LA-6560 -ProgressReport

R CC-14 REPORT COLLECTIONREPRODUCTION

COPYSpecialDistribution

Issued:November 1976

Applied Nuclear Data

Research and Development

April 1 —June 30, 1976

Compiled by

C. 1.Baxman

P.G. Young

)

)

ualamos.

scientific laboratory

of the University of CaliforniaLOS ALAMOS, NEW MEXICO 87545

\An Affirmative Action /Equol Opportunity Employet

UNITED STATES

ENERGV RESEARCH AND DEVELOPMENT ADMINISTRATION

CONTRACT W-7405 -ENG. 36

The four most recent reports in this series, unclassified, are LA-6472-PR,LA-6266-PR, LA-6164-PR, and LA-6123-PR.

This work was performed under the auspices of the Defense NuclearAgency, the Nuclear Regulatory Commission, the National Aeronauticsand Space Administration, and the US Energy Research and DevelopmentAdministration’s Dhisions of Military Application, Reactor Developmentand Demonstration, physical Research, and Magnetic Fusion Energy.

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CONTENTS

I. THEORY AND EVALUATION OF NUCLEAR CROSS SECTIONS .......... 1

A.

B.

c.

D.

E.

F.

G.

R-Matrix Analysis of Reactions in Light Systems ...... 1

Calculations of (n,xn) Cross Sections and Spectra. ... 2

Calculations of Charged-Particle Spectra Inducedby 15.1-MeV Neutrons ................................. 3

Fast Fission Cross Sections. ......................... 6

Neutron Spectra from Fission. ........................ 6

Evaluated Time-Dependent Photon Spectra from a235U

Fission Burst ........................................ 6

Computation of Specific Thermonuclear ReactionRates ––The STEEP Code. ............................. 7

II. NUCLEAR CROSS-SECTION PROCESSING. ............. ........... 11

A. Neutron Photon Coupled Sets from ENDF/B-IV ........... 11

B. Pointwise Cross-Section Library for MCNG ............. 11

c. LIB-IV-240 (Two-Hundred and Forty Group Library) ..... 13

D. NJOY Storage Allocation Package ...................... 15.—U E. Processing Photon Cross Sections ..................... 16r

CCCC Development ..................................... 16

Comprehensive CCCC Cross Section File -- MATES....... 17

MINX VSMC2 .......................................... 18

_Leakage Corrections to Self–Shielded Cross Sections. . 22

Spectral Corrections to Elastic RemovalCross Sections ....................................... 24

Effects of Weighting Spectra on Croup Collapse ....... 27—. -. d

L. Improved Cross Sections for ThermalReactor Analysis ..................................... 32

111. HTGR CROSS SECTIONS AND DEPLETION CALCULATIONS FORREACTOR SAFETY ANALYSIS .................................. 34

IV. COMPARISON OF MONTE CARLO AND S CALCULATIONS hTITH7

nLi PULSED SPHERE EXPERIMENTS USING FNDF/B-11’ DATA ....... 34

v. FISSION–PRODUCT AND DECAY STUDIES ........................ 37

A. ENDF/B Phenomenological Yield Model Improvements ..... 37

B. Fission Yield Theory: Statistical Model Development. . 41

iii

c. Calculation_vs Experiment: Comparisons of Time-Dependent ~ and y Spectra From Thermal Fission of235U

................................................. 43

D. Noble Gases, Halogens, and Other Fission Products. ... 45

E. CINDER-10 Code Development ........................... 58

F. Beta-Energy Averaging and Beta Spectra ............... 58

G. Absorption Buildup Studies ........................... 58

REFERENCES. .................................................... 59

iv

APPLIED NUCLEAR DATA RESEARCH AND DEVELOPMENTQUARTERLY PROGRESS REPORTApril 1 - June 30, 1976

Compiled hy

C. 1. Baxman and P. G. Young

ABSTRA.CT

This progress report describes the activities of theLos Alamos Nuclear 12ataGroup for the period April 1.throughJune 30, 1976. The topical content is summarized in thecontents .

I. THEORY AND EVALUATION OF NUCLEAR CROSS SECTIONS

A. R-Matrix Analysis of Reacticns in Light Systems (G. M. Haleand J).Dodder [T-91)-

Our program of analyzing reactions in light systems using multichannel

R-matrix theory has generally overlapped two areas of applied interest, light-

element standards and fusion reactions. In this quarter we have extended andi’ 11

modified analyses of the Li and B systems which were substantially completed

last quarter to provide standard cross sections for Version V of the Evaluated

Nuclear Data File (ENDF/B), and have”restarted analysis of the 4 and 5 nucleon

systems which contain r-any of the important fusion reactions.-1

1. Standards. New data have teen added to the ‘Li analysis which v7as used

to provide evaluated 6Li(n,c%)cross sections at low energies for Version t’. These.

include u-t cross section excitations~ measured over the resonance which occurs

at .250-keV neutron energy, and measurements of the6Li(n,t) angular d.istributions2

at energies above 2 MeV. The new data are fitted quite well with only slight

changes in the F.-matrix parar,eters, indicating, for instance, a preference for the

integrated 6Li(n,u) cross section values of Bartle2 over those of Clements and

P.ickard3 at neutron energies abet-e 2 FfeV. These results were reported at the

International Conference on the Interaction of Neutrons with Nuclei at Lowell,

Massachusetts.

Modifications in the analysis of reactions in the11

B system were required10

to reflect changes in the preliminary B(n,ay) cross section data4 measured at

the National Bureau of Standards which had strongly influenced the calculated10

B(n,ct) cross sections proposed for use as Version V standards. These changes,

which are significant only at energies above 500 keV, will be incorporated in the

final ENDF/B-V file.

2. Fusion Reactions. We have incorporated new data in our comprehensive

analysis of both the 5He and 5Li systems. In the case of 5Li, the changes in

data base have been extensive, since earlier3He(d,d)3He measurements of Konig5

have been supplanted by the newer, more complete measurements of Jenny.6

In ad-

dition, the vector analyzing power measurements of Klinger7 for the3He(~,p)4He

reaction have been included, as well as data in all reactions at higher energfes.

Our hope is that these new measurements are sufficiently reliable to sort out at

last the complicated sequence of overlapping d-wave (and possible odd-parity)

levels which exist in the 5-nucleon system above the well-known 3/2+ S-wave reso-

nance. New data have been accommodated in the5He system analysis, including

8measurements of the T(d,d)T vector analyzing power and precision values of the

T(d,n)4He cross sections.9with little change in the R-matrix parameters.

4A new charge–independent analysis of reactions in the He system has begun,

which will soon extend to energies above the d + d threshold. (he of the goals3

of this analysis is to obtain R-matrix fits to the D(d,p)T and T’l(d,n)He cross

sections which have reliable extrapolations to zero deuteron energy, as has al-3

ready been done for the T(d,n)4He and He(d,p)4He cross sections using analyses

like those described above.

B. Calculations of (n,xn) Cross Sections and Spectra (E. D. Arthur, P. C.Younz. and L. R. Veeser [P-31)

We have completed calculations of cross sections and spectra for (n,xn) reac-45SC 58Ni 59C0 89Y 93Nb 103Rh 169Tm 175LL, 181Ta 197

tions on , , , , ,209

9 Y 9 9 Au, and Bi..

For these calculations we used the preequilibrium-statistical model code GNASH

with global optical model and level density parameters with no attempt to adjust

parameters to better fit experimental data. The calculated spectra of first and

second neutrons from (n,2n) events and the spectra for first, second, and third10

neutrons from (n,3n) events were used by Veeser and Arthur to make efficiency

corrections to measurements made with a large liquid scintillator tank.

2

Comparisons c,fthe calculated cross sectior.s to recert (n,xn) measuren!ents11 12 1(?

of Frehaut anclMosinski, Bayhurst et s1., ad Veeser et al. were ~de irL a

paper Fresented at the 1976 International Conference cn the Interactions of Neu-

trons with Nuclei. Selected examples of the agreement of calculated to experi-P9Y 181

mental results are shorn in Figs. 1-3 for (n,xn) reactions m ,209Bi

Ta, and

. In crder to fit the experimental (n,2r.)and (n,3n) cross sectj.ons at

higher energies, it was necessary tG ir.elude contributions frcn!preequilikrium.

processes. For example, the lcng dashed curve in Fig. 4 illustrates cross sec-

tions calculated. withcut preeqcilibriur effects. Also important is the mass and

energy dependence of the absolute square of the average effective matrix el.em.ent

M of residual two-body interactions, which appear in the expressions used to cal-

culate the preequilibrium component. In Fig. 4 the short dashed curve illus-

trates results obtained when preequilibrium effects are included with the

quantity

]M]2a A-3 ,

as suggested by Braga-Marcazzan et

the curves in Figs. 1-3) shows the

ponent is included with a mass and

al.13 Finally, the solid curve (as well as

result obtained when the preequilibrium com-

excitation energy dependence

l~\ 2(1A-3E-1 ,

14as determined by Kalbach-Cline.

As a result of this work, we feel that calculations which include preequi-

librium effects and which use global input parameters can reproduce well the ex-

perimental data for (n,xn) reactions.

c. Calculations of Charged-Particle Spectra Induced by 15.1-Me~J Neutrons,~E. D. Arthur and P. G. Young’

We have made further calculations of the charged-particle production spectra

from 15.1-VeV neutron bombardment of27A1 46T1 and 48

9 Ti to compare with the most15 ‘

recent measurements of Grimes et al. These calculations are an extension of

earlier calculations made with the GNASH preequilihrium-statistica.l model code

with global optical model and level density parameters. l’reequilibriurceffects,

which are important in reproducing the observed spectral shapes and cross section

3

1.4, t

1,2.

3 1.0-c0

=u 0.8 -

b%

: 0.6 -

:

u 0.4 -

0.2 -

89y

o L., ,,, .ttk, .,,,A I8 12 16 20 24 28

En (MeV)

Fig. 1.Comparison of calculations and experi–ment for 89y(n,xn

!reactions to the

data of Frehaut, 1 Veeser, 10 and Bay-burst.12

2.5 ,

~ 2.0 -

:.-

2 1.5 -w

e

: 1.0 -u

0.5 -

08 R 16 20 24

En (MeV)

Fig. 2.The calculations for 181Ta(n,xn) reac-tions are compared with the measure-ments of Frehautll and Veeser. 10

2.5 .

~ 2.0 -Q

c

.: 1.5 -2w

: 1.0 -0G

0.5 -

0 .8 12 16 20 24

En (MeV)LJ /

2!I 22 14 ji la 20 22 2$

flMh2n mmv WIV2

Fig. 3. Fi . 4.The calculations for 209Bi reactions are Calculations of ?75Lu(n,xn) reactionscompared with the measurements of Fre- are compared to the data of Frehaut andhautll and Veeser. 10 Veeser. The - - curve was made with no

preequilibrium effects, the --- curveincluded a preequilibrium componentwhose normalization depended on mass,

while the solid curve was made with apreequilibrium component normalized toboth mass and excitation energy.

magnitudes, were made using the closed form exciton expression of Milazzo-Colli

et al.16 The preequilibrium component was assumed to be normalized such that

where M is the matrix element describing residual two body interactions. The

absolute normalization was obtained from a survey of experimental (n,n’), (n,p),

and (n,c%)results.

Comparisons with the data of Grimes et al.15 46

for proton production from Ti48

and Ti are shown in Fig. 5. The calculations reproduce well the striking dif–

ference in the spectrum of protons from these two isotopes. In Fig. 6, compari-46

sons of the calculations are made with the Ti deuteron and alpha production

data. Except for the46

Ti(n,d) reaction, no attempt was made to adjust parameters

to improve the fit to experimental data. In the case of the (n,d) data, direct

reaction effects, which are not included explicitly in these calculations, may

account for some of the disagreement between the calculations and experiment.— _—

7i J I I I I

j

(n, Xp) Speclro

+“+En= 15.1MeV

\

lx

-46Ti*-I

-+4eTi 3

t 1,V4L I I I I I I I

2 4 6 0 10 12

Secondory ProIon Eww (I14cV)

Fig. 5.

1 I I I I 1

46~i [n, xa)

Em= 15.1t.!cV

“t#3-2 . +- “~

+..-

% +

zp)-

+.>

: 10-3 ! 1

; I I

3 46 fi(n, d)& *

Em=15.1 MeV

*- 3_

,o- 4 I ! I I I2 4 G 8 10 12

Sccondoq P.rliclc En.KIY (hfcV)

Fig. 6.

A comparison between calculated and ex- A similar comparison for46Ti alpha and

perimental results for the proton pro- deuteron production spectra.

duction sFectra from 46Ti and 48Ti.

D. Fast Fission Cross Sections (L. Stewart)

Several recommendations were made at the NEANDC/NEACRP Specialists Meeting

on Fast Neutron Fission Cross Sections held at Argonne National Laboratory on

June 28-30. The most important, perhaps, were the agreement on the method of

shifting energy scales and the normalization of the 28/25 fission

urements. Above 10-MeV incident neutron energy, however, several

main. The disagreement among the experiments on the 49/25 ratios

derstood, even at 1 MeV.

A paper entitled, “What Happens to the Fission Process Above

Chance Fission Thresholds?” by Leona Stewart and Robert Howerton,

ratio meas-

problems re-

is not yet un-

the 2nd and 3rd

was presented

at this meeting.

E. Neutron Spectra From Fission (L. Stewart)

233U have a Max-All of the fissile and fertile materials on ENDF/B, except s

wellian representation for the fission neutron spectrum. Recent experiments indi-

cate somewhat better agreement with a Watt distribution rather than the Maxwel-

lian used in Version IV. A format to allow an energy-dependent Watt spectrum was

recently approved by the Cross Section Evaluation Working Group (CSEWG), and the

spectra for some of the important isotopes will be updated accordingly for Ver-

sion V. A paper on this subject entitled, “The Prompt-Neutron Fission Spectrum

for 239PU ,,9 by E. Kujawski (General Electric, Sunnyvale) and L. Stewart has been

accepted for presentation at the American Nuclear Society Winter Meeting.

While the Watt spectrum is quite reasonable, some of the recent measurements

have shown far too many low-energy neutrons (<1 MeV) to agree with earlier exper-

iments or with the Watt or the Maxwellian distribution. This problem is still

to be resolved and it is hoped that some explanation will be found in the exper-

iments. An additional problem is that almost nothing is known about the incident

neutron energy dependence of the fission neutron spectrum.

essentially the same average fission neutron energy used in

implemented in Version V with the above change in shape.

It is expected that

Version IV will be

F. Evaluated Time-Dependent Photon Spectra From a 235U ~ission Burst

(D. G. Foster, Jr., T. R. England, and M. G. Stamatelatos)

A preliminary evaluation of the time-dependence of the intensity and

spectrum of photons emitted following a very short fission burst (<<1 ns) was

6

17,18completed a year ago.in 235U and 239PU

. Special

than 1 s after fission, but

It covered fission induced by thermal neutrons

attention had been devoted to the time range less

only a crude extrapolation to 108s was included.

This extrapolation assumed a time-independent spectrum after 60 s, and used old

data normalized to recent data at 15 s, where the log-log slopes of the 2 sets

of data were equal.

We have now replaced the data for235

U at times greater than 15 s with de-

tailed calculations using ENDF/B-IV data in the CINDER code. The input data cov-

er 825 fission-product nuclides, but only 181 of these (selected to account for

most of the energy emitted at decay times greater than a few seconds) have spec-

tral information. The overall spectrum is assumed to be that of these 181 nu--4

elides. The calculations were made using an irradiation time of 10 S, so that

the results are indistinguishable from an arbitrarily short burst at decay times

greater than a second. The calculated absolute yield joins neatly onto the re-19

suits of Fisher and Engle at 50 s after fission, and is thus about a factor of

3 lower than the previous extrapolation at 60 s, as pointed out a year ago.18

The new intensity is roughly equal to the previous intensity between 105 and

107s, but is a factor of 10 lower at 108s. The new evaluation has also been ex-

tended to 109 (31.7 y). The accuracy from 50 s to a few hours appears to be * a

few percent.

The spectrum in the new evaluation displays a marked variation with time.

The average photon energy has 5 pronounced minima between 1 and 109 S, with an

overall range from 0.43 to 1.05 MeV. This is in sharp contrast to the constant

spectrum assumed in the previous evaluation.

We are currently working on the CINDER calculations for neutron-induced239PU

fission of . We expect to submit the completed work on both isotopes for

possible inclusion in ENDF/E-V.

G. Computation of Specific Thermonuclear Reaction Rates--The STEEP Code(D. E. Dei [CarnegieMellonUniversity], A, A. Husseiny [Iowa StateUniversity] and G. M. Hale)

A fast, efff.cient, and accurate program module, STEEP, has been developed

to compute specific thermonuclear reaction rates, <crv>. These quantities are

central in the design ”and analysis of various fusion devices, as well as other

areas (e.g., astrophysical problems). Because of this wide range of potential

applicability, STEEP is designed for a variety of plasma conditions.

7

The most common reaction rate computations involve the interaction of ion

distributions in Maxwellian equilibrium. In this case the specific reaction20

rate is written as a single integral over relative energy, Er,

<(JV> .M

1

dErMT(Er)a(Er)vr(Er) ,

0

(1)

where M is a Maxwellian distribution in energy. For accurate but rapid results

i?q. (l; is integrated numerically with a self-terminating trapezodial quadrature.

Values of cl(Er)are effectively supplied from an evaluated library of energy-

cross-section pairs (e.g., from R-matrix calculations) with suitable interpolation

formula provided to evaluate O(Er) for arbitrary energies.

In many instances, the plasma ions are not in thermal equilibrium and a

sizeable contribution to the reaction rate is produced by a high energy slowing

down component of the distributions. For this case STEEP assumes a continuous

slowing down model wherein

ment time is assumed to be

down component of the i-th

source energy EO is

leakage and absorption are neglected and the confine-

greater than the slowing down time, TqD. The slowing..

ion distribution, with source strength SO below the

so(E)=

‘SD i <dEf/dt> “

When the total ion density N isi

component so that

[Ni (I-ai) ~(Ei)

(2)

known, nSD is joined to a background Maxwellian

n(Ei) = I(3)

Ni {(l-ai) ~(Ei) +-E i~~> ~ ] , Em$Ei<Ei SD

-0”

Em is a lower cutoff, usually taken as 2kT, and a j,s given by S Ti

o sD/Ni. The

total specific reaction rate is

<(JV>= (1-a.) <~v> + -WV>1 M SD ‘

(4)

8

where

\

(-’ )m.v vri

sinh\ kT

. (5)

In tw&component fusion $.evices,21

a.primary design parameter is t}:eenergy mul-

tiplication factor F, which is related to ‘=% by

(6)

where Q is tb.eenergy release per fusion event.ij

Figure 7 shows typf.cal res~llts cbtained. with” STFFF for the D-T, R-.3fie,and

11E fusion reactions.

3P- D-T and P- lie cress sections were obtained from an F-

22 3matrix analysis which considered the T(d,n) and He(d,p) reacticns simultarle-

11ously in a charge-independent framewcrk. The F- 8 cross section ~-zs provided

by a preliminary R-matrix evaluation.23

The low temperature <C.>pf.alues zre2[!-26

generally higher (lC-?.C%) than previous results due to improved low energy

crGss sections. Also, Pale’s larger I?-3He cress section results in 10-15%24-27

increases over previcus results in both <uv>ll and F-factors for the D-3He

fuel system. Previous results suggest that the two-componmt l?--3Hescheme,

while having highly attractive features such as lack of neutron and tritium

production, is or.lymarginally capable of near-future breakeven. In this

light, our results for 12-3He are of particular interest and indicate the need

for continued study of ti-.issystem.

@

@

@!

@.1

g @

‘k &5

*

$ mu

@9

~31

@3

3.0

2s

2.0

L5

& 1.0.

g0.5

E!

~ 0.09

i

0.08

O.w

0.06

0.03

O.ot

0.0s

0.02

m

0.C3

mmwlJP& Id100

O-T

/

\

o-T

Tc - SrEv

T1-o

/

JrPJ’%i

TE-Z5KEV

T,- o

0 w 800 1200 lwo

IKJECTIONEllEf(!3V,azV

3

Fig. 7.Maxwellian-averaged specific reaction rate<Ov>M and two-component energy multiplicationfactor F for D-T, D-3He, and p-~~B fusion

reactions.

II. NUCLEAR CROSS-SECTION PROCESSING

A. Neutron Photon Coupled Sets from ENDF/B-IV (D. W. Muir and R. E MacFarlane)

During this quarter we have used NJOY to produce multigroup cross section1 2H 3H 3He 4He 6Li 7Li 10B llB 12C

sets for the following materials–– H,

14N 160 19F 27A1 Si 55Mn ~lo 197Au’ ~b’>> > 9

233; 2il 242P;Y 9 > 99 93 >> 9 Pu, and . These

28calculations utilize 0° pointwise cross sections from the T-2 PENDF library.

‘o through P4

neutron transport tables were prepared in the TD-Division format11 197

using basic data from ENDF/B–IV. For all materials except B, Au, and the

fissionable isotopes listed above, 30 x 12 gamma-ray production matrices and 12–29

group gamma-ray interaction cross sections were also prepared. Gamma-ray pro-33

duction evaluations are not given in ENDF/B-IV for H, He, and 4He, but the pro–

duction cross sections should be very small or zero for all 3 isotopes. Thus we

have entered zeros in the gamma-ray production matrices for these isotopes.

For all of the gamma materials (including3H 3

He, and 4He), neutron/gamma coup-

led sets were then prepared using PROSEC.30 ‘

The coupled sets were written, along with the usual TD–format edit cross

sections and uncoupled cross sections, to HYDRA photostore files (OAC = T02DWM).

As before, file marks separate the three data types and the usual naming conven-

tion is followed (HIMG, H2MG, .... SIMG, MN55MG, MOMG, .... plJ242MG). The five

materials for which gamma information is absent are written in the older form

(i.e., without internal file marks).6

The special T-2 evaluations for Li and12C

(Ref. 31) also have been processed. These evaluations treat the continuum break-6 12

up reactions Li(n,n’da) and C(n,n’3u) with the pseudo–level formalism. The

output files for these materials are on photostore files L16AMG and C12AMG, re-

spectively, in coupled–set format.

B. Pointwise Cross-Section Library for MCNG (R. J. LaBauve and D. George)

Over the past year and a half, T-2 has participated in supplying data for31

the TD-6 continuous energy Monte Carlo library. Thus far, data have been pro-

vided for 57-nuclide temperature combinations as shown in Table I. All materials

shown in the table contain photon-production data (MF=13,14,15) as well as neu-

tron data. Materials with 7000-series MAT numbers were taken from the Lawrence

Livermore Laboratory’s (LLL) evaluated nuclear data file (ENDL). MAT numbers 101

and 102 are local T-2 evaluations, and all others are taken from ENDF/B-IV.

Several different processing routes were followed in going from the orig-

inal data files to the photostore files given in the table.

H

-I---mm

Nm

r-NF

WI

.0u

nk

I

! .:..-.S

.C-----

AA

----------

-A---

-A-A

---..

<,.-.

..”C

C7C

CC

.-.C

Cc.c

.e-e

ee=

Oooocooeoa

00oaoaaooo

Ooocooeaoo

C-o

oooooooo

Oooeeoooa

-O

aoooo

--.-.=

OC

CO

OC

ceo-e

ooo

eeoee.

.ee

eecec--e-“------C

C.C

ececece0

00

::.

..

..

..

..

..

..

..

..

..

..

..

..

..

..

..

..

..

..

..

..

..

..

..

..

!72

u-u

..

..

...0

Uw

uuuun

wM

dk

Uu

uu

I&o

X+

..

..

..

..

..

..

..

.‘0

.e.a

”e”a

”a”o

”a”o

”oeoooooaooa

0000

12

1. Some ENDF/B evaluations do not contain resonance parameters; that is,

the cross-section data are completely described in MF=3. Materials of this type

type were first processed by the TD-6 code ZERO, which shifts threshold ener-

gies in the data files to make them consistent with given Q-values, and then by32

the T-2 versions of the TOPFIL and ETOPL codes. Tncluded in this category

are MATS 101, 102, 1120, 1160, 1193, 1269, 1273, 1274, 1275, and 1276.

2. The ENDL evaluations (the 7000–series MATS) processed are given point-

wise zs describeti above, and are generally in the ENDF/B format except for

slight differences. For example, ENDL omits all isotropic angular distributions

for secondary neutrons whereas the LASL code assumes these to be expressed ex-

plicitly. Modifications to the Eh~L evaluations to rr.akethem compatible with

LASL codes were made by R. Sean..onin TI?-6. The modified data sets were then

processed with ZERO and the T-2 versions of the TOFFIL and ETOPL codes.

3. The remaining materials are those containing resonance parameters that33

were first translated to pointwise data by the MINX code. Data for several tem-

peratures were produced for each material and only those data sets containing

less than 5000 points per reaction were processed directly by the T-2 codes.

Those containing more than 50C0 points were first processed by the TD-6 version

of the ETOPL code which has the capability of processing large data sets and

thinning to less than 5000 points, but it does not contain the module for pro-

cessing the photon production files. All these nuclides were checked with the

ZERO code before final runs with the T-2 codes.

All data sets were carefully checked by TD-6 with the aid of the TD-630

checking codes LOOK4, MYC~D, and COMPXS before being incorporated intc the

TD-6 Monte Carlo data library. Also , checks were made by generating multigroup

cross sections frcm these data sets with the MARK and LAPHA.NO codes and com-

paring them with multigroup cross sections derived frou,the original data sets.

c. LIB-IV-240 (’I’wo-Hundredand Forty Grcup Librarv) (P..B. Kidman)

LIB-IV-240 is a 240-&roup library that is being generated with MINX33

from34

ENDF/B-IV data. Last quarter the library was started and many of its charac-

teristics were described. This quarter, several nore isotopes were added tc

LIB-IV-240. The resulting 52-isotcpe library, shown in Table II, should be

complete encugh for most nuclear reactor calculations.

A new resonance-smoothed weighting flux was introduced in MINX. It is ex-

actly like the old thermal-1/E-fission function except above 10 MeV where a l./E-

13

TABLE II

LIB-IV–240 MATERIALS GENERATED WITH MINX FROM ENDF/B–IV

ISOTUF’L

ENDF/9VER IVtiAT NO

n-lm-.?H-3

ME-3Ht-4LX-6LX-78t.9Bwi O8-11C-12N-140*!6

NAw23AL-.27

51CA

11

vCR

ntJ.55

co-nNJ

CuhR-Q3

80co

CD-113Eu-151EuQ153

GDlk*i8i

Iiwltlzh*183n-184w-18b

Au.197

PB

lH.23.2

U-233

U-234U-235LI.23bU-238

NP9i?37Pu-23dPU-?3QPu-?ufiPu-?(llAB-2UJPUW2Q2

126Qllznilb91106127m127!1.?7?12891.273116P127cA1275127611561193119Q119512861!96119111971192119Q

119(3129511891287i281128?i29a1290jfi3012M5t12811291130113!128312881296

1?6010u3126!llb3126212b3

10501260126512661056llbl

PENn F’NAHt

VER N;

MIP

H2P !HJP

HE 3P ;MLIIP 1

L16P 1L17PBE9P :Rl@P 3B1l P 5C12P uNj4P \

016P 1

NA23P 2

AL27P 2

SJP. 1

CAP 1TIP 4

VP 1CRP 3XN55p 2

FEP

C059P :NIP 3CLIP ,2Nt393P 1MOP 4CDPcDlj3P :Eu151P .2Eu1531J 2GOPTA181P :H18.?P 2‘4183P 2

k’i8QP 2Wl@b P 2

AU197P i?

PtiP

TH232P :

U233P 5L123fJP 2

U235P 2

u23tP 2U238P 13

NP?$7P 1PU238P 3

PlJ23c2P 2

pu2avp 2

pu?fll P QA}!2LJ1P u

pU242P 4

Pt’NL)F

lIMIh C

(SEC)

13395

165102118157159516Q28182156593s9@66763151A654?2183ua

16U17ti5

1(375Q10

1251?07

297S53?n39

6059oFl

785

378jfi92

2023

1353

\352la8~

1685

6413853!

5s1672

28327t3Pl

645U208510a335056113

5QasunbbO

S8893

ISOTXSAt(i)

BRKuXSNAMt

VER N:

MIL 1H2L 1H3L

HL3L !HEfIL ~

L16L 1

LJ7L iRE9L

Bj@L :B1l L 1

C\?LNILIL :016L 1

NA?3L 1

AL27L 1

SIL 1CAL 1TILVL iCRL j

MN55L 1FELC059L !NILCUL :NB93L JHOL 1CDLC0113L ;EU151L 1EU153L 1GOL7A18i L jH182L 1M183L 1V.l I)UL 1W186L iAu\97L 1

PLILTH?32L ;U233L 1U23UL IU235L 1U23b L 1U2313L ]NP?37L 1PLJ238L 1PU23QL 1PU.?UflL 1PU241L 1AH2fll L 1PU242L t

ISOTXSANO

BROKXS

F13U~

PENDF

(SEC)

612595767279a51667733

Q363109$

llb6azn

1257lf196

9BI11551159131a

566568

2123803

17621158j 35012bb2179

~’aa877770913Q5R609

16781873

21fln

1659172615fJ218711922

661618

321265n

ai5213a6

Qah333637F12

8b5620689

69176

SIGOSET*

AAA8BAAAcDE

:

:0eD

:

:

:000BBD09BD0DD0BDBDBDBDDFD00D

14

fusion peak-1/E portion has been added. Thus we now have 10-5

ev < [thermal],

< 0.1 eV < [l/E], < 0.8208 MeI’ < [fissicn], < 10 NeV < [1/E], < 12.57 MeV < [fus-

ion peak] < 15.57 MeV < [1/E~ < 20 I,?eV. The intent is to make the high–energy

group cross secticr,s more appropriate for fusion calculations. The old spec–2- 3 4 6 7 9 10 I.1 12

trtm?t7asused tc generate ‘H, l’, H, He, Li, Li, Be, B, B, C, N,i4

16~ 23 239PU9 Na, Fe and . All of the other isotopes were generated with the

new spectrum..

After some testing, LI13-IV-240 will be released and shipped to those ex-

pressing an interest.

D. NJOY Storage Allocation Package (R. E. MacFarlane and R. M. Boicourt).

Large processing codes such as MINX and NJOY make extreme demands on the

Storage capacity of a computer. It is, therefore, impc.rtant to make effi-

cient use of the.available storage. ~~.fs requirement leads to syster,s of b’m]-

idle-chtmerxionifig where blocks of datz are stored in a large container array

at locations specified by pointers. In many codes (MINX is an example), point-

ers are computed directly by the code and remain static throughout a particu-

lar calculation. Such systems are sfmple and efficient, hut they are inflex-

ible for problems whose storage demands change continuously during execution.

In such cases, a system becomes desirzhle that dynamically allocates amd re-

allocates storage spzce.

lhring this quarter we have developed a dynamic stcrage allocation system

for NJOY called STORAG which combines features of existing systems into a sim-

ple and compact utility package. The package uses the four calls described

below.

STORM (h-, NIDMAX, A) -- initializes the package and allocatesspace for N%TIAX k-oralsand NTIPMAX different data identifiers in thecontainer array A.

RESERV (ID, NW, ID, A) -- reserve NW words in A for the data typeidentified by ID. The identifier can be integer or Hollerith. IfNW = -1, the routine reserves all available space and returns the

number of words in NW. This routine always tries to reserve spaceat the top of the container array. If insufficient room is available,it repacks the storage, eliminating any areas not currently in use andtries to allocate space again. Note that data in core may move around,but only if necessary.

RELEAS (ID, NW, A) -- release all but NW words for the data set identi-fied by ID. If NW = O, the ID is inactivated. The option NW > 0 is veryuseful in conjunction with the NW = -1 option of RESERV to read in datasets whose length cannot be determined in advance.

15

FmDEx (ID, IP, A) -- If data may have moved after a call to RESERVE,it is necessary to use this routine to locate the desired data set atlocation 1P in the container array.

This system has been implemented throughtout NJOY giving a great increase

in flexibility with no detectable decrease in efficiency.

E. Processing Photon Cross Sections (R. J. Barrett and R. E. MacFarlane)

The ability to produce photon scattering cross sections and photon produc-

tion yields was added to the NJOY processing system earlier this year. Near-

term plans call for the release of a photon production and photon scattering

library in CCCC format, although it is not yet clear whether the format will

consist of a combination of ISOGXS and ISONGX or the MATXS format described

below (Sec. II G). Before such a library can be released however, a great deal

of work must be done to develop methods of using it. Primarily this means ei-

ther that methods for handling gammas should be built into existing space-ener-

gy collapse codes, or that data calculated within these codes must be made a-

vailable to a separate gamma processor. For the time being, we have chosen the

second alternative, employing the logic depicted in Fig. 8.

Data needed from the space-energy collapse code includes resonance self-

shielding factors , zone mixture specifications, fine and coarse neutron group

bounds, fine-group neutron cross sections, and zone-averaged, fine-group neU-

tron fluxes. The lDX code has been modified and is now capable of outputting

a file called PHOCAL containing all of the necessary information.

The coding necessary to process the photon cross sections is embodied

in a program called NDULG (Fig. 9). It is designed to self-shield the photon

production for each isotope; collapse the neutron scattering, photon scatter-

ing, and photon production cross sections; calculate macroscopic cross sec-

tions by zone; and produce a neutron-gamma coupled set in ISOTXS format. Al-

though the code is completely written, it has not been debugged.

F. CCCC Development (R. E. MacFarlane and R. J. Barrett)

Group T-2 continued its involvement in maintaining and improving the CCCC

data files. In June, a set of revised specifications for the BRKOXS file was

submitted to R. D. O’Dell of IASL T-1 for inclusion in Version IV. Proposed re-

visions to Version 111 included an option to block the f-factor record by reac-

tions, and a parameter which specifies the number of reactions present. These

revisions allow the user to generate self-shielding factors for as many reactions

16

Ixm

INDULGI

ToSOTXS(COUPLED -s

Fig. 8.Calculational scheme for producingspace-energy shielded neutron-gammacoupled sets.

+

M4twaDsNsmss

MIX

+

COUPLE

bISOTXS

Fig. 9.Block diagram of NDULG code.

as he chooses and for large group structures, without creating

records. Both revisions have been included in the preliminary

fications, circulated on June 14, 1976.

unmanageably large

Version IV speci-

Go Comprehensive CCCC Cross-Section File -- MATXS (R. J. Barrett and R. E.MacFarlane)

At the May 4-5 meeting of the Committee on Computer Code Coordination

(CCCC), there was a great deal of discussion about the need for a comprehen-

sive isotope-ordered cross-section file. C. R. Weisbin of Oak Ridge Nation-

al Laboratory (OP~) argued that the present cross-section files (ISOTXS,

ISOGXS) were not flexible enough to handle neutron-gamma coupled sets. Fur-

thermore, there was no provision for specifying whether the files contained

microscopic or macroscopic data, or whether the data were cross sections or

multiplicities (particle yields). General agreement was reached that a com-

prehensive file was needed which could encompass a wide variety of data, and

which would have the type of flexibility discussed above. Specifications

for a file called CCCCCF, developed by J. L. Lucius of

for perusal and comment. It was decided that the ORNL

in conjunction with Westinghouse and General Electric,

suitable file specification.

ORNL, were distributed

and LASL data groups,

should work out a

17

In studying the ORNL proposal, we uncovered a number of difficulties

which we thought should be corrected.

1. The file was not similar enough to ISOTXS in the way it blockedand sub-blocked matrix data. We believed this would cause undue difficul-ties in converting existing codes and libraries to the new format.

2. It would be difficult to skip around within the file. For in-stance, within a given isotope, all vector cross sections for all typesof data were together, followed by all matrix data; furthermore there wereno location data (LOCA) for skipping isotopes or data types.

3, There were not enough descriptors to tell the user what type ofdata is present in a given file; for instance, there was no way to distinguishbetween a neutron-gamma coupled set and neutron-induced gamma production.

4. There was no provision for coupled vector cross sections. Evenwhen the matrix data are coupled, the vector data would not be.

5. There was a number of less significant points, including our be-lief that material composition data do not belong in the file.

Consequently, we chose to specify a new file MATXS to solve these

problems and to incorporate other features which we felt were desirable.

In addition, the new file was designed with the flexibility to incorporate

additional data types, such as self-shielding factors, delayed neutron data,

and delayed photon spectra.

Tentative agreement has been reached between LASL and ORNL to cooper-

ate on the further development of the MATXS file. We have written a code

which will translate an existing ISOTXS file into MATXS format and a general

printing routine for MITXS. ORNL is developing a code to convert ANISN for-

mat to MATXS. These codes will be exchanged, and additional development is

also under way.

H. MINX VS MC2 (R. B. Kidman)

The Processing Code Subcommittee of the Code Evaluation Working Group has

specified a simple reactor system that can be used to test and compare various

code systems. The problem is a zero-leakage, infinite, homogeneous, ZPR-6-7, with

the inner-core composition at 300°. All code systems are to begin with ENDF/B-

IV data.34

In an earlier comparison, the MINX/lDX system33,35

used at LASL36

gave an eigenvalue of 1.2140, whereas the MC2 system used at Argonne National

Laboratory (ANL) generated a multiplication of 1.2092. A detailed investiga-

tion was initiated this quarter in an effort to explain this difference.

Collapsed 28-group cross sections from MC2 were put into the lDX format

and compared on a group-to-group basis with collapsed 28-group cross sections

18

from the MINX/lDX system. An example of the comparison is shown in Table 111 for

239the Pu group cross sections. The results in Table III are percentage differ–

ences computed in the following manner.

Z Difference =(MC2 X-see)-(MINX/lDXX-see) x ~00 .

(MTNx/lDX X-see)

In Table III, 100.00 means that the MINX/lDX X-see = O, while the MC2 X–see +0;

-100.00 means that the MINX/lDX X–see # O, while the MC2 X-see = O. Similar re-

sults are available for every isotope in the composition and for the macroscopic

cross sections of the mix.

Exact perturbation can be used to determine what effect each cross section

difference has on the Km difference. In addition to the cross sections, adjoint

flux and Km from the MINX/lDX system, this method requires the regular flux and

Km one obtains by running the lDX-formatted MC2 cross sections through lDX.

This was first done using the fission source that LASL used in the MINX/lDX

testing. The resulting eigenvalue of 1.2118 was worrisome since it did not dup–

licate the original MC22

value of 1.2092. However, when the MC fission source2 2

was used with the MC cross sections in a lDX run, the original MC eigen-

value was duplicated. Thus , ~B difference of 0.0048, weinstead of the original K

are now trying to explain a difference of only 0.0022.

Following through with exact perturbation theory, we can determine the com-

ponents of AKm as shown in Table IV. An example of the particular effects of239PU

cross–section differences on the final AKm is shown in Table V for . The

numbers in this table actually represent the following calculation

(mcocaused by X-see difference

% Effect =Total ~Km

x 100

One should not be alarmed at the number and size of

in Table V for this is a normal consequence of analyzing

compensating effects

smaller and smaller

integral parameter differences. As before, similar results are available for

every isotope in the composition and for the macroscopic cross sections of the

mix.

Thus far we have explained .50% of the MINX/lDX vs MC2 difference. We

have also laid the groundwork for further investigation by clearly and conveni-

ently presenting cross-section differences and their effect on Km“

19

-------.

..

.=

“---d

-------

D6

-----------

<ml+

Co

I-lm.

..

-mm

GO

mAu-l

o0.00l-iI

+1+

Cm

l-11-i

U-em

Ucwu

Cw

m*

Ooc

000.

.0.00

t+2N00.

HHHE-1

l-l

~

.

o

+1+I

Ro

m.

;“r-

..

..

..

..

..

..

..

..

..

..

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..-.

..””.-..

,‘

##

●9L-w

sl-u

-mm

u-n

.*n

la●

●sem

-aru-

s-8

P.

a

20

k-lxHz0zcHHuE

lC

/J

x!2;k0mHvEkw

21

I

I. Leakage Corrections to Self-Shielded Cross Sections (R. B. Kidman)

Last quarter, several methods were introduced for adding zone-dependent

leakage corrections to the background cross section Os.. The correction which

yielded the largest changes is

where

(7)

L: = leakage rate from zone z for group g

@g = average flux for group g in zone zz

v = volume of zone zz

Dg = diffusion coefficient for group g in zcne zz

Nmz= atom density for material m in zone z. (8)s

This change increased the very low ZPR-111-54 eigenvalue by only .1.5%.

This fact, plus a serendipitous interpretation of a fortuitous error made during

the implementation of Eq. (7), led M. Becker of Rensselaer Polytechnic Institute

(RPI) to re-examine the traditional formula for the diffusion coefficient. If D

is defined as the current-to-flux ratio

I JD=-—

iB~ ‘

one can use a flux given by the BO

B1 approximation to obtain

22

(9)

approximation and a current given by the

z(lo)

z is the microscopic total cross section for group g in zone z, and X: zwhere .Zg

is the microscopic scattering cross section.9

Equation (10) reduces to the

conventional l/3Ztr for small B/Z.

After Eq. (10) was also incorporated Into 1DX,35 we obtained 1.014 for the

ZPR-111-54 eigenvalue as compared to 0.9532 with the unmodified IDX (including

in both cases a net correction of + 0.021 for heterogeneity, dimensionality,37

and transport effects ). The new eigenvalue is encouraging because ZPR-111-54

now no longer stands out as a singularly bad critical assembly.

We have also analyzed ZPR-6-7 which is a much larger and therefore less

leaky system. The change in multiplication for ZPR-6-7 (0.9708 + 0.9747, un-

corrected eigenvalues) is about 15 times smaller than that for ZPR-111-54 and

in a direction to also improve agreement with experiment. Thus, our leakage

corrections appear to produce large effects when and where they are needed,

and to generate small effects when leakage is relatively small.

In summary, this work has successfully identified and incorporated zone

leakage corrections into the Shielding Factor Method and has demonstrated that

their application can remove the long-standing low-eigenvalue problem of ZPR-III-

54 with no significant penalties in computer time and with no additional problem

requirements.

23

J. Spectral Corrections to Elastic Removal Cross Sections (R. B. Kidman)

Since more accurate multigroup elastic removal cross sections38

have be-

come available, it is appropriate to consider a new method for adjusting these

cross sections to problem dependent spectra.

This is now done in 1DX2 via an iterative procedure between flux @ and elas-

tic removal cross section, c_. At each iteration, the authors use a linear in-–i+l;i+l

terpolation between ~i~i$(ui~ and Ci

e @(ui+l) to determine the value at

u -.66~i and then assume

(11)

where i is the group index, ~ is the average logarithmic energy decrement, ~ ise

the effective elastic scattering cross section, u is the lethargy, and.

$’ = ~i$(u)du.

As Eq. (11) reveals, the locations of elastic scattering resonances do not

directly influence the elastic removal cross section. This scheme was probably

adopted because up to now the elastic removal cross sections provided to lDX

were also generated without directly accounting for scattering

tions.

The elastic removal cross sections provided by LIB-IV were

ing to the following algorithm.

Oi =f 1%adE@o(E)ue(E)P (E+E’<Ei+l)

ro ‘dE@O(E) ,.

resonance loca-

calculated accord-

(12)

wherefais an integration over that part of group i which can possibly elastically

iscatter a neutron out of the group,

sis an integration over group i, E is the

energy, $O(E) is the arbitrary intragroup flux weighting spectrum, Ue(E) is the

elastic scattering cross section, and P(E+E’<E ~+1) iS the fractional probability

that an elastically scattered neutron of initial energy E will be scattered out

of group i. Equation (12) explicitly accounts for scattering resonance locations

in the computation of elastic removal cross sections.

The new method makes simplifying assumptions about the intragroup shape of

$.s 0> ~e, and P in order to compute two new values of the elastic removal cross

section

24

JOi = /!ac?uo;(u) G:(u) p’(u) ‘du $;(U) ,(13)

rl

k

~i adu +’(u) C@ P?(u) ‘du $’(u) ,

J

r2 =(14)

where the primes refer tc the assumed simplified shapes. The $;(u), O’(u), and-.a:(u) shapes are derived

is simply given a linear

The relative values

behavior of $0 and $ can

tion in the new method a

by

from 3-pcint Lagrange interpolation schemes, while P’(u)

shape.i i

of o~1 and G=2 are a measure of how the gross intragroup

affect the removal cross section. Thus, at each itera-

new effective elastic removal cross section is computed

(15)

where F~ is the elastic self-shielding factor. Firste

required by an averagin~ with the new flux @ are thus

order cross-section changes

introduced without losing

the dependence on resonance location since all iterations are directly related

to the original cross section.

Results from the new procedure and lE% are compared in Table VI which shows238

the final ZPR-111-54 U elastic removal cross sections in terms of the 3.ni-

tial cross sections. The striking feature of these results is the much larger

changes developed by lDX than by the new scheme. Similar results exist for all

isotopes in the composition. The new eigenvalue is .0.9% less than the lDX

eigenvalue.

Since the LIB-IV elastic removal cross sections are very realistic, the new

method for introducing spectral changes appears to give much more reascnabl.e re-

sults than the old 111Xmethod. Future work will consist of introducing better

self-shj.elding effects for the transfer cross sections, introducing spectral

corrections to all cross sections and, of course, establishing the effect of all

of these modifications on more than one critical assembly.

25

TABLE VI

A COMPARISON OF TWO SPECTML COMPARISON

SCHEMES ON ZPR-111-54

!22!21234567891011121314151617181920212223242526

x29303132333435363738394041424344454647484950

LIB-IVInitialGr@&Sl

.0284

.0277

.0298

.0308

.0422

.0784

.1848

.2167

.2479

.2768

.3048

.3375

.3647

.3870

.4086

.4152

.4248

.4367

.4435

.4533

.4618

.4704

.4846

.4938

.5031

.3662

.5210

.3551

.90041.1823

.3099

.2253

.2109

.2541

.4264

.2859

.0399

3.1446.0355

1.5052

.0264

.0300

.1772

.0510

.1408

.1461

.1486

.1499

.0000

238U ELASTIC REMOVAL X-SEC

lDXFinal~r~.Initial6r1.00001.72251.37671.18381.24891.3071.9860

1.0027.9759.9690.9785.9836.9649.9800.9742.9708.9521.9752

1.0174.9570.9706.9552.9467.9717.9645

1.00881.3920.9568

1.4957.5434.3741

1.43711.86551.86811.4144.85811.50435.8707.0595

4,2387.1425

5.11504.6318.68683.3696.9934.7461.5938.9550

0.0000

New Hc:hodFinalor

+Inft~alZ=

.75531.04021:13081.17821.19681.15061.03131.0204.9934.9679.9547.9911.9772.9886.9766.9738.95271.0047.9913.9448.9624.9724.9521.9584.9710.9773.9687.9590.9517.9494.9412.9361.9353.9184.9180.9142.8948.7525.7209.6786.7551.7748.6656.7694.9271

1.0242.8451.5908.98o90.0000

26

K. Effects of Weighting Spectra cn Croup Collapse (R. B. Kidman)

The purpose of this study is to compare the effects of group collapsing with

an actual spectrum vs collapsj.ng w-ith an arbitrary spectrum. We have performed

this comparison using the Processing Codes Subcommittee’s infinite homogeneous

ZPR-6-7 specification. The procedure is outlined in Fig. 10.

If one begins with the 5C-group CCCC39

format library LIB-IV,38 4C

uses CINX35

to convert a 50-group lDX format library , and performs a K and 28-group crunchm

calculation with lDX, a value of K = 1.2140487 is obtained. On the other hand,m

if one begins with LIB-IV , uses CINX to crunch and convert to a 2&group lDX for-

mat library,1

and then performs a K~ calculation with lDX, he will obtain K =m

1.2191568. Thus, for this problem, we see that collapsing with an arbitrary flux

~ by 0.0051081, or 0.42%.increases K

Locking further and in more detail, Tables VII and VIII show, respective~y,

the 239Fu resonance-shielded cross sections resulting from collapsing with the

actual spectrum and from collapsing with the arbitrary spectrum. (In the inter-

est of presenting compact tables, the uninteresting C-9XG and G-1OXG terms were

dropped.) Table IX is a more convenient and comprehensible percentage compari-

son between Tables VII and VIII

Table IX =Table T7111

- ‘able ’11 x 100 .Table VII

TO determine how each of these differences affects Km, we have invoked exact

perturbation theory (which combines the cross-section differences, flux, adjoint

flux, Km, K:, and m,aterial densities). Table X shows what percentage of the final.

AKm (= 0.0051081) is caused by each cross-section difference.

WYiatwe find is arienormous number of differences that need to be explained.

The -40% differences in the transfer cross sections of Table IX are a result of

truncation effects caused by limiting the number of c?owmscattering terms to 10

in both CINX runs. All of the other differences and effects are real.ant?are

caused by the different weighting spectra used. Notice that groups 2-6 and

22-26 display the fewest changes because these groups also exist in the 50-group

structure. (Group 27 is composed of 3 fine groups, group 28 is composed of 5

fine groups, and each of the unmentioned rest is composed of 2 fine groups.)

Also note that there are a considerable number of compensating differences.

Finally, one should note that the largest cross-section changes do not necessar-

ily lead to the largest effects on Km ●

27

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..

.00.

s00

al-l-%

-c-a

CI-U

C=’=

=6

lu-----l-u

rwt%

nl

~~S

6S

5S

SS

SS

GJ

11

88

11

11

11

UL

4.1

WU

.UL

UW

UJ

IL.

UL

:ti==rtcccr-a=la

U-+

cc

-=U

TC

3?O

$=IS

r-G

Cs

U-r-t--c

t-b

ac

=e

es

..

..

..

..

..

..

..

..

..

..

.●

...***S

su-fw

l-m.t%

-c==zm

Ssr-lr’ssssssss

5sstu

----S

Z6

Ill~b

-1:

.-rus

=l-w

-.

..

mu

-r

-------S

F.6

-S6

Z0

11

81

1U

Jx

s.u-u

u.C

=C

L-I-<

nlz.%

,r=

tr&

aL

-=G

=J

..

..

..

Pt-u

rutu

nln

l

----S

sss0

41

1U

J.u

u.ld

I--cw.=

e

-l-ar-

,...

*Al

--

----C

S9S

++*+

L4.!u

d.

r-vll-s=90-

6S-C

U.

..

.----

-----6

=sssss

+++++*

t4J

iL.&

kl.A

Jt-

C.c

i<s

r-c<m

l--l-->N

---sI--

!O.

...0-----

e

++

++

-++

+*-*.

U.IA

UW

-I.4JUJU

.U

.A.u

W0.Z

3=71-IF

LO

I-.-.C

r-cm

t..zro+:>

ez.rz

-2

Sr-a

er-r-<

<r-c

s-

●..,....

..

..

n,

---------IN

N

cru

.c

6E

----9s’ss3

=s9

9.-

A-A

A*.

-u

J.u

ti.uJ

tuu

lL~.L

luC

IW=<=-N

P<

=).v-.-u

cm

=m

m=m

Icru

cc

---nw

nw

..

..

..

..

.C

31

r<r-u

--ml%

u5r.c

r.ri

---3=s=399

s-=*-

+..*.+

.U

ldL

JA

1.

.dd

lA

lr-r-.

.r-lrrru

--u-N

r--.ezs=

*

ZC

..mlr=

ll-=g

w.

..

..

..

..

nJ

Nr-=

?.c?----

bL

x6

cc

c6

6K

r.zszz-sxsa

+++.-+

.**U

IUI,

AI..J

.4J

W-.J

U.c

<n

Lcrr.u

-r--:,-e3

t-,nca

o

cccL=.a.-c

.uwf-

●***.****

d.lw

rur.

luw

+c

.0.,...

su-cN-@

l-.7

s.+

28

..

..

..

.6

s66

s6s

..

.m

-s

s1(u0’

-c

.-.6

!%

---*1-W

N(L

I*S

sssc=%

%s

11

11

11

11

UU

UJ

UJ

UU

JU

IXI’.

.cc--Ll-ca

-a

=.?rzm

t-a.r

Cc

b--.c

c%

h%

h.

..

..

..

.f-

N-=s

N---

-c!●

..-.:-.-.*.

.***.***

6Gu

-uP

-E*m

r.-=

6C

N=

●☛

✎☛

SS

6S

....0

...6

G6

ssm6

a

.*.,..**

●☛

✎

6SG

C6666S=

..

..

..

..

..

Csw

-m(rll--m

cvm

6=+wr.:.

u6s

6C

6S

ss.+

+.k

#L

&r.=

l-*-lrU

’r.’..c

..(

u-

l-c

‘ir4

L.

.C5

S,..

.u

--

9

-----------

.--.--NS

ZZ

CS

6%

6S

6S

Ca

ss1

18

18

80

81

88

?#@

..J

W$

uiu

u!u

.iu

w.u

u,U

Iwu

wC

ur-=

<-a

t-cet-

-nl=

Tm

rlr-c-cnl=

r--cr-

ma

ul

cs=

Lc

r-1-f-f-*c

=J

I-N”=

..

..

..

...

0.0

00

*--=J

---------J

=

..

..

.----

Kccscc

ccc

----s3

3c

ilc3

60

3c

=e

a%

C2

s.-

+++-.+

**+++

.uU

Ju

ldt.

wd

u.

-.ll.J

.u..J

Al

uI-I-=

7=r-r-m

%R

-r--r-a

--w-.-=

-.t=n

J-m

az-=

rau

-’ua

--zu

-r--c

..

..

..

..

....!

-nlm

ll’vnl

r-=1 <r----w

.-.-.--.

N&

9.9

smm

**+***

UJ

.MA

IUJ

WU

Jc

.cm

=J

al-

*’wr-ra

Ln

*.&

t--.u

&a

-a,..

.*.*

PU

-U’

.-9*

29

:0g

6rsr.5

6c

s6c

66

--66

1s5

1s&

Rm

6E

6E

66

6S

CS

CS

IS=S

SS

IS9

%6

6Z

X%

%S

S=S

Szsss.s

..

..

..

..

..

..

..

..

..

..

...0.

..

.sG

seJ

s6sssls2

=s9

L9

sw

al

2,.v

..

..

..

..

..

...0...0

..

..

..

..

..

..

SlE

91109~(9

~6

a9m

Ssa

Qa

*8

66

&c

66

cr-N

5--se

ts56

c5

66

S6

56

5C

56

Sls.s-sssx

Lr

cc

.<S

SS

6S

SS

SS

C=ssss5

9s

..

..

..

..

..

..

..

..

..

..

..

..

..

..

Sc

ssssssmse

I:ya

ss6

=C

ES

S

6c

E6

sK

6c

u?s6

fu--6

s66

66

6s

S=

S6

6W

56

slGs5

ssru

ssa<

Ssssc

s,s%x

szS

sssss...

..,...

●.*...**.

●...*.*..

.G

slssss1

ss=S

ss6

S6

SS

SJ

=a

m8s

SC

SS

6?C

+S

65

5C

+=7

Xb

-.c-u

ulse

=5

srscx

&-E

Els

5C

SS

61

11

ZS

6S

Cc

=zfi-.a

lsszv.Z

SS

=3

SS

S.

...,....

..

..

..

..

..

..

..

..

..

.E

swc

s1

Istsmza

r-<c

lss-=

ssssssms

aa

llmtn

l--w

LS

C6

CL

CC

CC

SC

7-

=1

.ru

I-=ic<l-Gc

EG

S5C

G0

6Z

S=-8

SS

GS

GP

,<S

&~

S’S

GP

J6S

SS

SS

6SS

..

..

..

..

..

..

..

..

..

..

..

..

..

..

SS

ssE

s5

-I

I-6S

-I-W

S6

SS

SS

ssa-b

Cslssh

ssslsse

..?-l-raK

s.,e?-ssss

S6

SS

66

Css-.

ssssse

r.s.-lrssct-t*csss

SS

sss$●

..

..

..

..

..

..

..

..

..

..

..

.6

=6

●.*.

SS

S6

6=

1-s6

:y6zsss

SS

66

S

IL00M

66

-c6

6a

c*G

au

cG

r-cssc

cs6

6s’s6

ss6

SN

C====Z

!-=J

.sr-l==e

.m=Z

==sslss

6s5

s...

..

..

..

..0........

.

61

S.

..

..

..

s19

t9a

ylss:~

sssssss!9

nc

2a

ln

Ee

ew

am

sr-r-wlfvu

rulrlrl-u

r-eE

t-r-L

n6

se

I-e.E

K.C

WC

-W-U

-31

-=Ir.c

s.csc

s=c

=P

-=’s-r.-il-ln

●...*,.

..

..

..

..

.●

0.,...0

..

..

9=

tIm

=ro

.-wru

sr-en

Jvi.-5

.l.l

Dyg

:a

si

l--w

-l-

et

1-

-tr-lrfvlN6

u5

Cc

m=b

-cc

r-ra

l-cIrtrc

sc.

ee

aa

ecrQ

iss-*--?nnJs

9-

I-S-S

----4239sszm

l-.

..

..

..

..

..

..

..

..

..

..

..

..

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.N

lll-

118

In

Ja

IB41

-1194

mm1:

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csc

ssac

s-(V

U-W

--*-IN4

2Q

.-66

SE

SL

2w

-Uc

=c

asstw

asa

s.s-lw

Sc

ml-u

.a-z

s96

=s”I-

..

..

..

..

..

..

..

..

..

..

..

..

..

..

11

11

18

88

8IUWIIe

SIS

IIt

I-.4

-nlift.-

N

.=C

SE

.S6

CS

6E

6-

Nlrlrt--l-u

”fv.cx

-GS

66

SU

UT

=S

CJ

GZ

-AIX

I-WW

.1,

z--lww

s.

ew

c.-m

am

lscas-b

●0.......

...*.....

..

..

..

..

,.

8111B

98

81

Ium

llea

lsll)l-a

“Mmm

-ii

30

SC

cr--s

cc

cC

vaccc

cc

-N

csc

e=c

cs

sS

SX

S’S

.S

%G

SS

Cssssssm

zzS

Sss.

ssss6

5fS

6&

5S

a&

CS

CS

SG

SK

GC

6S

S6

66

65

S.

..0....

..

..

..

..

..

..

..

..

..*DS

66

65

66

68

16

61

GC

Z6S

665S

S

SS

S.-6

66

66

WI-6

-S6

6S

SS

SS

SS

65

66

5C

SS

6S

X=C

EW

=%

SS

=S

F===S

Tsssssss

SS

sssssssss

=ssssssssss

S.s

ssss

....

..

..

..

..

..

..

..

..

...0●

**O

Sss

S666G

tS

S=1

SS

CS

=6

66

6t9

66

G5

66

cu

fuc

-tiG

ISa

mS

G6

6C

S6

aS

66

SS

zssszs=c

s====s-=

6s=

G=szx

csc

s6

66

SS

66

6S

6C

SS

6S

66

66

GS

6s6

0se

aa

..

..

..

..

..

..0..0

...O

.O

.0

***●

Es

S5

66

1:

LS

=l

66

56

S.

66

65

66

_

s6K

6sc

t95

5c

!zS

U6

K’5

6=6

SS

6C

SQ

6=6

Ws.zss=

ssmss

9ss=

==s%

ss3?2

s3ss3

S6

51

SC

G6

66

66

EI!2

C6

-S=6

66

6C

6s=

==

..

..

....0

...0

......

...00

.0●

=6

s56

6s

56

66

66

66

SS

66

=6

6S

6S

=S

5=

31

Similar complete results for the other isotopes in the zPR-6-7 composition

and for the composition as a whole can also be provided upon request.

The value of this worlc is that for the first time the excruciating details

of weighting function-caused differences are completely and conveniently pre-

sented to highlight the kinds of effects to be expected from using various weight-

ing spectra. It will be interesting to repeat this work after lDX has been modi-

fied for gross spectral changes on all cross sections. We WOUICI expect the dif-

ferences to be much less than we see in the present work.

I,. Improved Cross Sections for Thermal Reactor Analysis (R. E. ?facFarlaneand R. Boicourt)

With the support of the Electric Power Research Institute (EPRI), the NJOY

nuclear data processing system is being extended to generate improved cross sec-

tions for use in the analysis of thermal power reactor systems. During this41

quarter, we have concentrated on developing improved data for EPRI-CELL. This

code is designed to produce self-homogenized few-group cross sections for typi-42

cal power reactor cells. Thermal range calculations are based on THFRXOS and43

epithermal calculations are based on CAM-l modified to use equivalence theory44

in the manner of the WIMS systern.

The thermal library for EPRI-CELL contains multigroup capture and fission

cross sections, the group-to-group scattering matrices, and other quantities re-

quired for the thermal flux and power calculation. A new storage procedure has

been implemented for the scattering matrices which cuts the storage required in

half. Furthermore, a temperature interpolation capability has been added for

both cross sections and matrices. “Since all cross sections produced by NJOY

have been accurately Doppler broadened, interpolating between temperatures on

the library tape provides accurate cross sections with a smooth temperature de-

pendence without requiring the use of resonance parameters. In addition, the

size of the library can be further reduced since it is not necessary to provide

scattering matrices at so many intermediate temperatures.

The fast library for EPRI-CELL contains cross sections for fission and

capture; matrices for Poelastic, PI elastic, (n,2n), and inelastic scattering;

self-shielding factors for fission and capture; and fission ~ and x data. All.

these data are produced by the current version of NJOY; however, self-shielding.

factors are computed using the narrow-resonance approximation. In a thermal

reactor, the strong broad and intermediate resonances in the 0.1-100 eV range

32

are very important. In order to treat these resonances more accurately, a

simple infinite mediu~. flux calculator has been added to l?JOY. It is assumed

that the heavy absorber is mixed ~;itha light moderator so that all resonances

zre narrow with respect to moderater scattering. The weighting flux for group

averaging is then obtaine? from

4’‘e)=(#)0+F$:)(I?)(16)

where F is the solution of

E/a

J

Ue(E’)F(E’)

F(F) =+ (l-a,)E’[uo+o@] ‘E’(17)

E

In these equations, a is the moderator cross section per absorber atom, ~ iso t

the total absorber cross sections, o is the absorber scattering cross section,e

and u = (A-1.)2/(A+l.)2.Equation (17) is solved by iteration, using the point–

wise cross sections available within NJCY. Above some preselected energy,

the solution is assumed to be F = l/E (i.e, the narrow resonance limit). This

procedure gives self–shielding factors which incorporate broad resonance effects

in a manner consistent with the equivalence principles used in EPRI-CELL.

III. HTGR CROSS SECTIONS AND DEPLETION CALCULATIONS FOR REACTOR SAFETY ANALYSIS(R. J. LaBauve, M. G. Stamatelatos, and T. R. England)

The LASL 9-group cross-section library for HTGR end-of-equilibrium cycle

safety analysis has been expanded to include 21 nuclides. These are as follows.

ENDF/B-Nuclide MAT NO.

102.3.4.5.6.7.8.9.

10.11.12.13.14.15.16.17.18.19.20.21.

B-10C-120-16Si-28Xe-135Sm-149Th-232Pa-233Pa-233U-233U-234U-235U-236U-238Pu-238Pu-239Pu-240Pu-241Pu-242B-10C-12

115511651134119412941027111711191297126010431157116311581050126412651266116111551165

VERSION Region

IIIIIIIII111T-vI

IIIIIIINIvI

IIIIII111

IIvIVIv

111IIIIII

CoreII111!

17

II

1!

1!

11

II

11

!1

1!

11

11

II

II

t!

reflectorreflector

Cross sections for every nuclide in the above list are available for 12

temperatures including 300, 500, 600, 800, 1000, 1200, 1500, 1700, 2000, 2300,

2600, and 3000 Kelvin.

First Pass CINDER code calculations for actinide buildup and depletion

and associated fission product absorption are in progress.

IV. COMPARISON OF MONTE CARLO AND Sn CALCULATIONS WITH 7Li PULSED SPHERE

EXPERIMENTS USING ENDF/B-IV DATA (W. A. Reupke [Georgia Tech] andD. W. Muir)

As a test of nuclear data and methods, the neutron leakage fluence for a

0.5 mean-free-path 7Li sphere pulsed with 14-MeV neutrons45

was calculated with

one-dimensional discrete ordinates and pointwise Monte Carlo particle transport

codes using ENDF/B-IV data.

The pulsed-sphere problem specification46

was modified to include the steel

corrosion encapsulation because the encapsulation was not present in the target-47

out or blank run. Preliminary calculations demonstrated that omission of the

34

encapsulation leads to 2, -3, and -8% change in leakage fluence, integrated over

energy bands 15-10, 10-5, and 5-2 MeV, compared to the case with encapsulation

included,

The one-dimensional discrete ordinates calculation was performed with the

r),,cod~8 using ENDF/B-IV cross sections processed into multigroup form by the

NJOY code.49

Energy boundaries corresponded to the GAM-11 100-group structure,

within-group flux-weighting was flat, the dilution factor was infinite, and Pothrough P5 Legendre moments were generated. A one-dimensional problem specifi-

cation was obtained by transforming the experimental quasi–sphere into a system

of concentric spherical shells in which the volumes and densities were adjusted

to preserve the masses and the average radial positions of the original compon-

ents. Spatial mesh interval was 0.5 cm, well below characteristic mean-free-

path

LASL

code

lengths, and the order of angular quadrature was 16. Execution time on the

CDC 7600 was two minutes.

The Monte Carlo calculations were implemented with the continuous-energy

McN’O using pointwise cross sections processed from ENDF/B–IV by R. J. La-

Bauve and D. George (see Sec. II B). A time-dependent energy-angle- and inten-

sity-angle-correlated neutron source function and relativistic energy correction

as developed by LASL Group TD-6 were used in the calculations. The neutron spec–

trum at a point detector 765 cm from the sphere center was binned into 0.2-MeV

energy intervals, and represented neutrons accumulated at flight times between

130 and 410 ns. Approximately 80 000 neutrons were started to give a typical

standard deviation of 7-8% in a fluence energy bin. Execution time on the LASL

f31’JC7600 was 15 minutes. The results of the calculations, converted to compat-

ible units are compared with experiment in Fig. 11. While general agreement be-

tween both calculated spectra and the experimental spectrum is found, discrepan-

cies of up to 40% are observed in some regions below the elastic peak. These

discrepancies may be due to ENDF/B-IV data, to the data processing calculations,

to the neutron transport calculations, to the conversion from experimental time-

of-flight (TOF) data to energy spectrum data, or to an unknown experimental

factor.

Discrepancies common to both calculations tend to rule out inadequacies in

the two data processing procedures and in the neutron transport calculation. In

particular, the over-prediction in the region 10-12 MeV, where calculation-to-

experiment ratios (C/E) are as high as 1.4, and the under-prediction in the tail

below 4 MeV, where C/E values are as low as 0.7,suggest a problem either in

35

LIB-IV

5D-Cr..p

,/\ nCINX.2L1-GrOupI._

CINX

50-CrO.p

I

EXXIXCnmeh to 28-cPAdJohtc FluxShielded X-SeeSO

I

ElDX28-CropFluxShielded X-Se.u

\/

ElExact ?ert.rb.c ionTheory Analysis

Xffect m S_ ofevery x-sacdifference

Fig. 10Procedure for de~ermining spectra ef-fects in group collapsing.

i 1

NEUTRON ENERGY. MEV

Fig. 11

Comparison of Monte Carlo and Sn cal-culations with 0.5 m.f.p. 7Li pulsed

sphere experiment.

the ENDF/B data, in the experiment definition, or in the conversion from TOF

data to energy spectrum data. On the other hand, discrepancies limited to a

particular transport calculation tend to implicate the corresponding data pro-

cessing code or the transport calculation itself, as in the region 6-10 MeV,

where multigroup discrete-ordinates

Carlo data by up to 30%.

By additional calculation, the

rowed. For example, a previous C/EK1

under-predict both the experimental and Monte

sources of discrepancy may be further nar-

comparison of direct TOF results using a

different Monte Carlo coded’ shows the same low-energy discrepancy. This sug-

gests that the discrepancy in the low-energy tail is not due to the conversion

from TOF data to energy spectrum data, but should be attributed to the ENDF/B

data, or to a difficulty in the experiment definition. In another test, sim-

ulation of the discrete-ordinates results with a calculation of the one-dimension-

al model by Monte Carlo gives 2% agreement in the region 6-10 MeV, This result

36

suggests that the 30% discrepancy between 111discrete ordinates and 2D Monte

Carlo lies neither in the data processing stages nor in the discretization of

neutron transport, but is attributable to the essential two-dimensional nature

of the experimental neutron source and target sphere.

Appreciation is extended to J. Kammerdiener of Group TD-2 for helpful dis-

cussions of the sphere experiments, and to R. Schrandt, B. McArdle, R. Seamen,

and J. MacDonald of Group TD-6 for assistance with various aspects of the MCN

calculation.

v. FISSION-PRODUCT AND DECAY STUDIES

A. ENDF/B Phenomenological Yield Model Improvements (D. G. Madland and T. R.England)

1. Distribution of Independent Fission-Product Yields to Isomeric States.

Approximately 15% of the primary fission products in fission of actinide nuclei

are nuclides which have an isomeric state with a half-life T ~ 0.1.52

A simple

semiempirical formalism is described for calculating the distribution of the in–

dependent yield strength, IY, between the ground and isomeric states in these

cases. The calculated branching ratios are easily incorporated into the phenom-

enological (Gaussian) yield model to be used in Version V of ENDF/B. Previously

(ENDF/B-IV), most yield branching ratios were set equal to 1 for expediency.53

It is assumed that (a) primary fragments are formed with a distribution,

I’(J),of total angular momentum, J, which is cut off at some characteristic val-= <J2>l/2

ue, J~,~ Y and (b) the primary Eranching mechanism j.s,simply, that

fragments with J values close to that of the ikomeric state (Jm) decay to the

i~omeric state, and framents with J values close to the ground state (Jg) decay

to the ground state, the driving force being that electromagnetic transition

rates are generally strongest for minimum LJ.

The form of the fragment angular momentum distribution used is that of

Rasmussen:4

P(J) ~ (2J+1) exp(-[J+l/2]2/<J2>) . (18)

Consider, for example, the case with A odd (all spins half-integer), Jm> J and

IJ -J I = odd integer. Then one findsg’

mg

37

/,

m

F(J)dJ

IY(isomeric state) (Jm+J +1)/2

IY(g.s.) + IY(isomeric state) = ~~ —. (19)

All together

even or odd,

/

J?(J)dj

1/2

there are eight such cases depending an wheth~r A and IJ -J I are~~

ard k-hether Jm is greater or less than J . The resulting branchingE

ratios, defined by R = IY (isomeric state/IY(g.s.)), a~e given in Table XI and

are calculated with Eqs. (20)-(23)

s (20)

9 (21)

‘3=+“<J2’+Hwg+4)l

+(1/<J2>) @:l)ew[-(1/<J2>J(~)(J$:2)] ,

F4=exp (-(1/<J2>)(Jm+~g+1)~m~)~ .

(22)

(23)

38

TABLE XI

INDEPENDENT YIELD BMNCHING RATIOS,R, FOR ISOMERIC STATES

ODD A

Jn,-J = even integer Jm-J = even inte~er&3 z

Jm>J Jm<JE 13

()

‘1

()

l-F1—.—.

I-rl ‘1

J -J = odd integer Jm-J = odd integerm~ ~

Jm>J Jnl< Jg g

()

‘2

()

1 - F2

1.- F2 ‘2

EVEN A

J -J = even integerm g

Jm-J = even integer~

Jn,> J~ Jm<J

CT

()

‘3

()

1 - F3

1- F3‘3

Jm-J = odd integerE

.Tm-J = odd integer~

Jm > .T Jm<J1? $3

F/,

() ()

1 - F/,——1-F tl ‘4

J55

values were presumed energy dependent and were determined empirical-rms

ly as a function of neutron energy with the result that Jrm~ = (7.5, 7.5, 8.0,

9.0, and 10.0) for En(MeV) = (thermal, 0.5, 2.0, 10.0, and 14.0), respectively.

Comparisons of calculated and experimental56-59

results are shown in Fig. 12.

A total of 423 cases at 3 neutron energies has been calculated. A detailed

LASL report on the calculations has been prepared and will be published soon

tENDF-241). Where experimental data do not exist, the calculated results have

been recommended for the expanded ENDF/B–V fission yields.

2. Pairing Effects on the Distribution of Fission-Product Yields. Version

V of ENDF/B is expected to have > 20 yield sets for > 13 fissionable nuclides ap-

plicable at one or more fission neutron energies; the effects of neutron and pro-

ton pairing are needed. To date the Z pairing effects, based on assessments of233U 235U and 239PU at themal ener

measured yields, have been reported for , ,60-63 233 235

gies. For U and U, N and Z pairing effects for thermal fission and61

the Z pairing effect for fast fission have been reported. Experimental data

for other fissionable nuclides and energies are, at present, inadequate for sim-

ilar analyses.

For use in ENDF/B-V, we have developed semiempirical relations for the av-

erage Z pairing effect based on a correlation with the excitation energy of the

compound system relative to the outer fission barrier; to first order, the

smaller N pairing effect is proportional to the Z pairing. The relations can

be incorporated into the phenomenological model used in ENDF/B for isobaric53 235 53,61,64

yield distributions. The results, based on U yfeld data and meas-65-67

ured barrier heights, predict pairing effects for other even–even compound

systems in good agreement with experimental analyses.

There are four factors, Fi, which modulate the normal independent yields

(NIY), i.e., for each mass chain nuclide the independent yield is (IY) = Fi(NIY)

where

F =l?X?Y.i

Here X(Y) is the proton (neutron) pairing enhancement relative to the normal

yield, i refers to nuclide type (even-even, even–odd, etc.), and the + sign is

used for an even number of nucleons. Except for prompt neutron emission, X

and Y would likely be equal but, in fact, X is about five times larger than Y

(averaged over all masses) which explains the usual reference to the even-odd Z

ej’.fect.

40

235UFigure 13, which illustrates the values of (Fi-l) extracted from

thermal fission data, clearly demonstrates the existence of four factors; the

neutron pairing effect is obviously stronger for the heavy mass region.

Table XII lists selected results for 11 nuclides at 4 fission neutron ener-

gies (tabulated values represent pairing effects averaged over the entire fis-

sion product mass range). At 14 MeV, average X and Y values are 0.015 f 0.015

and 0.003 f 0.003, respectively. (The large uncertainties reflect the paucity241

of 14–MeV data.) For odd-Z systems, such as Am and243

Am, the X value is ex-

pected to be zero. The complete calculation is described in detail in Ref. 68.

The calculated results have been recommended for use in the phenomenolog-

ical yield model for the ENDF/B-V fission products in the absence of experi-

mental data.

B. Fission Yield Theory: Statistical Model Development (D. G. Madland, R. F.Pepping [University of Wisconsin], C. W. Maynard [University of Wisconsin],T. R. England, and P. G. Young)

Work is progressing on the initial version of a statistical model calcula-235

tion of fission product yields for U thermal-neutron-induced fission. This

case has been chosen to test model developments because it has been studied ex-

perimentally more than any other fissionable nuclide.

3

11-

2

t‘L

I Ir

Io.

!MERROR BAR =

th SIZECFPO!NT

Fig. 12Comparisons of calculatedmental branching ratios Rstates

and experi-for isomeric

220 /lxoz

o-1o -

2~

2-20 -

\

~-w0 liEAvY MASS PEAK

zQ~

5 003 z 009 z E&NNZu 003 N EVEN N Fti ;n

Fig. 13Deviation of the summed IY from thesummed NIY for odd-odd, odd–even,even-odd, and even-even fission pro-ducts and for the light mass peak,heavy mass peak, and the total massdistribution in 235U thermal.

41

FissionTar~t—.

232Th

233U

234U

235U

236U

238U

238PU

239PU

240Pu

241PU

242PU

a

b

c

TABLE XII

ESTIMATED VALUES OF X AT FOUR NEUTRON

0.0 l!eV 0.5 Mev—-.

----- —---

o 21+0.29 o ~4-F0.18. -o.Jb) ● -0.14

+1.83-----0’67-0.67

0.228t0.034 (c) 0.15::.;;.

----- -----

.---- -——

+0.96 o 23+0.330“46-0.46

.-0.23

0 ~7+o.22 o ~2+o.15.

-0.17.

-0.12

0 53+1.23..—--- -0.53

~ 21+0.28 o ~4+0.18\ -0.21 .

-0,14

. —— —-

1.0 MCI?

-----

+0.13O“ll-O.ll

+0.410’27-0.270 ~l+o.14

●

-0.11

FISSION ENERCIESa

2 MeV

o #o.54●

-0.33

0 63+1.67.

-0.63

—--

o ~5-Fo.19.

-0.150 ~o-Fo.12

●

-0.10

0 24+0.36.

-0.24

0 ~l+o.13. -0,11

0 36+0.65.

-0.36

0 07+0.09.

-o.07@)o ~2+o.15.

-0.12

0.078f0.063(c)

o ~7+o.22.

-0.170 33+0.55.

-0.330 09+0.11.9 -0.09

0 07+0.08.

-0.07

0 ~2+o.14. -0.12

0 07+0.09* -0.07

0 ~4~0.18. -0.14

Uncertainties for all nuclides are based upon uncertainties in model p~rameters;Y values arc given by ‘i=aX,where a=O.1$13 +and fast fission data.

—

233U values are in excellent agreement with

(which show much smaller uncertain~ies).

235U values derived from experimental data;

0.15? from an analysis of‘Z35U Lllcrmal

the results from data evaluations

used to determine model parameters.

42

Coding has begun on the calculation of deformation energies of the primary

fission fragments, based upon the binding energy optimization procedure given by

Seegar and Howard.69

The extracted deformation energies will be used in a rep–

resentation of the excitation energy of the primary fragment. The total exci-

tation energy is one of three major terms used in the argument of the statisti-

cal level density expression. The next steps will be to (a) incorporate the69

residual mass (difference between measured and calculated mass) into the ex-

pression for the fragment binding energy and (b) to perform an extrapolation on

the residuals into regions where they are unknown.

c. Calculation vs Experiment: Comparisons of Time-Dependent 13-and Y Spectram9r

From Thermal Fission of ‘J3U (T. R. England and M. G. Stamatelatos)

Beta and gamma energies and intensities for the 181 nuclides with spectral

data in ENDF/B-IV have been used to produce several libraries of group spectra.

One library contains 150 gamma groups (constant 50-keV width from O to 7.5 MeV)

and 75 beta groups (constant 100 keV width from O to 7.5 MeV). A corresponding

150-group gamma library was generated for use in comparing CINDER-10 calculations

with preliminary unpublished gamma spectral measurements by E. Jurney (LASL P–DO)

by folding in the detector energy resolution.

Table XIII provides a comparison of the integrated energy release rates at

the four average cooling times analyzed to date. Some fraction of the conversion

electron energy should be excluded from such comparisons. In these comparisons

only the conversion electron energy for the

version fractions in ENDF/B-IV is excluded;

and without this exclusion.

There are 711 unstable nuclides in the

38 nuclides having specified con-

Table XIII shows the comparison with

calculation of total decay energies.

The last column shows the percent contribution to the total gamma energy release

rate due to the 181 nuclides.

Comparisons of the absolute gamma spectra are shown in Figs. 14-17. The

spectral comparisons were normalized to the total calculated

for the contribution of the remaining 530 isotopes for which

not exist in ENDF/B–IV. The measured and calculated spectra

time of 20 000 s.

energy to account

spectral data do

used an irradiation

The calculated beta energy release rate is compared in Table XIV with exper-

imental values from Ref. 70. Calculation and experiment are based on an irradi–

ation time of 28 800 s. Except for the value at 6 s cooling, all values are well

inside the experimental uncertainties (7 to 10%). 43

MeV

Fig. 14

Gamma spectrum 5.56 h irradiation,70 s cooling.

Mt

Q ;0 2* 3il 40 6-0

MeV

Fig. 16

Gamma spectrum, 5.56 h irradiation,

MeV

Fig. 15

Gamma spectrum, 5.56 h irradiation,199 s cooling.

MeV

Fig. 17

_ - ~mcd

0- Experimental

I

Gamma spectrum, 5.56 h irradiation,388 s cooling. 660 s cooling.

44

TABLE XIII

Cooling Times

70199388660

COMPARISON OF ENERGY INTEGRATED y MeV/FISSION

(% deviation of calculation from experiment)

~ ~AL-EXP % of.

EXP Total yMeV/FIncluding Con- Excluding Conver- Due to Nuclidesversion Electron sion Electron Having Spectra(lsl)

+ 0.3 + 0.07 87.6+ 1.5 + 1.1 93.5+ 1.3 + 0.9 95.5+ 5.1 + 4.7 96.6

TABLE XIV

COMPARISON OF ENERGY INTEGIUITED 6 MeV/FISSION

(% deviation Of calculation from experiment)

COOLING”TIME~ CAJ.-EXP—iF

6s - 13.821s - 4.966s - 3.2

3750s + 3.410,950s + 6.0

Figures 18-22 show the actual ~- spectral comparisons. In the gamma and

beta comparisons, we have chosen to plot the energy relase rate (in units of

MeV/fis/bin) rather than multiplicities. This emphasizes the spectra at high

energies where we also see the largest departure of calculation from experiment.

The data library used in the calculations is described in Ref. 52.

D. Noble Gases, Halogens, and Other Fission Products (T. R. England and N. L.Whittemore)

A large number of CINDER-10 calculations using ENDF/B-IV data are in prog-

ress to determine various source terms for use in studies of spent or irradiated

fuel accidents. These include the content, absorption, beta and gamma energy,

and corresponding spectra for halogens, noble gases, and the total fission-pro-

45

I

h.=.10’ 1

Energy(cV)

Fig. 18Beta MeV/fis at 8 h irradiation and6 s decay.

1

-l

_ ~ CWedO=Experimental

T Io

1

-5”104 10’1

10”r1

Encr~(eV)

Fig. 20Beta MeV/fis at 8 h irradiation and66 s decay.

46

Energy(c\’)

Fig. 19Beta MeV/fis at 8 h irradiation and21 s decay.

++*

+

t

_* ~gpi12dO=Expcrimcntal

1 1

o’ 10’i

10’‘7

Encrgy(cV)

Fig. 21Beta MeV/fis at 8 h irradiation and3750 s decay.

i+++

T +~

70I I_I 1

-5”104 10’i

10” 1Energy(cV)

)’

Fig. 22.Beta MeV/fis at 8 h’irradiationand 9576 s decay.

duct ensemble. In addition, calculations of halogens and noble gases and their

progeny (subsequent to a partial or complete escape of these gases) are in

progress for use in radiolyses and synergistic studies. The calculations in–52

elude the 824 nuclides in the ENDF/B-IV fission product files. Of these,

there are 93 gaseous isotopes of Kr, Br, 1, and Xe, with 78 being radioactive.

‘Fissionburst calculations for those fissionable nuclides having yield data

in ENDF/B–IV have been completed. These results can, with additional effort, be

used to generate a burst kernel which can be folded into any power history if

neutron absorption can be ignored (as in the current ANS 5.1 Decay Heat Standard).

Calculations for the infinite irradiation of235

U where absorption in fis-

sion products is ignored have also been carried out. This type calculation is

equivalent to a fission burst in that one can be derived from the other. In ad-

dition, the case of a finite irradiation without absorption can be derived from

either type of calculation.

Of more immediate use, calculations for typical reactor lifetimes and power

histories where neutron absorption is permitted are in progress. Currently,

these calculations use four-group cross sections.

Tables XV-XXIII show aggregate summary results for the case of235

U thermal

fission for one year at a constant fission rate and constant flux. The thermal

47

TABLE XV

TimeStep.

BARNS/FISSION DURING AND FOLLOWING 235U + n FISSIONWITH ALL FISSION PRODUCTS INCLUDE&h

Elapsed 4 barns / flss ~

Z&!!QM. Group I Group II Group 111 Group IV

6,2208E+a6 4,9S?5EW02 203129Ew01 l,8012E+01 8,7$76E+0i!j,2U42E+a7 5,01\6Ew02 2,3511E00\ 1085J4E+91 4,7272E+02l,8662E+07 5,0U07E=02 2,3638E*(!J1 jo8656E+01 3,3698E+022oU883E+a7 50@S77E~ti2 i?,3678EQ0~ l,8612E+0~ 206777E+023,1164E+617 5,0702E~0i? 2,3680EcOl l,8487E+01 2,2550E+023,1104E+Fi7 5,fd702Ew02 203680Ew01 $,8487E+Q11 2,2550E+PJ23,1104E+07 500702E~02 ?,3680E001 l,8U87E+0! 2,i?9SfdE+f323,11134E+?17 5,0T02E002 2,3680C-fil l,8487E+01 2,25g0E+0?3,1$04E+n7 S,0702E002 2,3680C~0\ lo8487E+01 2,25SIE+L723,1104E+n7 S,67(3?EQQ2 2,3680E00~ lo8487E+el 2,2553EtPJ23,1104F+(!7 5,07@2Ew02 2036841CDQJ1 l,8487E+01 2,2S57E+023,1104E+a7 So0702E~02 2,3680Em@l l,8487E+f)l 2,?S66E+e23,!104E+07 50137(!J7E902 2,$680Ew0\ 1,8487E+(IJ1 2,2587C+023,1104E+PI7 5,070?Ew@2 2,3680Es01 l,8488E+01 ?02623E+(?23,11a41?+a7 5,0702Ew02 2,3680!!=01 l,8488E+01 2,2731E+Q123,1105E+k37 S,070SEW02 i?,36801!m01 l,8fJ88E+01 2,2905E+0il3o1106E+a7 5,070flEw02 2,3681!J-QJ1 lo8489E+01 2,3231E+0i23,1!09E+a7 5,0706E=@2 2,3682E991 l,8491E+01 2,4064E+Il123,1114(!+bI17 5,0709iI002 2,36841!-01 ~,84941!+01 2,5044E+8?3,1124E+97 5,0714Ee02 2,36871?m01 $,8497E+01 2,S838E+923,1\5UE+i?7 !3,Q1724Cw02 2,3694COfJl 1,84981!+91 2,3460E+0ii3,12dJ4E+a7 5,0736E-02 2,3703CW01 l,8494E+01 l,7047E+023,1304E+G17 5,0754EQ@2 203718EQ01 l,8494E+01 l,1652E+02301604E+a7 500801Es02 2,3752Cs01 \08519E001 l,08S0E+02302104E+c47 5,0864E=02 2,3792EwQ11 l,8S66E+01 lo09!J3E+02303104E+fJ7 5,0944Ew02 2,3844CWQ11 l,8648E+@! l,0Q31E+O?3,61C)4E+(B7 S,10!3iE-02 2,3924EwOI$ l,8794E$0t l,08271!+Oi?401104E+I?J7 5ollSlEm@2 203987Ce01 lo8875~+01 l,07S71!+025,1104(!+07 !S,lS16ES02 2,4026t001 $,8838E+01 l,0695E+tl?8,11194E+P17 501638E002 2,400SC=9$ $06487E+fd\ l,070SC+02

48

TABLE XVI

ENERGY RELEASE RATES IN235U + *

~h FISSION

WITH ALL FISSION PRODUCTS INCLUDED

Time Cooling

=M!d!Q

$ 0,z 0,3 0,4 0,5 0s6 9,9 Q982EwflJ37 lcOOaaeE+OO8 2,afJFNIrrjE+009 S,eOeeOE+O@

10 1,00a0OE+OJ!1 2.000eaE+O$12 5,00000E+0113 l,00000E+0214 2,00000E+0215 5,0e0e0z+ai?16 l,F)CJ0(l10E+0317 2,00000E+@316 5,e0a00E+eJ319 t,0e00JaE+0420 2,e0aPJ0E+0U?1 50000@J0E+llU?? l,fJ@JoordE+05?3 2,0001B0E+0S24 5,efJ000E+052s l,e0eJmlEt06~6 2,a0PJe@E+0617 5,0fJ@100E+0628 1,RMMQJGW+07?9 ?,ee000L+07se s,fB000011+e7

Beta

6,28870E+006,32487E+CJ06,34551E+006,39976E+4J06,37073E+0fd6036$55E+00S,80535E+0(B5,49999E+@104,9S911UE+00Uo46457Et003,93103P+O(II3,24463E+002,763i!81!+0QJ?,34289E+@fd1,88V36E+PJ13~057556E+00$,?(lslsl!+ee9,67499Em017,85Q22E-Oi6,279151!wGI$U,42586E0015038616E~@I2,70304E9012,118Q8EDlIl\,73337E001$,34600ED618,67027Ew02S,68440E~02S,32274E*8Zl,3!J5681!w@~

– MeV/fis —

Gamma

b,iu?ealc+akf6oa4695Et006,a6585E+@J66,@7609E+006008202fZ+0Gl6,07504EtG105,66059C+0kl5043899Et005,1a5419E+0@4,70236EOOiJ4,2~688E+003,69909E+003,239111E+e@?081344E+OILI2,3~770E+01B?,04058E+00l,70177E$00l,i?5068E+00906g772Ee017,584fJ@E~01s,82e27E9@l4,79899Ew013,95293EcL312,99207E9@l?,25817Ew4J11,!$64071!04J18036024E*9?4,ss015E.Oai,$8~14E=@?203U086E~03

Total

‘f,=W5E+011,23718!!+041,2U114E+011,243!39E+01$,i?4527E+01l,Z4366E+01l,14659E+01l,09390E+01l,0e136E+Qll9,16693E+0(il8022791E+0fil6,9U372E+00So99839E+005,15633E+004,24157C+003,61613E+QJ02,98693E+002,i?1818E+0el,75169E+00l,3863i?E+00l,f12461E+00e,18s16E@0;6065S97Em@l5,11!UJ5E-QJI3,9915UE.IBJ2,91WJ6E=01l,703051!.ell;0214SEdJlu,90388EdJ?1,589TIEQ03

49

.

ut%

21 :mCJ

n

II

5Q

u-i

1+

dm

Pa

140z

wog

51

TABLE XIX

INTEGRATED ENERGY VS COOLING TIME IN 235U + nth

FISSION WITH ALL FISSION PRODUCTS INCLUDED

MeV

52

53

TABLE XXI

INTEGRATED ENERGY FROM HALOGENS AND

PROGENY IN235

U + nth FISSIONa

MeV

aAt the beginning of cooling, all progeny are set to zero.

54

.

l-l!-lawo

55

TABLE XXIII

INTEGRATED ENERGY FROM NOBLE GAS AND PROGENYa

CoolingTime (s)

MeV

Total

aAt the beginning of cooling, all progeny are set to zero.

56

flux level was 1013 2

n/cm -s. The ratios of the three fast-group fluxes to this

value are six, eight, and five, where the.latter is the epithermal ratio. The

group cross sections were processed from ENDF/B-IV using a typical mid-life

P1o!Rspectrum for a weighting function. It should be noted that the thermal

(group 4) flux is applied to an effective 2200 mls cross section defined by

--0 = (7/0eff lIV ‘

where

c = average thermal cross section in the PWR spectrum,

‘l/v =average of l/v energy dependent cross section in the PWR spectrumspectrum haying a 1 b value at 0.0253 eV. (In the PWR spectrumused here, o

I/v= 0.55402 b.)

Therefore, the 1013

n/cm2-s should be interpreted as a neutron density, and the

calculated group 4 aggregate cross section is an effective 2200 m/s value. Sim-

ilarly, the corresponding group flux ratios are, in effect, equivalent to a re-

duction by the factor ~l/v”

In these tables, the first five time steps are of equal duration (1728 h)

and are at power (100 k!/cm3). The remaining time steps follow shutdown and ex-

tend out to 5 x 107 s. Tables XV-XIX include all fission products. Tables XX

and XXI include only halogens and those progeny generated after shutdown (fol–

lowing time step 5). Tables XXII and XXIII include only noble gases and those

progeny generated after shutdown. h’bile the first five tables are based on all

fission products, Tables XX-XXIII include only gases and their progeny, which are

built up from decay following shutdown. Where actual values, rather than frac-3

tions, are listed all results are given per cm . The constant fission rate

prior to shutdown uses a nominal 200 NeV/fission to produce a power of 100

watts.

One interesting result noted in the last progress report and even more pro-

nounced for short irradiation times is the fraction of energy due to noble gases

and halogens (Table XVII). At 5000 s cooling 13.2% of the products are gases

but only 0.6% are radioactive gases, yet these account for 217 of the activity,

16% of the beta energy rate, 35% of the gamma energy rate, and 27% of the total

energy release rate. Of the 78 radioactive gases at 5000 s cooling, 6 contribute

1% or more of the beta, gamma,87Kr 88Kr 131xe

or total energy release rate -– 9 9 7

57

1331 1341 and 135xe> 9 . (Tabular results for individual nuclides are too exten-

sive for inclusion in this report.)

E. CINDER-10 Code Development (T. R. Fngland, N. 1..Whittemore, and W. B. Wilson)

Improvements were made which reduced the charge per run by approximately

a factor of ten. Other algorithms and edits were added to produce information

requested by the Nuclear Regulatory Commission.

Normally CINDER-10 calculations use LASL’S CDC 6600 (Machine 0) because of

the large storage required for the l?NDF/B-IV library. An untested version is

operational on the CDC 7600 using LCM. Other work is in progress to reduce

the required storage.

F. Beta-Energy Averaging and Beta Spectra (M. C. Stamatelatos and T. R.

England)

A simple, efficient, and highly accurate method for approximately calcu-

lating spectrum-averaged beta energies and beta spectra for radioactive nuclei

was developed and partially discussed in the last progress report. The final

version will be published as LASL report LA-6445-MS (ENDF–242).

G. Absorption Buildup Studies (W. B. Wilson, T. R. England, M. J. Stamatelatos,and R. J. LaBauve)

A new fission–product absorption data set for a revised version of the

CINDER71 code has been completed using ENDF/B-IV decay constants, branching frac-

tions, fission yields, and processed neutron radiative capture cross sections.

The details of procedure and codes used in the data processing have been described72

previously. The data set describes the temporal coupling of 186 fission pro-

duct nuclei using 84 linearized nuclide chains and a total of 484 linearized

nuclides. Each chain describes a unique path via neutron absorption and radio-

active decay.

A reduced 12-chain data set has also been completed, describing 27 principal

fisson-product nuclei with 11 chains and 34 linearized nuclides. The balance

of neutron-absorption accumulation is described in a single, non-saturating

chain of 4 pseudo-fission product nuclei.

Macroscopic absorption calculations for a typical reactor lifetime with the

two data

after an

58

sets differ by less than 12. These quantities vary less than 2% even

additional equivalent period of decay.

In contrast to the data libraries and code version used to produce results

in previous sections of this report, these libraries are intended for use only

in absorption buildup studies, including transients, in reactcr design. The 12-

chain set is suitable for spatial depletion codes, and the 84-chain set, in ad-

dition to its use in parametrizing the pseudo-chain, is useful in providing

the inventories of nuclides having half-lives longer than .4 hours. The 4-group

cross sections used in these libraries were collapsed from a 154-multigroup set

described in the previous progress report.

REFERENCES

1.

2.

3.

~

5.

6.

7.

8.

9.

10.

11.

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