 2 3 4

E,n ~MeV)6 7 8 0 10

C o m p o uf o rc s ef t s cob 1 6i t as ti dt t o F 3

T V

N EC R O SC O MF 1I n c i d e nN eE n e r= 1 k e

G r o u nS t a tl s t - E x c iS t aD i f f eC r o s sS e c( r( r(

T o1 41 3-

E l a7 5 -I l e7 8 1C oN 7 8 1T oI n6 9 3C a p2 2 3

I n cN eE n e r= 1 0k e

G r o u oS t a tl s t - E x c iS t aC r o s sS e c t i o n( r( r

T o t a l1 0 2 88 9 7

E l a s t i c5 4R e a4 34

C oN u4 34

T oI n1 16

C a p6 9

D i(

-

-

3

3

-

5

4

T AV ( C)

N EC R O SC O MF 1

I n cN eE n= 1 M

G rS tl s tS D iC rS e c( r( (

T o7 7 0

E l a4 3 -

R e a3 3 1

C oN u2 3 1

T oI n2 3 1

C a p1 1 1

I n cN eE n= 5 M

G rS tl s tS D iC rS e c( r( (

T o5 5 - 0

E l a2 2 3

R e a3 2 -

C oN u2 2 -

T oI n3 2 -

C a p9 8 -

T H a u s es t a t ic a lw p u

t c oC O Mt o bt c oe lc oi na c

t uc rs e ca a f uo i nn ee o t r 1

k t 8 M w ht ( nr ec ho T c oc

c h at r a nc o es T (f g ra f

c i t es c a td e sa w u i t c aT

c a pc rs ew c a li t B rg d m a

p r o x i m a tf ot hg a mt r a n s mc o e f f

0 . 0 7 9w au sa n2 d ic as tw

t uc o mw c a l c

R e sf rt s t a t ic a l

3 a 3 a a g iq u a ni T V

A v o 2 T=

i nN d c

a i li F

f f i n

e n e rT t oi n e l a s( dp c oc s

i s hi F i3 f t t ai t g rs a i t f i

s tO o b si t f i r s tc a “ ac

s e cv a rf - 3 b at - 0 b a t n e i

f r1 k t 1 0k t e x ce no t 5 s r t

4

w o

3 a o o

a

1 o

I a+ n t t .i h t c rs e

— Gs- - - - - - Fs

,.,8 , -, ,,8s ,, .9 ,* ,8 .s

●

#8‘‘‘‘‘ ‘ ‘ ‘ ‘ ...

0 * , , , / ,, # , , I , , , I 1 m , , 1 1 1 , I 1 , 1 t

1 01u

fE 1~I I

F i3 8T oi n e lc rs e( .p c cf t s

t e ro n e ub I Gi t as ti dt t o F 3

+ n c a pc rs e

— G rs t- - - - - - F is t

I ~ . d, - I ~, I1 01 1

E ( MI I

F i g3 9C a pc rs e cf t s c ao n eb 1 i

t a rs t ai d e nt t ho F 3

4

t h ao t h3 /s t a tT “ a c cc s ei j t i

t r a nf rt 3 t as tt t 1 t g s i w

t n e ug at e no t t r aT “ ac s

t ie xf a n ee n eb i i t o a i

t r a nf E < 1 0k i t f i r s tt c O a

o b si F i3 t t t h rf e xs uh l

s ti i n es c aa ld ib t s a 8 k i

c o m pc o r r et h rf g r oa f i r

t as c a tT i o c ob et e xe d

e nb e tt t t as ti 8 k

T c a pc rs e ca s i F 3 H t c c

s e cf rt t ai t f i rs d ot f t

t ai t g rs to m o t e nr c oO a

o b st 8 . 4s hi t t h ro c o ri s

t et r a n sd e sa bw a s h v c ow

i n e ls c a t

O o t m i n ta so s tt t i a

c a pc rs e ci g r o ua f i r st c

u r ai t ht m a go t c s ec b q d

f t t c o n f iw a t s t t m ao t c

s p oc o m p o uf o rc s ea a t s A T

V s hf E = 1 k t c o m pf oc s d

b 3 .w ht t oi n ea c ac s ed b -

a 5 0r e s p eT hi i n c ot a t n e

c o m p o uf o rc rs ei n e c oo t

c o m p o u n d - n u cf o r m ac r os e c t

L C a l co E x c iC S ef A cN ( G

M a d

C o u p l ec a l ch b p ef t s9 9

o

n e u t r ob ‘ “a ‘ Jw t ht ae xi t g s a

i t f i r s ts tT c a lw p eu t c

J L J( sR e2 p 2 8T t os e lr d

i n e la c o m p of oc s ew c

t o gw it c o r rc o mt r ac oT

a a f u no i n cn ee no t r 1 k t 1 M T

4

r e s ut r a nc o es f b g ra f

c i t ec aw b u i H a u ss t ac

t i

P e rd eo t c a la a f oT a c7p l e d -p o to M aa Y w u t hI p

u lt f i r s t - ec a lw c o b u o t

p o t et o gw a e nt r at i d ef r

p r oT d e f op a ru f 2 a ~ = 0.200 and ~4 =

0 .f rR 7 a t hu f 2 a $ = 0 a ~ = 0

f rR e7 T e x po ro t c of f u i J i

A = 8 ( L ep o lP A m ar o 1 F w c a t

a l g of t m ap r oo ra nm o2 i Q +

1 = 2.5(kR + 1) + Imax, w hk i t n ew n R i t n

r a da I i t m as o ci t s o c s‘ aI t c ao U t hs to t g b w c w I =

4 w h ei t c o2

P f s to t g b w c

w iI = 9r nR e sf t c a l ca i li F 4 t 4

w hc o m po g r o ua f i r sc s a

m af b o2 a 2 3C o nt f r o o

t ht t oa c o m p of oc s ea s i t

t a r gn u c la ri t hf i r s t - es ti no t ( ug

s tw h et e lc rs ea l aT s d i

e l a s t i cc rs ea s mf t t n i t

f i r s ts to m o t e nr c oP t m

i n t ec ua t ho c on uf os i F 4

a 4 T hi n di t f er et t c c

e l ac o mi n ec aa f ic s a a

m a1 t 1 l f t t t an i t f is

c o mw ib ei t g rs tT r w a o i t7e aJ Ut c a l cf t c o 2 T t f c

2 a2

s e cf P i t f i rs m b s l

t ht c o r r ef ic s ef t n i t g

s t aW i nt t t s u pu t c at

c o e fs T ! j i s t a t ic ao t c s

t if f i sa c o mr e a

4

1 1 0 0 01 I I 1 I 1 1 I I

I o m on ‘ + n t c s

s aJ 1 1 I 1 1 I 1 I I 10 1 2 3 4

E,AB?MeV) 6 7 6 ‘ 10F i4 T oc rs e$ t s a to n eb 2 i t O

+

0 .g rs ta i t 2t i n cn e ue n

0 .f i rs a a f o

M 1 1 I 1 1 1 1 1 1

1

t

1000O \

2 + n t c s

Hwoo \ — sn - -e s ;

~ 6 0 0 0

I- -- -

b

7 0 r m

6 0 0 0

5 o o1 I 1 1 I 1 I I I 10 1 2 3 4

E,A,~MeV) 6 7 ‘ 9 1°

F i4 1T o tc r os e c tf ot $ c a to n eb Z i t1 0 .g rs ta i t 3 0 .f i rs a a ft io t i n cn ee n

4

9 1 I 1 [ 1 1 1 I 1 !

I8000’

a8U + n elastic cross section 17M)0

h

—Ground statez -----Firs t-excitedg 6000‘:;

i ‘:;,,,,:-b

stat e

4

44mxl

XKm

2ax)-‘“ 1 1 I I 1 1 I 1 1

0 1 2 3 4ELAB~MeV)6 ‘ 8 ‘ 1°

Fig. 42. Elasticcrosssectionfor the scatteringof neutronsby 238U intargetstatesidenticalto thoseof Fig. 40.

6000

7000

6(X)0

-5000

gg 4000Eiib-

Zmo

1 1 I 1 1 1 1 1 I

-----First-excited state

11000

0 I I 1 1 1 I 1 1 !

o 1 2 3 4ELAB~MeV)6 ‘ 8 ‘ 1°

Fig. 43. Elasticcrosssectionfor the scatteringof neutronsby 239Puintargetstatesidenticalto thoseof Fig. 41.

47

1“‘ ‘ “ ‘ “ ‘ ‘ ‘ ‘ ‘ “ “ ‘ ‘ ‘ “ ‘ “ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ “ “ ‘ s‘ “ “ ‘ ‘ “ ‘‘1

500

400

300

200

ml

o

!J

----...... direct inelastic cross section.,’##

-------First-excited state1’:

1....1....1....!... .1....1..,,1,..1.s. .It..l...,lo 1 2 3 4

ELAB~MeV)6 ‘ 8 9 ‘“

Fig. 44. Directinelasticcrosssectionfor the scatteringof neutronsby 238Uin targetstatesidenticalto thoseof Fig. 40.

600 1 1 1 I I 1 1 I 1

Soo

1(XI

0

L

-..,

,

,

,

,.

,

,’

1’

;

1 I 1 1 1 1 1 1 1 I

direct inelastic cross

—Ground state-------First-excited state

10 1 2 3 4

E,AB~MeV)6 ‘ ‘ g ‘0

Fig. 45. Directinelasticcrosssectionfor the scatteringof neutronsby 239Puin targetstatesidenticalto thoseof Fig. 41.

48

3600*

26m

26000 1 2 3 4

E,AB?MeV)‘ 7 8 g ‘0

. . . . . . . . . . . . .I 1 4 1 r r 1

2W + n compound-nucleus cross section.

-----First-excited stateo,

‘.-.’ ----------------

1 1 1 1 1 1 1 t I

Fig. 46. Compound-nucleusformationcrosssectionfor the scatteringof neutronsby 238uin targetstatesidenticalto thoseof Fig. AO.

4000

3800

1 I I I 1 I I I I

239pu+ n compound.nucleus cross section.

-----First-excited state

,

‘. ,’‘. .--..

t

1.,..l...,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ..:o 1 2 3 4

ELAB[MeV)‘ 7 ‘ ‘ ‘0

Fig. 47. Compound-nucleusformationcrosssectionfor the scatteringof neutronsby 239puin targetstate5identicalto thoseof %. Al.

49

M. Coupled-ChannelCalculationsfor n + 237Np Scattering (D.G. Madland)

Preliminarycoupled-channelcalculationshavebeenperformedfor the scat-

tering of neutronsby 237Np. The calculationswere performedusing the code

JUPXST\6 The total,shape elastic,reaction,directinelastic,and compound-

nucleusformationcrosssectionswere calculated,togetherwith the correspond-

ing compactedtransmissioncoefficientsT(Q,j),as a functionof incidentneu-

tronenergyoverthe range1 keV to 20 MeV. The resultingtransmissioncoeffi-

cient sets will be used in Hauser-Feshbachstatistical-modelcalculations.

Pertinentdetailsof the calculationsare as follows. The actinidecou-77pled-channelpotentialof Madlandand Young was used throughout.The defor-

mationparametersused are ~2 = 0.214and @4 = 0.074. Theseare obtainedfrom

the theoreticalcalculationsof M611er and Nix80

Nix\’

and M611er, Nilsson, and

However,the valueof ~4 was scaleddownwardfromthe theoreticalvalue

0.104to the abovevalueusinga scalefactorobtainedfromcomparingtheoreti-238cal and experimental(neutronscattering)~4 values for U and 239Pu. This

procedurewas followedbecausethereare no knownexperimentalvaluesof ~4 for237Np. The theoreticalvalue of ~z was not similarlyadjustedbecausethe

scaledvalue (0.210)is only slightlydifferent. The expansionorder of the

complexformfactorused in .JUPXSTis A = 8 (LegendrepolynomialP8). A match-

ing radius of 14.0F was chosenand the algorithmfor the maximumprojectile

orbitalangularmomentum,Q is Q = 2.5 (kR+l)+ Imax,where k is themax> maxneutronwave number,R is the nuclearradius,and Imax is the maximumspin

occurringin the set of coupledstates. For thesecalculationsthe firstthree

membersof the ground-staterotationalbandwere coupled. Theseare the (5/2+,

0.00),(7/2+,0.0332),and (9/2+,0.0758)states.

The resultsof these preliminarycalculationsare shown in Figs. 48-51

where,respectively,the total,elastic,summeddirectinelastic,and compound-

nucleusformationcrosssectionsare shown.

50

‘Np + n total cross section

12aoo

\-

Wm , , , 1 I , ,

104 ?’EM 1MeV)Id

Fig. 48. Calculatedtotalcrosssectionfor the scatteringof neutronsbyZSTNPas a functionof the incidentneutronenergy.

4W0

, , , , , I , , 1 u , 1 r

‘Np + n elastic cross section

2UOOI , t a , , 1A. , . . . . . .

10-’

Fig. 49. Calculated237NPas a function

?)EwlMeV

elasticcrosssectionfor the scatteringof neutronsbyof the incidentneutronenergy.

51

MO , 1 I , , 1 1 m I B 1 r r n I I n

237NP + n direct inelastic cross section-

4m

3a-“200

j

P’ :b=

loo

0 * , , , 1 , , & , , 1 *10-’

hd

Ew 1MeV

Fig. 50. Calculateddirectinelasticcrosssectionfor the scatteringofneutronsby 297NP~5 ~ functionof the incidentneutronenergY.

4500 , , 1 I , , , , I 1 , u 8 1 m u u

237NP + n Compound.nucleus cross *ction--

3g

i- i8Ii~8

am

rmao , , , 1 * , , , , I104

t)id

EulMeV

Fig. 51. Calculatedcompound-nucleusformationcrosssectionfor the scat-teringof neutronsby ZSTNPas a fmction of the incidentneutronenergy.

52

N. InitialCalculationof PromptFissionNeutronSpectraand ; for the Neutron-237N P

InducedFissionof (D.G. Madland)

Preliminarycalculationsof the prompt fissionneutronspectrumN(E) and

the averagepromptneutronmultiplicity; havebeen carriedout for the 237Np+P

n system. Althoughfairly completemeasurementsof ; have been made, veryP

little data exist on the prompt fissionneutronspectrumfor this nucleus.

Moreover,the ENDF/B-Vrepresentationof the fissionspectrumis inadequate,

consistingof a simpleMaxwellianwith a singletemperatureparameter,1.315

MeV, for all incidentneutronenergies. Sincethe fissionspectrumN(E) and ;P

are stronglycoupled,we calculateboth in order to obtainthe best physical

representation.

Pertinentdetailsof the calculationsare as follows. The constantcom-35pound-nucleuscrosssectionapproximation was used in the calculationof both

N(E) and ; . The seven-pointapproximation35P

was used in the calculationof

the averageenergyreleasein fission<Er> and the averageneutronseparation

energy <Sn>. 100The peaks of the fragmentmass distributionwere taken as 39Y

and 138~4Xe,basedon systematicof nearbyactinidesand the empiricalresultof

an average departureof 1/2 charge unit from the unchangedcharge density

assumptionin fissionfragmentformation. The totalaveragefissionfragment

kineticenergy<EftOt> and totalaveragepromptgammaenergy<E tot> were cal-1!

culatedto have the values 174.3MeV and 6.754MeV, respectively.The effec-

tive level-densityparameterused in the calculationsis aeff = A/(10.OMeV),

fromRef. 35.

Some of the resultsthus far are illustratedin Figs. 52 and 53, where

comparisonsof our calculatedspectraand the ENDF/B-VMaxwellianare made for

neutronenergiesof 1 and 3 MeV. Thesecomparisonsshowthe energydependence

of our spectrum(theENDF/B-Vspectrumis independentof energy),and they show

that our spectrumis, in general,harderthanthe ENDF/B-Vspectrum. The cal-

culationsperformedthus far haveused defaultparametervalues. Our next step

is to takeintoaccountthe influenceof the ;P experimentaldata.

53

Id’

— Los Alamos Theory

5 10 15Laboratory Neutron Energy E (MeV)

Fig. 52. Comparisonof calculatedpromptfissionneutronspectrafor the neutron-inducedfissionof 237NPby 1 MeV neutrons.

Id I I I I I I [ I I I I I I I 3-?

— Los Alamos Theory

10+ I 1 I I I 1 1 1 1 1 1 1 I I

o 1!5Laboratory Neutron Energ~”E (MeV)

Fig.53. Comparisonof calculatedpromptfissionneutronspectrafor the neutron-inducedfissionof 237NPby 3 MeV neUtrOnS.

54

II. NUCLEARCROSS-SECTIONPROCESSINGAND TESTING

A. Time-DependentPhotonSpectrafromFissionof 235Uand 2B Pu (D.G. Foster)

At the request of P-15, we have resurrecteda small computerprogram,

FISGAM,that calculatesprompt-photonyieldsand time-dependentdelayed-photon235intensitiesfollowingfissionof U and 23’Pu. This work is describedin

Ref. 82, p. 3, which discussesthe sourcesof the dataand the ❑annerin which

theywere adaptedfor thisuse. Briefly,the promptspectrumis representedin

histogramform,and the delayedintensitiesare reconstructedfrom the half-

livesand initialintensitiesof discreteemissionlines. We approximateun-

resolvedcontinuumemissionwith a two-termexponentialseriesfittedto each

originalbroad experimentalbin. This techniqueallowsone to calculatethe

spectraand their integralsover time from less than 1 ns to 50 s after fis-

sion,with an estimatedaccuracyof 20%.

In the processof resurrectingFISGAM,we have also made someneededim-

provements. The inputdata now residein a FORTRANblock-datasubroutine,in-

steadof being read from an externalfile. The originalroutinefor rebinning

histogramshas also been replacedwith an improvedversionof REBIN (seeRef.

83, pp. 29-30). All of the inputdataare now representedin the energygrids

that were used in the originalmeasurements.

grid suitableto the application,and FISGAM

thisgrid.

The usernow suppliesa spectrum

convertsall sourcesof inputto

B. New Versionof NJOY (R.E. MacFarlaneand D. W. Muir)

Work continueson correctingand refiningthe most recentlyreleasedver-

sion of the NJOY nucleardataprocessingsystem,NJOY (10/81). The latestset

of corrections,reportedin NJOY Note 10/81-4,are summarizedin the following

paragraph.In addition,a numberof new capabilitieshave been implementedin

the Los Alamosversionof NJOY. Thesenew capabilities,becauseof the substan-

tial number of line changesrequired,have not yet been releasedto the NJOY

general-usercommunity.A new resequencedversion,NJOY (6/83),which incorpo-

ratesall currentcode corrections,as well as thesenew capabilities,willbe

releasedto the codecentersin June 1983. The new capabilitiesof NJOY (6/83)

are also describedbelow.

55

The correctionsreportedin NJOYNote 10/81-4fix a numberof minorerrors

and improvetransportabilityto IBM, VAX, and FORTRAN-77systems. Other up-

dates affectthe calculationof gammaproductionforK and Cl in ENDF/B-V,the

linearizationof small cross sectionsin RECONR,the subdivisionof the unre-

solvedenergyrange in RECONRand UNRESR,discretescatteringfromthe highest

energygroupin GROUPR,and the controlof precision(SIGFIG).

The additionalchangesin NJOY (6/83)includemany “clean-up”and IBM-and

FORTRAN-77-compatibilityupdates. Significantnew capabilitiesinclude:addi-

tionof the Los Alamos80-group,SAND-II640-group,and EURLIB100-group“built-

intlstructures,plus 80-groupand CLAW weight functionsin GROUPR;a full

treatmentof ratio-to-standardcovariances(seeRef. 26, pp. 45-49)in ERRORR,

as well as new lumped-partial,LB=4, and LB=6 covariancecapabilitiesin that

module;a new compressed-libraryoutputformat(theBOXERformat84) in COVR;a

new photon productionformat and FORTRAN-77output in ACER; delayedneutron

outputin POWR;and finally,betterfission-matrixpackingin NMATXS.

Changeswere also made in GROUPR,ERRORR,COVR,and MODERto supportfull

use of largegroup structures(upto 64o groups)in thesemodules. Anyonein-

tendingto use NJOY on IBM or VAX machines,as well as users needingERRORR,

COVR, ACER, POWR, or NMATXS, shouldmove to the new versionas soon as pos-

sible.

c. IAEAProcessingCodeComparison(R.E. MacFarlaneand D. W. Muir)

SinceJune 1981,we have been participatingin a nucleardataprocessing85,86code verificationproject, organizedby the NuclearData Sectionof the

InternationalAtomicEnergyAgency (IAEA/NDS).The firstroundof comparisons

requiredthe calculationof the 36 reactionson the ENDF/B-VDosimetryTape

(Tape531). All cross sectionswere linearizedand resonance-reconstructedat

zero degreesKelvin,both to an accuracyof 0.1%, using the RECONRmoduleof

NJOY. Then, infinite-dilution,flat-weightedcross sectionswere calculated

with the GROUPRmodule in the 640-groupSAND-IIgroupstructure,as a meansof

reducingthe volume of data to be compared. These resultswere sent to the

IAEA/NDSfor comparisonwith the resultsof similarcalculationsperformedat

otherresearchinstallations.

Overall,the resultsfrom these comparisonshave been reassuring.Some

disagreementswere foundfor very smallcrosssections,for example,near reac-

tion thresholds. As a result,we have tightenedsomewhatthe linearization

56

Iaccuracycriterionused in RECONR. Also some 1-2% disagreementsoccurredin

the unresolved-resonancerange becauseof the use of parameterinterpolation

insteadof cross-sectioninterpolation.As discussedin the followingsection,

both RECONRand UNRESRnow use cross-sectioninterpolationfor materialswith

energy-dependentunresolvedparameters. A minor exceptionis that parameter

interpolationis retainedin any unresolved‘!panell?that is unusuallywide,

becausethe l/v behaviorof low-energycrosssectionswould be poorly repre-

sentedthereby linearcross-sectioninterpolation.The situationis somewhat

differentin the case of materialswith energy-independentunresolvedparam-

eters. At least some of the codes in use elsewherehave been using (incor-

rectly)cross-sectioninterpolationfor thesematerials,ratherthanparameter

interpolation,as is done in NJOY.

As a

dosimetry

available

by-productof this work, a complete640-group

crosssectionshas been generatedwith the latest

fromthe Los AlamosNuclearData group.

libraryof ENDF/B-V

NJOY versionand is

D. Energy-Dependenceof Unresolved-RegionCrossSections(R.E. MacFarlane

and D. W. Muir)

Cross sectionsin the unresolvedenergyrangeare computedfrom average

resonanceparametersgiven by the evaluator. The parametersare either (1)

independentof energywithinthe givenenergyrangeor (2)theyare givenon a

particulargrid of energiesin thisrange. For earlierversionsof the ENDF/B

format,the full energydependenceof the crosssectionswas definedby either

(1)computingthe crosssectionsfrom the energy-independentparametersat each

energyor (2) computingthe crosssectionfromparametersobtainedby interpo-

latingbetweenthe valuesgivenat the adjacentenergygridpoints.

For ENDF/B-V,it was decidedto use cross-sectioninterpolationinsteadof

parameterinterpolationin many cases. However,the procedureswritteninto

the formatmanual87 were ambiguous(seeespeciallyp. 2.20and pp. 2.23-2.25).

This ambiguityshowed up in the IAEA-processingcode comparisonsdiscussed

above. The followingcommentsare intendedto call attentionto the differ-

encesseen,and to suggestthe bestprocedureto use for each case.

When energy-independentparametersare given, the manual statesclearly

that the cross sectionmust be computedfrom the parametersat intermediate

energiesand not obtainedby interpolatingbetweenthe cross sectionsat the

ends of the unresolvedrange (p.2.23). Someversionsof someof the process-

ing codes have incorrectlyused cross-sectioninterpolationin this case.57

For evaluationsusing energy-dependentparameters,cross-sectioninter-

polation should be used. However, some evaluationsdo not have a “dense

enoughtfmesh (seep. 2.24) to representthe approximateI/v energydependence

of the captureand the possiblymore complicatedshape of the fissionat the

sametime. Usingthe ‘official”cross-sectioninterpolationcan leadto errors238as large as 50% for Pu and 25% for 237Np. For suchevaluations,parameter

interpolationgivesbetteranswers.

The ultimatesolutionto this problem is to re-evaluatethe unresolved

resonanceparametersfor the problemisotopes. Thiswill takeseveralyearsat

currentlevelsof activity. In the meantime,we are recommendingto the Cross

SectionEvaluationWorking Group (CSEWG)that the proceduresbe changed.We

suggestthat any energy intervalin the unresolvedrange that is wider than

some specifiedvalue (for example,a factorof 3) shouldbe subdividedusing

parameterinterpolation.This proceduregives reasonableresultsfor all the

materialsof ENDF/B-V.

E. New NonlinearCapabilityin ALVIN (D.W. Muir)

In least squaresdata-adjustmentstudies,the measuredintegraldata can

be stronglynon-linearfunctionsof the cross sections. The most commonnon-

linearityoccurswhen the integralquantityT(Z) is approximatelyan exponen-

tial function,

T(Z)= a exp(-Zr) ,

where Z is the macroscopiccrosssectionand r is the spatiallocation.If the

crosssectionZ has an uncertaintyAZ, thenthe conditionfor linearityof T(Z)

overthe rangeof adjustmentof 2 is, in this case,

AZ” r << 1 . (1)

This conditionis not satisfiedin typicalneutron-shieldingintegralexperi-

ments,88for example. In a linear least squaresadjustmentprogramsuch as

ALVIN,8’a linearmodel is used to approximateT(2) in the neighborhoodof the

evaluatedcross-sectionvalues,but, in these nonlinearproblems,the model

breaks down before the solutionpoint is reached. Becauseit is the linear

model,and not T(2), thatis actuallyused to calculatethe calculation/measure-

ment discrepanciesin the least squaresmethod,deficienciesof the modelwill58

distortthe adjusteddata in the sameway

measurement.

Fortunately,this calculationalbias

tions by an iterativeprocedure,wherein

firstpass is used as the referencepoint

as systematicerrorsin the integral

can be reducedto negligiblepropor-

the least squaressolutionfrom the

for the linearmodelfor the second

pass, and so on. Such a procedurecan now be followed,using a new user-se-

lectedoptionin ALVIN. With this option,a distinctionis drawnbetweenthe

evaluatednucleardata set and the referencenucleardata set. The evaluated

set (for example,ENDF/B-V)is based solelyon differentialmeasurementsand

doesnot changefromone iterationto the next. The inputcross-sectioncovari-

ances are a propertyof the evaluatedset and, likewise,do not change. The

referenceset, on the otherhand, is simplythe mathematicalreferencepoint

for a Taylor-seriesexpansionof T(Z), and this point is allowedto vary.

The inputsensitivitycoefficientsare evaluatedat the referencepoint,

and thus they must be recalculatedfor each iteration. By convention,sensi-

tivitiesare normalized(whetherproducedby the sensitivitymoduleof ALVINor

by a separatesensitivitycode)by dividingthe fractionalchangein the in-

tegralsby the fractionalchangein the referencecross sections. Thus, the

referenceset must be suppliedexplicitlyto ALVIN,when using the new option,

so thatALVINcan renormalizethe sensitivitiesto the evaluatedset.

To explainthis step in more detail,the relationshipbetween

linear functionti(x) and the cross-sectiondata can be expandedinrefseriesaboutthe referencepointx ,

the non-

a Taylor

ati(x)ti(x)l = ti(xref)+2 ax (Xj- X;ef) .

lin j j ref

Next,dividethroughby the evaluated(thatis, measured)valuesof the integral

and differentialdata,

ti(x)

tieval

‘:i:i:)+K2refl(@--)”lin i

Denotingthe quantityin squarebracketsS:;, we obtainthe explicitform of~J

the linearmodelused in ALVIN,59

ti(x)

tieval

refti(x )

()

ref

= + 2 s.. &_& .eval

lin ‘i j IJ ‘j

‘j

The sensitivitycodes do not provide the elementsof S directly,but

ratherS, where

ref ati(x)E .+ij ax .

ti(x ) j ref

Thus, ALVIN performsthe followingrenormalizationof the inputsensitivities,

ti(x‘ef) xevals = 3.. +.ij IJ teval

i ‘j

The user input is only slightlychangedfrom that describedin Ref. 89.

First, the control-parametercard, which previouslycontained4 parameters

(KSENS,KADJST,MI, MJ), now contains5 parameters(KSENS,KADJST,KREF, MI,

MJ). KREF=lmeansuse the originalcalculationalpath wherethe referencedata

are identicalwith the evaluateddata, and KREF=2meansthatthe referencedata

may be differentfrom the evaluateddata, as in the caseof non-linearitera-

tion. If KREF=2, one enters (withtitle cards)two new arrays,namely,XR(J)

and YR(I),and not YC(I). XR(J)is the referencedifferentialdatavector,ex-

pressedas ratiosto the evaluated(measured)differentialdata, and YR(I)is

the integraldatavectorcalculatedat the referencepoint,expressedas ratios

to the evaluated(measured)integraldata. Upon input,the arrayDYDX(I,J)in

ALVINis equalto the relativesensitivity,Eq.(2),as calculatedat the evalu-

ateddatapoint (KREF=l)or the referencedatapoint (KREF=2).

In all test calculationsperformedto date using the new option,the

referencedata set is observedto approachthe solutionset very rapidly.

Adjustmentfactors(adjusteddata+ evaluateddata)approachasymptoticvalues,

reachingfour-placeagreementafter just 3 or 4 iterations. The new ALVIN

versionis availableon requestfromthe Los AlamosNuclearData Group.

60

(2)

III.FISSIONPRODUCTSAND ACTINIDES:YIELDS,DECAYDATA,DEPLETION,AND BUILDUP

A. SummaryFission-Productand ActinideData [T.R. England,W. B. Wilson

(R.E. Schenter,and F. Mann,HanfordEngineering I)evelopmentLaboratory)]

A summaryreportof the fission-productand actinidedatacontainedin the

ENDF/B-Vdata fileshas been prepared.90 An expansionof the descriptivetext

of this reportwill be added, along with an Appendixidentifyingerrorsand

data correctionsto ENDF/B-V;it will be issuedas a reportby the Electric

PowerResearchInstitute.

Summarydata for all 877 fissionproductsand 60 actinidesin Rev. ‘OH are

includedin Ref. 90. Appendicescontainsome additionalaugmentationof the

data; theseare noted on schematicsof all coupledfissionproductsand acti-

nides (a total of 144 actinides). The main text consistsof Rev. “Oftdata.

(Inthe caseof groupcrosssectionsprocessedfromRev. ‘O,Herrorcorrections

are discussedin the main text.) Mass chainyields,decayparameters(half-

lives;branching; beta-,gamma-,and alpha-energies),processedone-groupcross

sectionsfor fast reactors,and the resonanceintegralsand 2200-m/s cross

sectionsare included,as well as other informationpertinentto the ENDF/B-V

files. We have preparedthis documentto serveas a relativelyconcisesource

for the most frequentlyrequesteddata and as a convenientreferencefor the

fission-productand actinidedata containedin ENDF/B-V.

As noted,the reportcontainsprocessedgroup cross sectionsfor typical

fast-and thermal-reactorspectra. The thermalspectrumused is givenin Ref.

91, and three diversefast spectraare plottedin Fig. 54. Thesespectrawere

used with the 154-multigroupcross sectionsoriginallyprocessedwith NJOY92

and to collapsethe cross sectionsto fourgroupsfor thermalreactorsand one

groupfor the threefast-reactorspectra, in the mannerdescribedin the TOAFEW-

V manual.g2

B. DelayedNeutronData and Spectra[T.R. England,W. B. Wilson(R.E.

Schenter,and F. M. Mare,HanfordEngineeringDevelopmentLaboratory)]

Revisedprecursorspectra (15 in number)were used in the 105-precursor

librarydescribedin Ref. 93, and all calculatedaggregatespectraand compari-

sons were redone. The calculationsand comparisonswith evaluatedspectraare

extensive. Equilibriumspectrain the conventionalsix-timegroupsand total

spectraare includedfor eleven fissionablenuclidesat one or more neutron

fissionenergies. The resultsare summarizedin Ref. 94, a paperacceptedfor61

Fig.

lo-

1 I Illlq

1O-i

I

1; ld Id 1(? 104 1($ d’Energy(eV)

54. Fast fluxspectraused for one-groupcrosssections.

publicationin NuclearScienceand Engineering,and all resultsare available

in an Appendixto the Los AlamosNationalLaboratorydocument.94

Pn valueswere revisedand preliminaryvaluespublished.95 Final values

are beingpreparedforpublication.

c. FissionProductYieldStatus[T.R. England,D. C. George,and B. F.

Rider (GeneralElectricCo., retired)]

The effortto get codesoperationaland to correctthe masterdata librar-

ies for 50 yield sets was describedin the last progressreport(seeRef. 26,

p. 63). That efforthas continuedfor a shorttime intothe currentreporting

period. All masterdata sets have now been correctedand the firstten yield

sets for VersionD have been produced. A draftmanualdescribingthe use of

the evaluationcodeshas also been preparedas well as additionalrecentdata

in the requiredformat for use with the codes. We

effortto add nevi data and to completean evaluation

lasthalf of calendaryear 1983.

62

anticipatean increased

forENDF/B-VIduringthe

D. Developmentof CINDER-2Librariesfor SpecialPurposeCalculations[W.B.

Wilson,T. R. England,Il.Davidson(HP-3),R. A. Michelotti(AT-4),C. A.

Mangeng(S-4),M. A. Battat(T-Div.Consultant),and G. R. Thayer(S-4)]

1. Eight-hundred-MeVProton AcceleratorTarget InventoryCalculations.

Experimentsare plannedwith the Los AlamosMesonPhysicsFacility(LAMPF)

acceleratorfor 800-MeVprotonson targetsof CaC03,Al, and W. Calculations

by GroupHP-3 performedwith the HETC Monte Carlo transportcode,incorporat-

ing intranuclear-cascadeand evaporationreactioncalculations,have identified

328 reactionproductnuclidesfor the three targetmaterials. An additional

117 nuclidesare producedby radioactivedecay. A 246-chainlibraryof 1158

linearnuclideshas been constructedto describethe temporalinventoryof the

445 nuclides. Many of the nuclidesare far above the line of stabilityand

have unmeasuredhalf-livesand/or decay modes. One-secondhalf-liveswere

asignedto 40 nuclideswithoutmeasuredvalues,and decaymodes were assumed

for 42 nuclides.

Reactionnuclideyields from HETC and averagedecayenergiesremainto be

added for irradiation/decaystudies. Radionuclideinventorycalculationsare

plannedfor the identificationof majorradiationcontributorsat coolingtimes

exceedingone hour followingtypicalirradiationperiods. Multigroupspectral

data will be accumulatedfor thesemajor contributorsfor the descriptionof

the radiationsources of the three target materialsfollowingirradiation.

2. FMIT PrototypeAcceleratorTargets.

The prototypeof the Fusion MaterialsIrradiationTest Facility (FMIT)

acceleratoris under constructionby Los AlamosGroupAT-4. Accelerationof

0.1 A of 2-MeVH2+ ions on a Cu-beamdump is plannedfor the near future,and

accelerationof 0.1 A of 5-MeVH2+ ionson a C-beamdump is proposedforFY 84.

Each beam is assumedto contain300 ppm contaminationof2H+ ion5

. We have

examinedthe nuclearreactionsassociatedwith each of the beam/targetsystems

relativeto the radiationhazardsof the prototypeoperation.

The low-energybeam will deliver1.23 x 1018

l-MeVprotons,eachassumed

to react independentlyof its looselyburnedneighbor 14and 1.85 x 10 2-MeV

deuteronson the Cu beam stopeach second. Thesehave approximaterangesof 13

pm and 25 pm, respectively.The 63Cuandti Cu of the beam stophave 16 nuclear

reactionswith positiveQ-valuesor thresholdsbelow the incidentprotonand

deuteronenergies;however,the potentialbarrierof eachparticle/targetcom-

binationfar exceedsthe incidentparticleenergy.

63

The higherenergybeamwill deliver2.5-MeVprotonsand 5-MeVdeuteronson

C with approximaterangesof 60 pm and 110 pm, respectively.The 12C and 13C

of the beam stop have 13 nuclearreactionswith positiveQ-valuesor thresh-

olds below the incidentprotonand deuteronenergies,and none of thesereac-

tionsare precludedby the lowerpotentialbarrierof the lighttargetnuclides.

The productsof thesereactionsare 1O,llB 14C and 13-15N9 9 .

The high intensityof the beam leadsto the considerationof 58 additional

reactionson theseproductnuclides. This systemof incidentprotonsand deu-

teronson principaland first-generationproductnuclidesresultsin the produc-

tion of 13 radionuclides:tritium,7,8,10Be 9,12B> 9

11,14,15C913,16N

> and14,150.

The temporaldescriptionof these radionuclidesrequiresthe formationof

a libraryof radioactivedecay and reactioncross-sectiondata. Proton and

deuteroncrosssectionsfor most of thesereactionshave not beenmeasuredover

the energyrangeof interest. Cross-sectioncalculationsand libraryformation

have

from

beenproposedfor futureconsideration.

The productionof x rays by the intensebeamshas not yet been addressed.

3.241Am Irradiationin ThermalReactors.

Group S-4 is studyingthe economyof the irradiationof 241Am, separated238spent fuel, for the productionof Pu via 242Cm decay. A libraryfor

these calculationshas been preparedto definethe importanceof all irradia-

tion/decaypaths to 238Pu and fissionablenuclidesand of the contributionof

each fissionablenuclideto samplepower. The actinidelibrarycontains13 lin-

ear chainsand 103 linearnuclidesto describe20 actinides.The standardfis-

sion-productlibraryis used to samplepower. Fissionof Am and Cm nuclidesin

reactorfuelsis not typicallyconsidered.ENDF/B-Vdoesnot containfission-

productyields for thesenuclides,and they have been approximatedin the li-

brarywith the substitutionof fissionyieldsof relatedfissionablenuclides.

Our initialcalculationsof a 245-dayirradiationof241Am in a BWR flux

241,242g+mhshow that the fissionsin 239PU, and 243

9 Cm resultin initial,

average,and peakpowerdensitiesof 24 W/ghm,154W/ghm,and 179W/ghm,respec-

tively,comparedwith 24 W/ghmwithinthe BWR fuel.

4. ICF BlanketStudiesfor Pu Production.

The CINDER-2code and libraryare being used

of Pu in an ICF Li/Ublanketin a groupS-4 study.

to calculatetheproduction

Crosssectionsfor eachof

eleven regionsof the blanketare obtainedwith the TOAFEW-Vcollapsingcode91

and libraryof 154-groupprocessedENDF/B-Vcross sections, using regional

multigroupfluxesobtainedin transportcalculations.

64

E. Developmentof the SOURCESCode and Data Libraryfor the Calculationof

NeutronSourcesand Spectrafrom (a,n)Reactions,SpontaneousFission,and

~-DelayedNeutrons[W.B. Wilson,R. T. Perry (TexasA & M Univ.),J. E.

Stewart(Q-l),T. R. England,D. G. Madland,and E. D. Arthur]

During the past three years we have calculatedneutronsourcesfrom the

spontaneousfission(SF)of actinidenuclidesand from the (ujn)reactionsof

theirdecaya-particleswith lightnuclides. Neutron”sourcematerialsstudied

includeoxide fuels,carbidefuels,plutoniummetal with contaminants,pluto-

nium aqueousprocess solutions,uraniumenrichmentprocess constituents,and

others. These calculationshave requiredthe accumulationand evaluationof

measured and calculated(a,n) reactioncross-section,threshold,potential-

barrier,and thick-targetneutronyield data for a varietyof targetnuclides.

AlSO accumulatedwere a-particlestoppingcross-sectiondata (describingthe

slowing of a-particlesin various materials)and actinidedecay constants,

a-spectra,SF branching, and V values. These data permit the calculationof

themagnitudeof-awidevarietyof SF and (a$n)sources.

This effort has recentlybeen expanded to include $- delayed neutron

sourcemultigroupspectracalculationsfor neutronsfrom SF, (ajn)reactions

and ~ delayedneutronemission. SF neutronspectraare calculatedfrom Watt

Spectrumdescriptionsusing ~ATT and ‘WATTParametersobtainedfor *5 pri~-cipal SF actinidesfrom fits to more precise spectraldescriptionsor using

parametersfor 41 additionalSF actinidesobtainedfrom fits based on the 15

nuclides. Neutronspectrafor (a,n)sourcesare calculatedusing the simpli-

fying assumptionof isotropicneutronemissionin the center-of-masssystem96attributedto Whitmore and Baker. These calculationsrequire a-particle

energy-dependentbranching for the compound-nucleusdecay to productnuclide

energy levels. These branching have been evaluatedfor a number of (a,n)

reactionsfromavailablemeasuredpartialcross-sectiondata,reciprocal(nja)11 0

data, and/orGNASH nuclearmodel code calculations.GNASH calculations,in

turn,have requiredthe accumulationof a libraryof opticalmodelparameters

and nuclearenergy level data for target,compoundnucleus,and productnu-

clidesfor (ajn)and competinga reactions.A typicalmultigroup(a$n)neutron234spectrumis shown in Fig. 55 for UF. gas, calculatedwith a-particlestop-

ping cross-sectiondata of

Balakrishnan,Kailas, and

usingproductnuclidelevel

uZiegler and (a,n)reactioncross-sectiondata of

Mehta.’:7The spectrumcalculationwas performed

branchingdata fromboth the partialcrosssections

65

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.00

Z2Na ~,(D~.e ] ~ral]chjngs......,. ..,.,, ‘..,,,“-,,,..,‘“~

‘“ ‘-- P.R.171,1311(1968).0. -----GNASI1Calculations..

1.

.:’,J.:’

0.5?Ne~tron Energyl.MeV)

2

Fig. 55. Normalized234UF6 (a,n) neutronspectrumcalculatedwith SOURCEScode.

of Lehmangg11

and the partial cross sectionsfrom GNASH calculations. The

data of Lehman,though smoothed,show considerablestructure,are limitedto22energy levelsof Na at or below 1.54MeV, and combinedata associatedwith

branching to the lowest two excitedstatesat 0.59 MeV and 0.66 MeV. The

GNASH calculationincludesall 8 levelsat or below 1.98 MeV that may be ex-234cited by U a-particlesbut cannotrepresentthe structureof the measured

data. The calculatedspectraare in closeagreementfor neutronenergiesabove

1.1 MeV becauseof the dominanceof branchingto low levelsof22Na in reac-

tionsof higherenergya-particlesin bothbranchingdata sources. Belowthis

energythe structureof the measureddataand smoothnessof the calculateddata

are reflectedin the respectivecalculatedspectra.

SF and (a,n)neutronspectrumcalculationsare made in an arbitraryuser-

specifiedmultigroupenergystructure.The spectrumof ~- delayedneutronsfor

any inventoryof fission-productand actinidenuclidesis obtainedusing the

10-keV-binnedspectraldata and ~- delayedneutronbranching(Pn) values of

Englandet al.94

Documentationfor the code and data libraryis currentlyin preparation.

66

IV. NEUTRONICSFOR CARBIDELMFBRCORECOMPONENTDEVELOPMENT

(R.J. LaBauve,R. E. MacFarlane,and D. C. George)

We have prepareda preliminaryset of carbideliquidmetal fast breeder

reactor(LMFBR)cross sectionsbased on the CDS homogeneouscarbidecore. The

processingpath used is shownin Fig. 56.

The basic libraryis an 80-groupMATXS file100 producedby the NJOY nu-

92clearcrosssectionprocessingsystem. The groupstructureis givenin Table

VII. Figure57 showsthe weightfunctionand the groupboundaries.Note that

this is a typicalLMFBR spectrumwith a low–energytail appropriatefor the

outershieldregionsof a reactor.

TMSX

I

QISOTXS

80-groupmacroadefaultflux

80-groupRZcalculation

I JTRANsx collapseto 8groups

elasticremovalcorrectionfissionspectra/ x

Fig. 56. Processingpath for preliminarycarbidereactorcrosssections.

67

TABLEVII

GROUP

:3456789

1011121314

151617181920212223242526272a293031323334353637383940

BOUNDARIESFOR

MAXIMUM ENERGY2.00000E+07f.69046E+071.49182E+071.34986E+071.19125E+071.00000E+077.78801E+066.06531E+064.72367E+063.67879E+062.86505E+062.23130E+061.73774E+061.35335E+06

1.19433E+061.05399E+069.30145E+05B.20850E+057.24398E+056.39279E+055.64161E+054.97871E+054.39369E+053.87742E+053.01974E+052.35177E+051.83156E+051.42642E+051.1109OE+O58.65170E+046.73795E+045.24752E+044.08677E+043.18278E+042.C0879E+042.60584E+042.47875E+042.18749E+041.93045E+041.70362E+04

80-GROUPSTRUCTURE

41424344454647484950515253545556575859606162636465666768697071727374757677787980

EMIN

1.50344E+041.32678E+041.1708BE+041.03330E+049.11882E+038.04733E+037. IO174E+036.26727E+035.53084E+034.88095E+034.30743E+033.80129E+033.35463E+032.96045E+032.61259E+032.30560E+032.03468E+031.79560E+031.58461E+031.39842E+031.2341OE+O31.08909E+039.61117E+027.48518E+025.82947E+024.53999E+023.53575E+022.75364E+021.67017E+021.01301E+026.14421E+013.72665E+012.26033E+011.37096E+018.31529E+O05.04348E+O03.05902E+O01.12535E+O04.13994E-011.52300E-01

1.38879E-04

This librarywas first convertedto 80-groupmacroscopiccross sections

for each of the ten regionsof the RZ reactormodel shown in Fig. 58. Thehomogeneousself-shieldingoptionof TRANSXIOOwas used. Thisneglectsthepin

size,Dancofffactor,and disadvantagefactoreffects. The finalsmearedden-

sitiesfor each regionare summarizedin TableVIII.

The 80-groupISOTXSoutputfrom TRANSXwas used for an 80-groupDIF3D101

flux calculationusing the full-coremodelof Fig. 58. The resultingkeffwas

1.0051 (controlrods out in this calculation). The zone-averaged80-group

fluxesfrom this calculationwere savedin RZFLUXformat. The problemwas run

twice,oncewith controlrodsin and oncewith rodsout, to get fluxesfor con-

trolregionsfor each case.

68

1.,,,

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1,,,,,

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69

345. =$4

1’ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ “ ‘ ‘ ‘ ‘ ‘ ‘ ‘ 1 ‘ ‘ 8 ‘ ‘ ‘ ‘ ‘ ‘ z ‘ ‘ ‘ ‘ ‘ 1 ‘ ‘ r ‘ ‘ ‘‘d

RSZ8Z8

—

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R8Z4Z4

D2Z2Z2

IWZ828

REZ3Z3

1

SIZ7Z7

Fig. 58. CDS Carbidefull-coreR-Z model. Dimensionsin cm.

70

HOMOGENIZEDDENSITIESBY

tlaterial D] D2 RB— .—

U235 1.64-5 1.51-5 3.41-5U236 7.97-7 8.37-7U238 8.888-38.713-31.761-2Pu238 1.02-5 1.41-5Pu239 9.169-41.046-38.10-5PU240 2.65-4 3.13-4 1.02-6Pu241 1.03-4 1.34-4Pu242 3.42-5 4.08-5FOP.* 5.61-4 4.35-4 1.73-5Cr 2.8803 2.880-32.058-3Fe 9.920-39.920-37.087-3Ni 1.968-31.968-31.406-3MO 2.230-42.230-41.594-4tln55 2.727-42.727-41.949-4Na23 9.590-39.590-37.400-3Carbon 1.125-21.119-21.852-2BIOBll

inner outer radialdriver driver blanket

*F.p. densitiea ahould be divided by 2 for

A secondTRANSXrunwas

TABLEVIII

REGION FOR PRELIMINARY

AB DP BP— ——

2.02-5

1.050-2

6.20-54.73-7

1.16-52.880-3 2.880-3 2.058-39.920-3 9.920-3 7.087-31.968-3 1.968-3 1.406-32.230-4 2.230-4 1.594-42.727-4 2.727-4 1.949-49.590-3 9.590-3 7.400-31.105-2

axial driver radialblanket plenum blanket

plenum

HOMOGENEOUSCARBIDECORE

RS

1.147-23.951-27.837-39.659-41.086-35.236-3

radialahield

use with ENDF/B-Vlumpedfiasionproduct.

AS CI co— —

1.232-24.242-28.416-39.537-41.166-33.771-3

axialshield

4.611-31.588-23.151-33.570-44.366-47.434-39.149-33.367-22.928-3controlin

usedto collapseto the 8-groupstructuregivenin

3.163-31.089-22.161-32.449-42.995-41.965-2

controlout

Table IX and to write the constituentmicroscopiccross sectionsfor each re-

gion in the desiredformat. Becausea flux file was availablefor this run,

improvedfissionspectrumvectorsand improvedelasticremovalcross sections

could also be produced. The region fissionspectraare given in Table X.

TABLE

ENERGYBOUNDARIESFOR

Group UpperEnergy

1 20.0 + 6eV2 2.2313+ 63 8.2085+ 54 1.83156+5

TABLE

IX

8-GROUPSTRUCTURE

Group UpperEnergy

5 6.73795+ 46 1.93045+ 47 2.03468+ 38 1.28879-4

x

FISSIONSPECTRABY REGIONFOR PRELIMINARYHOMOGENEOUSCARBIDECORE

Region Group1 Group2 Group3 Group4 Group5 Group6 Group7 Group8

D1 3.662E-01 4.009E-01 2.015E-01 2.412E-02 6.129E-03 1.074E-03 2.924-05 8.043-06

D2 3.662E-01 4.009E-01 2,016E-01 2.414E-02 6.138E-03 1.077E-03 2.934E-05 8.085E-06

RB 3.576E-01 4.031E-01 2.064E-01 2.533E-02 6.352E-03 1.086E-03 2.853E-05 7.366E-06

AB 3.591E-01 4.030E-01 2,054E-01 2.510E-02 6.305E-03 1.081E-03 2.852E-05 7.426E-06

71

The DTF-formatcross sectionsproducedfor the two-dimensionaldiffusion

Code”’ containthe fissioncross sectionin position1 and the totalin posi-

tion 4, and the table lengthis 12. A list of the materialnumbersand names

is given in Table XI. The last two lettersof each materialname definethe

regionfluxused for collapsingthatparticularmaterial. Note thatposition2

containsOa (approximatelyabsorptionminus n2n) and shouldnot be used for

accurate burnup calculationswithout correction. Separate

crosssections

123456-?89

1011121314151617181920212223242526272829303132333435363738394041424344454647484~505152

are availableon the ISOTXSlibraryif needed.

CROSSSECTIONDID2I?BABWBPRSASCICDU235DIU236D1U238D1PU38DIPU39DIPU.40DIPU41DIPU42D1FPD1CRD1FED1NIDIMDD1MND1NAD1CD1U235D2U236D2U238D2PU38D2?W3902PU4002PU41D2PU42D2FPD2CRD2FED2NID2MOD2MND7NAD2CD2U235ABU238ABPU39A8PU40ABFPABCRA8FEABNIA8MOABMNAB

TABLEXI

MATERIALNUMBERSAND NAMES535455565758

::616263646566676869707172737475767778798081828384858687888990919293949596979899

100101102103104105

n2n and capture

NAABCABU235RBU238RBPU39RBPU40RBFPRBCRRBFERBNIRBMORBMNRBNARBCRBCRDPFEDPNIDPMODPMNDPNADPCRBPFEBPNIBPMOBPMNBPNABPCRRSFERSNIRSMORSMNRSNARSCRASFEASNIASMOASMNASNAASCRCIFECINICIMOCIMNCINACICCI81OCIBIICICRCOFECONICDMDCDMNCONACO

72

We made an additionalseriesof 8-groupcalculationsusingthe ISOTXSver-

sion of the librarywith DIF3D. Results for k-effectiveare summarizedin

Table XII. The k-effectivefor a three-dimensional,triangular-Zproblemis

alsogivenin thistable. The mid-planehexagonalmodelfor the 3-D problemis

shown in Fig. 59. Note fromTableXII thatk-effis increasedby about .2%in

going from 80 to 8 groups (R-Zgeometry)and it is increasedby about .3% in

goingfrom2-D to 3-D geometry.

TABLEXII

RESULTSOF DIF3DFUNS OF CDS CARBIDECOREPROBLEMS

Prob.No. Type No. Of GpS Remark k-eff

1 R-Z 80 rodswithdrawn 1.00505

2 R-Z 80 rods inserted 0.88015

3 R-Z 8 rodswithdrawn, 1.00691

8-gpscollapsedfrom

probs.1 and 2.

4 Triang-Z 8 rodswithdrawn, 1.00957

8-gpscollapsedfrom

probs.1 and 2,

19-axialplanes.

73

mInn

74

DIF3DAuxiliary Codes

ary

the

In conjunctionwith developmentwork on the DIF3Dsystem,severalauxili-

codeshave been written. The first set of codes readsand printssomeof103standardinterfacefiles producedby DIF3DincludingRZFLUX,zone-aver-

aged group fluxes; PWDINT,power

atomicdensities.

The second set of codes is

of displayingpowerdensitiesand

densityby interval;

plottingcodesthat

and ZNATDN,zonenuclide

providethe capabilities

the reactor geometry. One code,HEXPLT,will

read the DIF3D input file and produceplots of each plane showingthe region

boundaries. This is a very useful error-checkingfeature. Another code,

PLTPWR,reads the power densityfile generatedfrom an R-Z problemand plots

two pictures-- a 2-D plot of power in the driverand radialblanketregions

(Fig.60) and a contourplot (Fig.61). Severalcodeshavebeenwritten

?m.

----------------?0 — 01------ 02‘“— RB

To

To-

=usL=

%: ‘/

: /

+: “ L.—.\

~o-

;0- 0.0

t , , I+0.0 80.0 120.0 160.0 2m.o 240.0 200.0 320.0 360.0

RXIS(CM)

Fig. 60. Axialpowertracesin two driverregionsand radialblanket.Powerunitsnormalizedto 1 Watt.

75

--. -__-----— - — -. <“——-----------

~>

-, ,----. . .---------------------------------------------

‘.----------- ‘.<

------- ‘,

-11”*—------lj ~ ------ \....----------------------------------------------

>>\-------------,--------------------------—----------------------

\ ,,

DI____.,,,,1, (::: I

1, !,: ; : ,

,,, ,f, ,

:: !,!,,, !,, ,

!,,1,, ,

,, l,,,!

:: 10,1 ; ~ <

~, ,, I,! 1,0 ,

\

l,, ,;,

J 1:;:!,, ,

$( l:’$,!,

;~ ,,,

!,, ,1,, ,:!

~ It\\,, ,,!,,( l,!,

1, ,,at -- _ - _---_---, , , -,1,,

$—

--------------------------------- --- ----

-..‘.

‘. .

t

,$I,

\

-----------------

rn~’

---------

,,,

;!,

;~-~~~::;~{~,,,;

-------------.\’a““ “ /’------------------- >/’ ..’

~---- - -...y...~j;------------

, , , , I , , , I , , , , , , ,

8 16 24 32 40 48 S6 64 72 80 88 96 104112120128136144152 160168176184192200206 21w

Fig. 61. Powercontoursfor CDS R-Z model. Contoursto 1/2decadesteps. Powernormalizedto 1 Watt

to produce a contourplot superimposedon a plot of the geometricregions

(Fig.62). These types of plots are availablefor nodalDIF3Dand Trian@e-Z

(both6 and 24 trianglesper hex)problems. Logarithmiccontourplotsshowthe

contoursall the way out to the edgeof the reactorcore. Linearcontoursare

also available;these contoursare superimposedon a region geometricplot

terminatedat a maximumringvalue.

76

comf’Ir.-l

Ln

d+r--l

ml

r+

o

-...

--

.e03

mh

cou

)d+

r)(-N

r-l

WI

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85

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