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.’

LA-3528

UC-34, PHYSICS

TID-4500

LOS ALAMOS SCIENTIFIC LABORATORYof the

University of CaliforniaLOS ALAMOS ● NEW MEXICO

Report written: July 1968

Report distributed: September 4, 1968

Neutron Cross Sections for 239PU

and 240Pu in the Energy Range

1 keV to 14 MeV

by

R. E. Hunter*J.-J. H. Berlijn**

C. C. Cremer

*Work begun while a LASL Staff Member, completed whilein capacity of Consultant. Present address: ‘Physicspartment, Valdosta State College, Valdosta, Georgia.

**Present addre SS: Physics Department, Valdosta StateIege, Valdosta, Georgia.

De-

col-

1

.

.

NEUTRON CROSS SECTIONS FOR 239PU

AND 240PU IN THE ENERGY RANGE

1 keV TO 14 MeV

by

R. E. Hunter, J.-J. H. Berlijn, C. C. Cremer

ASSTRACT

240 Recommended cross sections for 239Pu andPu are presented. Comparisons of calculated

and experimental values of integral systemswere used as a guide in choosing the fits tomicroscopic cross-section data.

.

.

I. INTRODUCTION

This report presents the results of a

compilation of the available experimental

data on the neutron-induced reaction cross

sections for plutonium isotopes, with the

objective of providing consistent sets of

cross sections for neutronics calculations

in fast critical and super-critical systems.

Because of the neutron flux spectra in these

very fast systems, cross sections at inci-

dent neutron energies of 1 keV and lower are

relatively unimportant. Cross sections are

presented from 1 keV to 14 MeV.

Extensive comparisons were made with a

host of integral experiments, such as bare

and reflected critical assemblies, spectral

indices, and central core reactivity contri-

bution. Each of these comparisons provided

a further check on the experimental data,

and in some cases led to alteration of the

previously chosen best fit to the data.

Several compilations of experimental

and theoretical neutron cross sections

already exist in which the author has rec-

ommended “best fits” to the data presented.

The experimental uncertainty of these data

is usually about 5$ or greater, and varia-

tions in these fits may justifiably be made

within this uncertainty. However many inte-

gral experiments exist in which certain

choices of these fits to the data lead to

calculations of the integral quantity which

lie outside the range of experimental error.

A good example is the critical mass of

plutonium (94.134% 239Pu) which was measured

in the Jezebel assembly. The critical mass

is known to within * 0.1%. However, an un-

certainty of * 5% in the fission cross sec-

tion of 239Pu leads to a calculational un-

certainty of * 13$ in the critical mass. It

is believed that the calculational tech-

niques available on modern computers are

capable of calculating the critical mass of

this assembly to k 0.2% Integral experi-

ments such as this may therefore be thought

of as placing one more constraint upon the

~~bestfit~~to the microscopic CrOSS-Section

data.

The purpose of this report is to pre-

sent such a set of recommended data which

has been found to give agreement within

experimental error for all such integral

I

I

I

quantities that have been calculated. It iS

not intended that these curves should be

considered as being a refinement on the ex-

perimental data, or *vbetterl*in some nebu-

lous sense than the experimental data, nor

do the authors contend that the experimental

uncertainty in the data has been somehow re-

duced. All that is claimed is that these

recommended curves represent a particular

set of fits to the experimental data which

is consistent with the integral experiments.

It is recognized, of course, that this

recommended set of curves is not unique.

However, it is felt that it represents a

useful step in the processing of neutron

cross-section data for use in neutronics

calculations. Indeed, the cross section

user may often find that to achieve the

degree of accuracy that is required of his

calculations a normalization of this type

is essential. Needless to say, the final

element of responsibility for checking his

calculations against those experiments

which bear most directly on the problem

under study must still fall on the user.

In this respect it should be noted

that the sensitivity of the calculations

of integral experiments to variations in

the cross sections within an energy range

is proportional to the total neutron flux

within that energy range. Since all inte-

gral experiments used in the above tests

were performed on fast assemblies, confi-

dence in the recommended curves is highest

in the range 0.1 - 6 lieV,and drops at both

the low and high ends of the energy range.

This report is not intended to repre-

sent a comprehensive compilation of experi-

mental data, with best fits to these data

alone. Rather, the best fits were used as

initial input to calculations for compari-

son with the series of integral experiments

as described above. These results were

then used to modify the initial best fits

in such a way that consistent results were

obtained for all calculations. Attempts

were made to keep these modifications with-

in the experimental errors on the data. In

fact, for the cross sections presented in

this report, these modifications were 3$ or

less.

The calculational techniques used in

computing the integral experiments were

carried to the point at which numerical and

calculational approximations introduce

errors which are comparable to, or less

than, the experimental errors on the inte-

gral quantities. These calculations and

comparison with the integral experimental

results are described in detail in the

authorsf report LA-3529.1

II. CALCUIATIONAL PROCEDURE

The energy region of interest extends

from 1 keV to 14 MeV. Over this region the

cross sections of importance are:

total cross section - On ~

fission cross section - Ln,F

elastic scattering cross section -un,n

inelastic scattering crosssection - a

n,n’radiative capture cross section -

0

(n,2n)n;loss section - On Zn

(n,3n) cross section - Un’3n9

To accurately represent the final-state

neutron spectra, it is desirable to repre-

sent the fission cross section as the sum

of three cross sections:

un,F -u n,f +U n,nvf +0 n,2nf” (1)

un,f

will denote the direct fission cross

section, with IJnF the total fission cross>

section.

The cross-section data, along with

neutron energy and angular distributions,

were processed by a digital computer pro-

gram which calculated a flux-weighted aver-

age of each cross section over a specified

set of energy groups. These group cross

sections were then used in a calculation

employing the Carlson discrete Sn approxi-

mation to the Boltzmann transport equation

to teat the cross sections with integral

.

4

.

experiments. The microscopic data were then

adjusted where necessary to give agreement

with the integral experiments. For details

of the calculational techniques the reader

is referred to IA-3529.

III. PLuTONIUM-239

For the well-established cross sec-

tions, no attempt has been made to catalog

every report on the subject; rather a ref-

erence is given to an already existing com-

pilation. Individual reports are referenced

if they are not included in such a compila-

tion.

A. Total Cross Section

The total cross section is well de-

scribed by the compilations of Schmidt2 and

Hughes and Schwartz.3 Between 1 and 10 keV,

there is considerable spread in the data,

resulting in a rather large uncertainty

(- 10%) in the total cross section in that

energy range.

B. Fission Cross Section

Considerable data exist for the fis-

sion cross section. In addition to the

compilations of Schmidt and of Hughes and

Schwartz, the data of Ferguson and Patten-

den,4 James,5 6and White et al. were used.

Although the data of White et al. lie some-

what below those of other authors, they are

the most accurate available. Also, these

data give much better agreement with inte-

gral experiments. Hence, the recommended

curve is based largely on these points be-

tween 40 and 500 keV.

The thresholds for on ~tf and Un,2nf

are at about 5.5 MeV and 16.5 MeV, respec-

tively. The curves of on,ntf and 0n,2nfare given along with on,F in Fig. 3.

c. Radiative Capture Cross Section

The radiative capture cross section is

based on the compilations of Schmidt,2

Hughes and Schwartz,3

Stehn et al.,7 and

Douglas and Barry,8

and on the data pre-9

sented by Okrent and Thalgott on the cap-

ture-to-fission ratio, a.

D. Elastic Scattering Cross Section

Very few direct measurements of on,nhave been made. However, below about 10 keV

we can write

un,n - On,T - ‘%y - ‘n*F”(2)

From Eq. 2 and the recommended curve of

Schmidt,2 the elastic scattering cross sec-

tion was established up to 10 keV.

Above 10 keV, this procedure is compli-

cated by the onset of inelastic scattering.

There are some data on the scattering cross

sections, primarily those of Andreev10 at

0.9 MeV, Cranberg11

at 0.55, 0.98, and 2.0

MeV, and Allen12 from 0.15 to 1.0 MeV.

These measurements consist of partial cross

sections for ranges of the Q value at a

given incident neutron energy, En. Since

different Q values were used at the same

En, it was possible in some cases to use

subtraction techniques to separate the

different cross sections. (See Sect. III-E.)

Also, there are measurements between 8

and 14 MeV of the nonelastic cross section,

on ~, given by Stehn et al.7

and by

De~tyarev.13

From the relation

on,n - ‘n,T - On,X~(3)

the elastic scattering cross section was

then obtained at these energies.

Since an,n is a slowly varying func-

tion of A and Z, the s;ape of the curve

recommended by Schmidt was used in extra-

polating between the above data. The data

between 200 keV and 2 MeV lie somewhat

above the recommended curve. This differ-

ence is due to the inclusion of the lower

levels of On,n, in the experimental values

of the e~astic cross section at these

energies, and to the uncertainties in the

experimental data.

E. Inelastic Scattering Cross Section

We can write

on,n!= %,T - ‘n,F - ‘n,n (4)

- ‘n,y -0 n,2n - an,3n”

5

Equation 4 was used to establish the general

behavior of the total inelastic scattering

cross section.

The Inelastic scattering cross section

is, in reality, a sum of cross sections for

excitation of residual nuclear levels.

Dzhelepov et al.14

found levels at 8, 57,

76, 164, 193, 286, 330, 358, 388, 392, 432,

480, ancl517 keV. Since the level density

becomes quite large above about 300 keV,

statistical theory can be applied to the

inelastic process for levels above that

energy.

The data of Andreev,Cranberg, and Allen

combined with the results of Eq. 4, were

used to establish the magnitudes of the

excitation curves for the levels below 300

keV. The same general shape was assumed

for all levels.

Above 5.5 MeV o becomes nonzero.n,2n

The cross sections, on,nvand o

n,2n, were

taken from the recommended values of

Schmidt,2 modified so that the sum, ‘n,n~ +

an,2n’agreed with the values obtained from

Eq. 4. The relative values of the cross

sections were determined so that the curves

were smoothly continuous at all points.

l?. Neutron Energy Distributions for

Evaporation Processes

The energy distributions of secondary

neutrons from inelastic scattering as given

by Andreev10 at about 1.2 MeV, and Cran-

berg~~ at 2 MeV, can be fit with an evapo-

ration formula of the form

F(E) e-E/T;2 9 (5]

where 1’characterizes the nuclear temper-

ature. These fits give nuclear tempera-

tures of about 0.35 and 0.38 HeV, respec-

tively. Zamyatnin et al.‘5 measured the

neutron energy distribution of all second-

ary neutrons for an incident neutron energy

of 14 UeV. The evaporation component of

the spectrum included n,n~, n,2n, and n,3n

neutrons, as well as the prefission evapo-

ration neutrons. The spectrum of all

6

evaporation neutrons can be fit with W. 5

with a temperature of 0.53 MeV.

For the uranium isotopes235U and 238U

I

it appears that the energy distribution for

all evaporation neutrons can be adequately

fit with a single temperature for a given

incident neutron energy, in the sense that

the overall neutron energy distribution will

thereby be correctly described.16

It is

assumed that this also holds for the plu-

tonium isotopes.

Batchelor et al.‘7 have found that the

nuclear temperatures for both thorium and

uranium isotopes increase steadily up to an

incident neutron energy of about 4 to 6 UeV,

and then level off at approximately con-

stant values. It was assumed that the plu-

tonium isotopes exhibit similar behavior,

and the nuclear temperature for239Pu as a

function of

taken to be

incident neutron energy was

as follows:

(M%) (M:V)

0.55 0.30

1.0 O*35

2.0 0.38

7. 0.53

14. 0.53

The final-state neutron energy distributions

for all evaporation processes were then

obtained from Eq. 5, using the above tem-

perature specification.

As was noted in the previous section,

the level density of239

Pu is high enough

to warrant the application of statistical

theory to the n,nt process for all excited

states whose level energies lie above about

300 keV. From an incident neutron energy

of some 300 keV up to 1 MeV, final state

neutron”energy spectrum is represented by

an evaporation spectrum, plus contributions

from low-lying levels (with energies below

300 keV) superimposed. Above 1 HeV the

evaporation spectrum is completely adequate

to describe the neutron energy distribution.

The average contribution of an excited

.

.

.

level to the neutron energy distribution can

easily be calculated. If the excitation

energy of nuclide A is given by E;, and the

energy of the incident neutron in the labo-

ratory system is A, then, on the average,

the final neutron energy after an inelastic

collision is given by

{Efina~}i=l’+A2[1-(~)flE.(.)(1 + A)

The graph of the partial inelastic

cross sections in Fig. 6 at the end of the

report gives the relative weights of the

energy levels and the statistical model in

calculating the final-state energy distri-

bution. It should be noted that, at energies

above 300 keV, the statistical model includes

an increasing fraction of the excitation

curves even for the low-lying levels. This

procedure adequately describes the overall

neutron energy distribution; in neutronics

calculations, that is the only requirement.

G. %,2nand a

n,3n

an,2n was based on Schmidtfs recommend-

ed curves, as described in Sect. III-E. The

n*3n cr08s section Was assumed to be essen.235U ~hich istially the same as that of ,

18given by Parker. The neutron energy dis-

tributions are described in Sect. III-F.

H. Number of Prompt Neutrons per Fission

The mean number of pro.nptneutrons per

fission, ~9 w=7taken from the compiled data

of Stehn et al.19and Smith, as well as the

thermal data of Critolph20 and l#onard.21

A least-squares fit to the data, weighted

by relative errors, was made. Assuming suc-

cessively higher powers of En led to the

conclusion that a linear fit was the best

fit to the data, with the resultant equa-

tion,

;= 2.888 + 0.117 E (MeV) (7)

I. Fission Neutron Energy Distribution

given by the term

an,f+(;-l) un,n,f ‘(T-2) un,2nf*

These are distributed according to the

final-state prompt fission neutron energy

spectrum. A number of measurements of the

fission spectrum have been made. The spec-

trum has been fitted by a MaxwellIan dis-

tribution:

(8)

and by the well-known sinh law:

e+ff e- ()2 GEE/Tfsinh ~ (9)8(E) =&f

where Tf

and u are parameters. The errors

are generally such as to preclude a clear

choice between Eqs. 8 and 9. For consist-

ency the authors have used Eq. 8 to fit all

experimental distributions. Barnard et

al.22 give a compilation of values of the

nuclear temperature for various isotopes at

different incident neutron energies.

Terre1123 has obtained a function re-

lating the nuclear temperature to F :

T (E)c-[

A+B i(E)+l 14* (lo)

Using the functional relation in Eq. 10,

with T (thermal) - 1.38 MeV and T (14 MeV)

= 1.59 MeV, a curve of T vs E was obtained.

From this curve, the final-state prompt

fission neutron energy spectrum was obtained

from Eq. 8.

The prefission (evaporation) neutrons

from the (n,nlf) and (n,2nf) processes

were distributed in energy according to the

statistical model, which is described in

Sect. III-F.

For 23’Pu, Zamyatnin et al.15

measured

the ratio of fission spectrum neutrons to

all secondary neutrons, excluding elastic

scattering; they obtained 0.72 i 0.1 for

this ratio at 14 MeV. This compares withSince one neutron from 0n,ntf and two

from on ‘nf are treated as prefission evap-

oration’neutrons, the prompt neutrons are

7

0.84 obtained from the recommended curves

given in this report.

J. Delayed Neutrons

The delayed neutrons were distributed

in energy according to the graph in Fig.

10, with a total delayed neutron fraction,

b, of CIJO021taken from th& data given by

Keepin and Maksyutenko. The energy

distribution was assumed to be the same asfor 235U

.

K. Angular Distributions

The experimental data on the differ-

ential elastic scattering cross section

(angular distributions) were fit with the

expression

[‘+-* 1 + FJipim

1,(11)

where Pi(p) are the Legendre polynomials

and p = cos o. There are only a few exper-

imen;;l points, primarily those of Cran-

berg and Allen.12 The values of Wi for239

Pu were then taken to be the same as for238

U, as given by the authors.16 As can be

seen from the graphs in Fig. 9, they are

consistent with the experimental points for239PU

.

Nonelastic reactions were assumed to

have isotropic angular distributions.

L. Recommended Curves

239PUThe cross-section curves for ,

along with the Legendre coefficients for

n n, are shown in Figs. 1 through 10.%

The experimental data from the above

references are also plotted on the graphs.

No attempt is made to identify the sources

of the individual points. The cross sec-

tions are tabulated in ‘IhbleI.

IV. PLUTONIUM-240

A. Total Cross Section

There are no data on the total cross

section for240Pu above 100eV. Therefore,

the total cross section was determined

entirely by the sum of the partial cross

sections.

B. Fission Cross Section

In addition to the compilations of

Hughes and Schwartz and Stehn et al., mea-

surements have been reported by Nesterov26 4

and Smirenkin, Ferguson and ~attenden,27

Zamyatnin, and Perkin et al.

The threshold for fission is not well

established. Early data given by Hughes

and Schwartz indicated a threshold near

0.1 MeV. More recent laboratory experi-

ments have found nonzero measurements as

low as 23 keV, with considerable scatter

in the data up to 150 keV.

Very recently the technique of using

the neutron flux from underground nuclear

devices has been used to measure cross

sections; in particular the fission cross240

section of Pu has been measured by

Byers et al.29

Although the scatter of

data is large, there appears to be a non-

zero fission cross section down to about

1 keV. An average of these measurements

was taken from around 100 keV to 1 keV.

Above this range, the fission cross

section is well established up to 8 MeV.

Between 8 and 14 MeV, the239PU fission

cross section was used to establish the

shape of the curve, with the data at 14

MeV providing the normalization.

The (n,n’f) cross section has a thres-

hold at 5.5 MeV, with the total fission

cross section exhibiting the characteristic

sharp increase at this point. Above 5.5

MeV, on f was assumed to be a constant.

The (n,~nf) reaction threshold was assumed

to be 10.5 MeV, with crnn,f taken to be a

constant above this ene;gy.

c. Radiative Capture Cross Section

No data on a have been reportedn~y so

above 1 keV. Hamilton has given semi-

empirial calculations of an,Y

at decade

intervals from 1 keV to 1 MeV, and Buck-

ingham et al.31

and Douglas32

give recom-

mended curves for on,Y

up to 15 MeV.

8

Table I

CROSS SECTIONS FOR 239Pu IN BARNS

.

.

Energy(MeV) un,F un,n o

np Y ~,nl ‘n,2n ‘n,3n

0.00100.00150.00200.00250.0030

o*C0400.00500.00600.00700.0080

0.00900.0100.0150.0200.025

0.0300.0400.0500.0600.070

0.0800.0900.100.150.20

0.250.300.400.500.60

0.700.800.90

;::

2.02.53.03.54.0

4.55.05.5

:::

%:8.08.59.0

5.803.111.752.622.80

2.652.482.332.222.10

2.011.911.631.521.48

1.451.441.441.441.47

1.481.491.491.511.52

1.521.531.571.571.57

1.581.601.621.651.86

1.951.921.901.891.88

1.821.821.821.871.97

2.102.212.302.352.40

14.0013.6513.5013.2013● 10

12.8312.6312.4012.3512.32

12.3012.2012.1011.9111.70

11.3010.9110.7010.3510.10

10.009.909.779.008.39

7.857.356.636.055.65

5.274.944.714.593.98

3.894.124.404.474.50

4.494.484.474.414.33

4.153.873.673.533.37

4.402.671.301.871.95

1.811.631.421.261.14

1.071.010.8300.7300.654

0.5900.4650.3630.2920.270

0.2530.2470.2410.2190.198

0.1790.1640.1430.1230.108

0.0830.0680.0560.0470.026

0.0190.0140.0110.010

0.0560.0950.1650.1990.217

0.2260.2370.2390.2480.266

0.2640.2800.2960.3790.453

0.4810.5210.5740.6520.71

0.780.860.900.941.19

1.431.591.631.661.64

1.641.621.501.290.86

0.5720.4100.3070.2420.202

0.0300.160

0.2680.3090.3370.3600.378

9

Table I (Continued)

Energy(MeV)

o u u u un,F

on,n nv Y n,nt n,2n n,3n

9.510.010.511.011.5

12.012.513.013.514.0

2.412.412.422.442.47

2.502.512.532.542.55

3.253.183.123:073.04

3.033.033.033.033.03

The On,Y

curve was chosen to connect

Hamiltonls values smoothly, going to 10 mb

at 14 MeV.

D. Elastic Scattering Cross Section

No data exist for an,n. Since elastic

scattering is only slightly dependent on A

and Z, the 239Pu curve was used, along with

the recommended values of Bucklngham et

al.3132

and Douglas, to establish o forn,n

24°Pu.

E. Inelastic Scattering Cross Section

The excited levels of 240W have been

33determined by Bunker et al. ~ Bjornholm

34et al., and Lederer.35 Since the level

density becomes large above about 900 keV,

statistical theory should be applicable

above that energy. The procedure for deter-

mining the partial cross sections for the

Individual.levels is the same as that used

for 23’Pu, described in Sect. III-E. The

magnitude of the total inelastic cross sec-

tion was chosen to follow generally the

recommendation of Buckingham et al.

F. Neutron Energy Distributions for

Evaporation Processes

As was described in Sect. III-F, it is

assumed that the final-state neutron energy

distributions from all inelastic processes

can be represented by Eq. 5, with a single

curve of temperature versus incident neu-

tron energy. No experimental measurements

of the evaporation spectra have been re-

ported.

0.1s4O.1760.1620.1490.132

0.1230.1170.1110.1060.102

0.3960.4000.389003430.305

0.2470.1980.1600.1100.061

0.0240.055

Between about 900 keV and 1.5 MeV, the

neutron energy spectrum was represented by

the evaporation spectrum plus contributions

from the low-lying excited states, as de-

scribed in Sect. III-F. Above 1.5 MeV, the

energy spectrum was represented entirely by

the evaporation spectrum. The behavior of

T vs. E for240PU was assumed

to that for239Pu, giving the

table:

to be similar

following

(M%) (M:V)

0.8 0.30

1.5 0.32

7 0.45

14 0.45

G. on Zn and an,3n.

No measurements are available on these

processes. The recommended values are the

same as those given for239PU (Sect. III-G),

assuming that the dependence on A is very

small.

H. Number of Prompt Neutrons per Fission

Only three measured points of the in-

duced fission of240Pu have been reported.

Kuzminov36 gives values at 3.6 and 15 MeV,37

while Barton et al. have inferred a value

from a fission spectrum centered around 2

MeV. These points were fitted with a func-

tion linear in incident neutron energy, for

energies above the fission threshold:

Z(E)- 3.118 + 0.089 E (MeV). (12)

.

. I

10

I. Fission Neutron Energy Distribution

The direct fission neutrons are dis-

tributed according to the final-state prompt

fission neutron energy spectrum, which was

assumed to follow Eq. 8. The nuclear temp-

eratures were taken from the recommended32values of Douglas, which follow the func-

tional form of Eq. 10, with T (thermal)

1.34 MeV and T (14 MeV) - 1.48 MeV.

J. Delayed Neutrons

The delayed neutron fraction, B, is

given by Keepin24to be 0.0027. This frac-

tion is distributed in energy in the same

fashion as those from 239put as given in

Fig. 10.

K. Angular Distributions

The differential elastic scattering

cross section (angular distribution) was

assumed to have the same angular dependence

as that for239PU.

The Legendre polynomial

coefficients from Eq. 11 are given for both

239Pu and 240Pu in Fig. 9.

Nonelastic reactions were assumed to

have isotropic angular distributions.

L. Recommended Curves

The cross-section curves for 240PU are

given in Figs. 11 through 18. The experi-

mental data from the above references are

also plotted on the graphs. The cross sec-

tions are tabulated in Table II.

Table II

CROSS SECTIONS FOR 240Pu IN BARNS

Energy(MeV)

un,F on,n on,Y un,nt ‘n,2n an,3n

0.00100.00150.00200.00250.0030

0.00400.00500.00600.00700.0080

0.00900.0100.0150.0200.025

0.0300.0400.0500.0600.070

0.0800.0900.100.150.20

0.250.300.400.500.60

0.0100.0170.0250.0310.037

10.09.949.909.869.83

6.704.423.342.752.33

0.0470.0540.0610.0680.073

0.0780.0820.0910.0940.095

9.799.759.729.699.66

1.831.521.311.191.08

1.000.940.7720.6890.645

9.639.609.559.509.45

0.0950.0950.0950.0950.095

0,0950.0950.0950.0950.095

9.409.349.289.229.17

0.6020.5590.5210.4950.468

0.4420.4200.4000.3230.277

0.0130.0240.036

9.119.069.008.558.12

0.0500.0630.0750.1150.169

.

.0.2260.3130.3120.1620.086

0.1170.1410.2100.3900.64

7.727.32

0.2410.2160.1790.1530.137

6.656.085.72

11

Table II (Continued)

Energy(MeV)

o 0n,F n,n un, y un,nt on,2n ‘n,3n

.

0.700.800.901.01.5

0.851.111.411.691.62

1.6710681.671.671.62

1.531.501.531.661.83

1.962.042.112.162.20

5.385.094.834.634.08

0.1230.1140.1070.1000.076

0.0610.0510.0430.0380.034

0,2080.3670.4250.4851.66

2.02.53.03.54.0

4.55.05.56.06.5

7.07.58.08.59.0

4.194.414.664.724.74

1.721.721.721.721.72

4.754.744.724.704.67

4.574.334.003.733.49

0.0300.0270.0250.0230.021

0.0200.0190.0180.0170.016

1.721.72

0.0300.160

1.691.551.40

1.200.820.570.3780.262

0.2680.3080.3370.3600.378

9.510.010.511.011.5

2.212.212.222.252.31

3.333.213.143.123.11

0.0150.0140.0130.0130.012

0.1830.1320.1130.1080.105

0.3960.4000.3890.3430.305

0.0120.0110.0110.0100.010

0.1030.1020.1010.1000.100

0.2470.1980.1600.1100.061

12.012.513.013.514.0

2.362.412.442.472.49

3.103.093.083.073.07

0.0240.055

ACKliOWLEIXMENTS with Integral Experiments for Plutonium

and Uranium Critical Assemblies,” LA-

3529 (1968).

J. J. Schmidt, *#NeutronCross Sections

for Fast Reactor Materials,” KFK-120

(EANDC-E-35U), (1962).

D. J. Hughes and R. B. Schwartz, “Neu-

tron Cross Sections,” BNL-325, 2nd Ed.

(1958).

A. T. G. Ferguson and N. J. Pattenden,

~~NeutronCross Section Measurements at

Harwell in Support of the U. K. Fast

Reactor Programmed,” ANL-6792, p. 11

(1964).

G. D. James, llThe Fission cross section

of Pu23’ from 1 keV to 160 keV,”

The authors are very happy

ledge the help of C. P. Cadenhead and K. F.

Famularo of LASL Group W~4 in providing many

suggestions and critical evaluations of the

results of this effort. Also, the authors

would like to acknowledge the tireless asis-

tance of Beverly Wellnitz and Nora Sanchez

of W-4 in the physical preparation of this

report.

to acknow-

2.

3.

4.

5.

REFERENCES

1. C. C. Cremer, R. E. Hunter, and J.-J.

H. Berlijn, t!comparisonof Calculations

12

References (Continued)

6.

7.

8.

9.

10.

11.

12.

13.

14.

Symposium on the Absolute Determination

of Neutron Flux in the Energy Range 1-

100 keV, St. Johns College, Oxford,

Sept. 10-13, 1963, EANDC-33U (Paper a)

(1963); “Fission Cross Section Mt?ZLBUZW-

mentson Pu239, PU241, U232and a Search

for Fission Components in Pu238

Reson-

ances,“ IAEA Preprint No. SM-60/15

(1965).

P. H. White, J. C. Hodgkinson, and G.

C. Wall, “Measurement of Fission Cross-

Sections for Neutrons of Energies in

the Range 40-500 keV,” PrOC. Symp. Phys.

Chem. Fission, Salzburg, 22-26 March

1965, p. 219, IAEA, Vienna (1965).

J. R. Stehn, M. D. Goldberg, R. Wiener-

Chasman, S. F. Mughabghab, B. A. Magurno,

and V. M. May, “Neutron Cross Sections,”

BN&325, 2nd Ed.,

A. C. Douglas and

Cross Sections of

Range 1 keV to 15

(1964).

Supp. No. 2 (1965).

J. F. Barry, “NeutronPU239

in the Energy

MeV,” AWRE-O-79/64

D. Okrent and F. W. Thalgott, “The

Physics of Plutonium in Fast Reactors,”

HW-75007, p. 14.1 (1964).

V. N. Andreev, llInelMtiC Scattering

of Neutrons of the Fission Spectrum

and Neutrons with an Enerzv of 0.9 MeV

in U235 and Pus9, f’ ‘-Soviet Progress in

Neutron Physics, Consultants Bureau

Enterprises, New York: 1963, p. 211.

L A. Cranberg, ~tNeutronscattering by“235

, PU239 and U238,N M-2177 (lg59)0

R. C. Allen, ~~TheInteraction Of 0.15

to 1.0 MeV Neutrons with U-238, U-235,

and Pu-239,r~ Nucl. Sci. Eng. 2, 787

(1957).

Yu. G. Degtyarev, I~crossSectionS for

Neutron Inelastic Interactions with

7Li, 12C, 12A1, 56Fe, Cu, Pb, 235U,238

U, and 23’PU,” At. Energ. (USSR) ~,

456 (1965).

B. S. Dzhelepov, R. B. Ivanov, V. G.

Nedovesov, and V. P. Chechev, “Alpha

Decay of Curium Isotopes,” Zh. Eksperim.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

i. Teor. Fiz. 45, 1360 (1963); JETP @

937 (1964).

Yu. S. Zamyatnin, I. N. Safina, E. K.

Gutnikova, and N. I. Ivanova, “Spectra

of Neutrons Produced by 14 MeV Neutrons

in Fissile Materials,” At. Energ. (USSR)

~, 337 (1958); Soviet J. At. Energy ~,

443 (1958).

J.-J. H. Berlijn, C. C. Cremer, and

R. E. Hunter, “Neutron Cross Sectionsfor 235U and 238

U in the Energy Range

1 keV - 14 MeV,” LA-3527 (1968).

R. Batchelor, W. B. Gilboy, and J. H.

Towle,2389~Neutron Interactions with U

and Th232 in the Energy Region 1.6 MeV

to 7 MeV,” EANDC(UK) 48S (1964); also

Nuc1. Phys. ~, 236 (1965).

K. Parker, V*Neutroncross Sections ofU235 and U238 in the Energy Range 1 keV

- 15 MeV,” AWRE-O-82/63 (1963).

A. B. Smith, *~RecentChanges in Heavy

Element Cross Sections,” ANL-6792,

p. 31 (1964).

E. Critolvh. ItEffectiveCross Sections

for U235 ;ni Pu23’ ,1!CRRP-1191 (1964).

B. R. Leonard, Jr., “Plutonium Physics:

Contribution to Plutonium Handbook,”

HW-72947 (1963).

E. Barnard, A. T. G. Ferguson, W. R.

McMurray~ and I. J. VanHeerden, “Time-

of-Flight Measurements of Neutron235 238

Spectra from the Fission of U , U ,

and Pu239,t1Nucl. _Phys. 71, 228 (1965).

J. Terrell, **FissionNeutron Spectra

and Nuclear Temperatures,v’ Phys. Rev.

113, 527 (1959).

G. R. Keepin, ttBasicKinetics Data and

Neutron-Effectiveness Calculations,”

TID-7662, p. 334 (1964).

B. P. Maksyutenko, “Delayed Neutrons

from PU239,” At. Energ. (USSR) 15, 157—(1964); Soviet J. At. Energy 15, 848—(1964).

V. G. Nesterov and G. N. Smirenkin,240~*FissionCross Section of Pu by

Fast Neutrons, *’Zh. Eksperim, i Teor.

Fiz. ~, 532 (1958); JETP~, 367 (1959).

13

References (Continued) for Use in Neutronics Calculations in

27. Yu. S. Zamyatnin, Mmoss SectionS for

Fission Induced by Fast Neutrons,” At. 32.

Energy (USSR) Supplement No. 1, 27

(1957); Physics of Fission, P. 21 (1957).

28. J. L. Perkin, P. H. White, p. Field-

house, E. J. Axton, P. Cross, and J. CRobertson, ‘lTheFission CrOSS Sections

of U233, U234, U236, NP237, PU239,PU240 -, and Pu

241 for 24 keV Neutrons,”

J. NUC1. Energy ~, 423 (1965).

29. D. H. Byers, B. C. Diven, and M. G.

Silbert, “Capture and Fission cross

sections of Pu240,V*Conf. Neutron Cross

Section Technology, Washington, D. C.,

Mar. 22-24, 1966, PaPer F-5 (1966).

30. R. A. Ii.Hamilton, “Neutron CaPture

Cross Sections for Uranium and Plutonl-

um Isotopes in the Energy Range 1 keV -

1 MeV,” AWRE-O-3S/64 (1964).

31. B. R. S. Buckingham, K. parker, and

1%.D. Pendlebury, *fNeutron (kOSS SEX%

tions of Selected Elements and Isotopes

33.

34.

35.

36.

37.

the Energy Range 0.025 ev-15 MeV,”

AWRE-O-28/60 (1961).

A. C. Douglas, v~NeutronCross Sections

of Pu-240 in the Energy Range 1 keV to

15 MeV,” AWRE-O-91/64 (1964).

hf.E. Bunker, B. J. Drowsky, J. D.Knight, J. W. Starrier,and B. Warren,

~~Decayof U240 240

and 7.3 Min. Np ,“

Pbys. Rev. 116, 143 (1959).

S. Bjornholm, M. Lederer, F. ASUO, and10 per~an, 9~AlphaDecay to vibrational

States,” Phys. Rev. 130, 2000 (1963).co Me ~derer, 9VTheStructure of HeavY

Nuclei: A Study of Very Weak Alpha

Branching,*t UCRL11028 (1963).

B. D. Kuzminov, llAverageNumber of

Prompt Neutrons in Fission of Pu240 by

Neutrons with Energy of 3.6 and 15 MeV,”

AEC-tr-4710 (1960).

D. M. Barton, W. Bernard, and G. E.

Hansen, IvCriticalMasses Of Composites

of Oy and Pu239-240 in Flattop Geometry,”

LAMS-2489 (1960).

14

.

91111I

II

?

L

rb..

●......

.

●

.

....

1111I

II

.0.

co~

$

SN

W9

NI

1

15

1111I

II

—

●

————11111I

II

)~

1111I

II

#Lu

-u-L

5

SN

W8

NI‘C

um

z

.i!mmNm“

G

..

1111I

1I

IL

w-

13;-

\r’;

...~8.●

-..*

—:●...,.t.

.-4

<●

t.,

......

——:

—.

.

—:.

.

—.

●..

—.

—.

..

.

—“.

*/—

%.

.——

.:—

.—

9

—

.

—\

.*

●

.●

:●

.—

“e..

●

.

Ill2~

SN

W8

-1--i

17

10.0

I .0u)zuam

~

~

b= ().1

I I I I iil T

-0

?

I I I I [11( 1 I I I 1111 I I I I II14-

10

●

●

I 1 I I 111!

●

●

●

I I I I IIll IO.:;l. 0.01 0. I I .0 I 0.0

ENERGY IN MeV

Fig. 4. Radiative capture cross section for239PU

.

10.0. I I I I 1111 I [ I I 1111 I I I I I Ill I I I I I Ill I I I I Ill+

(nz 1.0_(Eamg

-cb~

0.10_ ri

0.01 [ I I I II I I I I I 1111 I I I I 1111 I I I I 1111 I I I I 1[11.0.001 0.01 0.1 1.0 10.0 100.0

ENERGY IN MeV

.

.

Fig. 5.239PU

Inelastic scattering cross section for .

18

,

.

I .0rU)~

am t

1 I 1 I I I I I 1 1 I I I I II I 1 1 I I 1 I IJ

STATISTICALMODEL

Y--I4o. I

[

b

I

0.01 I I I I I I I I I

0.001 0.O1I I I VI I II I I M I I I I I 111 I I I I I I I I

o. I I .0 I 0.0ENERGY IN MeV

Fig. 6. 239PUPartial inelastic scattering cross sections for .

L

u)z

5m

o. Iz

b

0.01 I I 1 1I.0

[

I 1 I1(

—I

un,2n

-a n,3n

I I I I I I I I10( D

ENERGY IN MeV

Fig. 7. an Zn and o for 239PUn,3n .$

19

.

..

20

.

5.0 ‘ I I I I I Ilr

4.0● WIA w2

■ W3

3.0

2.0

1.0

0.0

5.0 ● W4~ W5

● w6

4 .0

Wi

3 .0

2.0 “

I.0

0.0

I I I I I Ill I I I I I I II

W3

W8

3.0 -W9

20‘$40

I .0Ill

I0.0 I I I I I I 1111 A

0.1 I .0

)YIlllll I I I I I Ill

10.0 10( o

ENERGY IN MeV

Elastic scattering Legendre coefficients for239

Fig. 9.Pu and 240PLI.

I I I I I 1 I I I I I I I

1 1 I I I I I I I I) 0.4 0.8 I .2 1.6 20 2.4

.

.

8

NEUTRON ENERGY IN MeV

Delayed neutron energy distribution for239 240PU

Fig. 10. Pu and .

22

.

.

100.OL I I I I 1111 I I I I 1111 I I I I \lll I I I I 1111 I I 1 I I [m

cl-lzmam

~ loo

>-

b’

,1.a I I I IIIll I I I IIIII I I ( I1111 I I 1 I1Ill I I 1 1 [Ill.

0.00( 001 0.1 1.0 Iao 100.0

ENERGY IN MeV

Fig. 11. Total cross section for 240pu.

locio~ I 1 I I I Ill] I I I I I III I I I I I 111 1 1 I I 1111

(nz(Kam 1~ loco .

c-

b’

Lo I I I I I Ill I I I I I 1[1 I I I 1 I Ill I 1 1 1 Ill.aool aol 0.1 I .0 Ii

7=!

I I I I !111) 100.0

ENERGY IN MeV

Fig. 12.240PU

Elastic scattering cross section for .

.

23

-L●●

●

II

fI

II

c

w-w-

-c5

b=”

be

.

;NW

3N

I““Q

(

-1-1Q

,00

B●

*●a“●

6.-

0

III

II

1I

o

>a)

....

24

.

.

looo.o~ I I I 1 111~

,00.>

I.0r

I I I I Ill I I I I Ill

\

I I I I 1111 I I I 11114-J

o~l+_u-uL~&l~ I I I I 1111 I1.0

I I 1111110.0 100.0

ENERGY IN MeV

Fig. 14. Radiative capture cross section for 240Pu.

10.0 I I I I 11[1 I I I I [Ill I I I I 1111

I.0@t%amz

-c-

b’o.l_

/

I0.01. I I I I I 11110.0I I I I 11111

0.[1

I.0 10

T

I I I I 1111100.0

ENERGY IN MeVFig. 15. Inelastic scattering cross section for 240Pu.

25

o

1-

t-laII

I1

II

II

IllI

II

II

~

II

II

II

1I

*>coo1

...

01-1II

II

II

I1111

II

I1

IJo

qG

o-

0-

SN

W:

NI

Qf=l

..

26

.

.

1.0 I I I I 1 I I r

mzu~

o.Iz

b

0.0I 1 1 I I I I II.0 Ic

ENERGY IN

Fig. 17. on ~n and On ~n# s

~

/un *“

1

-an,3n

I I I I 1 I I 1 LIoc

MeV

~Or 240PU.

5.0- kI I I

4.5 -

4.0 –

v

3.5 -

3.0 –

2.5 –

2.0 1 I0.0

I5.0 10.0 15.0 20.0

ENERGY IN MeV

Fig. 18. Mean number of neutrons per fission for 240W.

27