•JKASLKi.l) AND EVALUATED FAST HtlTRO:* CROSS SECTIONSOF ELfcllEHTAL JUtKEL

byP. Guenther, A. Soitlt, I«. SrJth and J. Mialen

Argonne National Laboratory

andP.. Hover ton

Lawrence Llveraore LaboratoryJuly 1971

In January 1975, the research and developeent functions ofthe forcer U.S. Atonic Energy Comission vere incorporatedinto those of the U.S. Energy Research and DevelopmentAdoinistrat icn.

Applied Physics DivisionArgonne National Laboratory

9700 South Cass AvenueArgonne, Illinois 60439

U.S.A.

NUCLEAR DATA AND MEASUREMENTS SERIES

The Nuclear Data and Measurements series presents results

of studies In Che field of microscopic nuclear data- The pri-

mary objective is the dissemination of information in the

comprehensive forn required for nuclear technology applications.

This Series is devoted to: a) Measured microscopic nuclear

parameters, b) Experimental techniques and facilities employed

In data neasurecents, c) The evaluation of nuclear data. Con-

tributions to this Series are reviewed to assure technical con*

petence and, unless otherwise stated, the contents can be

foraaily referenced. This Series does not supplant forcial

journal publication but it does provide the r-ore extensive in-

formation required for technological applications (e.g., tabu-

lated numerical data) in a timely manner.

-1-

fc tit"

Kage

ABSTRACT 3

I. INTRODUCTIOM 4

II. EXPERIMENTAL HEXiiUUS 3

III. EXPERIMENTAL RESULTS 7

1. Total Neutron Cross Sections . . . . . . . . . . 7

2. Elastic Neutron Scattering Cross Suctions. . . . 8

3. Inelastic Neutron Scattering Cross Sections. . . 10

IV. INTERPRETATION AND DISCUSSION 12

1. The Optical Model and Elastic Scattering , . . . 12

2. The Statistical Mootl and inelastic Scattering . 15

V. THE EVALUATED FILL IV

1. Total Neutron Cross Sections . . . . . . . . . . 19

2. Elastic Neutron Scattering Cross Sections. . . . 20

3. Inelastic Neutron Scattering Cross Sections. . . 23

A. Discrete Excitation Cross Sections . . . . . 23

B. ContinuuK Excitation Cross Sections. . . . . 29

4. Radiative Neutron Capture. . . . . . . . . . . . 32

5. (n;X) Reactions 33

A. The (n;2n*) Reaction 34

B. The (n;3r.') Reaction 36

C. The (n;p) Reaction . • 36

D. The (n;a) Reaction 43

E. The (n;a,n*) Reaction 49

F. The (n;p,n*> and (n;U) Reactions . . . . . . 49

G. (n;t) Reaction 54

H. (n;2p) and (n: he) Reactions 34

I. (n;2p,n"), (n;p,2n'> and (n;p,a) Reactions . >4

J. Photon Production 54

VI. CONCLUDING REMARKS 56

REFERENCES 58

TABLES . t>4

FIGURE CAPTIONS 67

APPENDIX: NUMERICAL EVALUATED DATA FILE IS TOL EMDF/k

FORTJAT A

-I-

AND EVALUATED FAST NEUTROK CROSS

SECTIONS OF ELEMENTAL NICKEL*

by

P. Cuenther. A. Smith, D. Smith and J. Whalen

Argonne National Laboratory

and

R. Hoverton

Lawrence Livemore Laboratory

ABSTRACT

Fast neutron total and scattering cross sections

of elemental nickel are measured. Differential elastic

scattering cross sections are determined from incident

energies of 0.3 to 4.0 MeV. The cross sections for the

inelastic neutron excitation of states at: 1.15610.015,

1.32410.015, 1.443*0.015, 2.136*0.013. 2.255*0.030,

2.44910.030, 2.614*0.020 and 2.79110.025 HeV are mea-

sured to incident neutron energies of 4.0 MeV. The

total neutron cross sections are determined from 0.25 to

5.0 MeV. The experimental results are discussed In the

context of optical and statistical models. It is shown

that resonance width-fluctuation and correlation effects

are significant. The present experimental and theoreti-

cal results, together with previously reported values,

are used to construct a comprehensive evaluated elemen-

tal data file in the ENUF format. Some comparisons are

nade with previously reported evaluated files. In addi-

tion, some selected reactions which are widely used in

dosimetry and other applications are presented as supple-

mental evaluated isotopic-data files. The numerical

quantities are presented in tabular form.

This work is supported by the U.S. Energy Research andDevelopment Administration.

-3-

1. J.ViIS

Mcl.el is widely etployttJ In neutronic applications

both In the eleneutal fore and as a ferrous alloy (1).

Sone of the latter alloys are rich In nickel and particu-

larly resistant to radiation danage. in view of this ap-

lied usage. It is curious that the fast neutron cross

sections of nickel are not well known. Indeed, only re-

cently lias the resonance behavior of the total neutron

cross section been reasonably established in the several

hundred-keV region (2).

tlenental nickel consists prinarily of the two iso-

topes Ml and ° Ni., They are in the region of stronp.

i-0 strength functions where resonance width-fluctuation

and correlation corrections to the liauser-Feshbach fonaula

should be pronounced (3,4). These corrections are impor-

tant at MeV energies where the excitation of a few dis-

crete levels is a dominant feature of the inelastic scat-

tering process. The width—fluctuation correction enhances

the average cross section for reactions in which the en-

trance-and exit-channel fluctuations are correlated with a

corresponding reduction In cross sections for reactions

without such correlation. The low-energy excited levels

of these isotopes exhibit the characteristics of two-phonon

vibrational excitation and channel coupling between the

ground and low-energy excited states may be appreciable.

It is of Interest to compare ellipsoidal-(coupled-channel)

and spherical-optical model interpretations of the observed

cross sections. Furthermore, the energy-averaged nodels can

be related to the statistical properties of the fluctuating

cross sections observed in high-resolution measurements with

a consequent improved insight into the nature of the energy-

averaged models (5).

Thus, from both basic and applied points of view, the

interaction of fast neutrons with nickel is of consider-

able interest. It is the objective of the present work

-4-

to examine such processes using experimental and calcu-

latlonal neans ar.d to use the results, together with

those available froa other sources, to construct an

evaluated nuclear data file in the ENBF foroat for ap-

plied use (6). The following sections deal with: II} a

brief outline of experimental eethoda, III) a suorutry of

experimental results, IV) mm interpretation of the pres-

ent measured values In the context of optical and

coupled-channel models including the statistical nature

of the fluctuating structure and the implication of the

energy-average nodels, and V) the formulation of the

evaluated data files Including a general elemental file

and supplenental isotoplc files. The complete numerical

files are presented In the Appendix.

II. EXPERIMENTAL METHODS

The sanples were cylinders of high purity netalllc

nickel. One set was selected to provide axial neutron

transmissions of 50 percent or greater in the total cross

section aeapurenents. A second set consisting of 2 cc

diameter and 2 en long right cylinders was used for the

scattering neasureaents with neutrons incident on the

lateral surfaces. The sacples had negligible chemical

impurities.

Throughout the measureoents the Li(p;n) be reaction

was employed as a neutron source with the metallic-

lithium film selected to provide the desired incident

neutron energy resolutions.

The total neutron cross sections were deduced from

the observed transmissions of approximately monoenergetlc

neutrons through Che sanples (7). The data were obtained

from three separate sets of experiments distributed over

a decade. The first set spanned the energy range 0.25 to

0.65 MeV. It utilized an automated facility and BF_

-5-

neutron detectors (8). The second set of

extended fro- U.JO to 1.5U ::eV. The cctiwiu vas essen-

tially the sare as that of Che first set witii a proton-

recoil scintiilator replacing die BF detectors. Tlie

recoil sciutlllator was ! iaseu to reject the second

(minority) neutron group fro: the source reaction and

f>anna-ray sensitivity was suppressed with appropriate

circuitry. The Cliirti set of neasurera>nts extenoeu fror

1.5 to 5.0 MeV. The netiioc w.ts essentially the sane as

enployeci be lot 1.5 MeV with t.ie addition of tine-of-

fliftht techniques to control the background anti reduce

other experimental perturbations (y). Absolute energy

scales were deten-iineu relative to the threshold of the

neutron-source reaction vita a:> estitiateti precision of a

few IceV. Much of the total cross section data wn« ol>-

tained in an energy-rantior. nar.ner wisici: tended to iciti-

r.ate systenaclc uncertainties.

The scattering neasurettents enj>loyed tine-of-fiiftht

techniques using ar. 8-10 an;;ie detection syster (10).

The scattered neutron velocity resolutions were in the

ranp.e 0.4 to 1.0 nsec/n with the better velocity resolu-

tion at the higher incident enerpies. The scatrerinp

angles ranged fror. approxinately 2U to 16u dcy. At in-

cfdent energies of - l.!> MeV ceasurcrwnts were rade at

8 to 10 «catterinp angles distrionted over the angular

range. At hieher incident neutron energies tjeasurer.ents

were made at 10 to 2U scattering; angles. Tiie relative

energy dependence of the detector efficiencies ana the

absolute values of the cross sections were measured

relative to the il(n,n) process at energies > 1.5 MeV

(11) and relative to the C(n,u) process at - 1.5 MeV

(12). All neasureti scattering cross sections were cor-

rected for angular resolution, bean attenuation and

Multiple collision effects using Monte-Carlo procedures

(13). All cross section values reported herein are ex-

pressed in units of barne per atom of the decent unless

otlierwlse specified. The particular apparatuses ana

procedures are described in detail elsewhere (8,9,1U).

111. tAPt-KlMtNTAL KEStLTS*

1. Total Neutron Cross Section*

The total neutron cross sections were measured from

0.2a to 5.0 MeV. While the resolution of 2.0 to 2.5 fceV

was good, it was not in Itself a goal. More attention

was Riven to the accuracy of the energy-averageu magni-

tudes to provide a good foundation for the development of

energy-averaged Models and to assure accurate itorctaliz-

atlon of evaluated cross section sets. The statistical

accuracies of the inuivluual data points were in the range

1-2 percent and considerable attention vas given to the

minimization of systecatic errors. The results are sunar-

ized and compared with the angle-integrated elastic scat-

tering values and vith tiie evaluated total cross section

in Fig. 1. iielov 1.5 MeV the present values are in good

agreement with the white-source results of Ferey et al.

(2), considering that the latter have appreciably better

resolution with correspondingly greater maxima. The

present values nay tenu to have slightly lower cinina.

The energy scales appear consistent. Above 0.5 MeV the

present values are in good agreement with Che white-source

results of CierJack* et al. (14). The latter provide

better resolution to about 2.0 MeV. At higher energies

the resolutions of the present measurements are probably

superior, and thus the data fluctuations are larger. The

present values confirm, wit:: a different technique, the

major features and magniti-des of the two comparable sets

of higher resolution white-source results. When broad

energy-averages are constructed from these measured data

a. All measured data reported herein has been transmittedto the National Neutron Cross Section Center, BrookhavenNational Laboratory.

-7-

sets the ap.reeaent 1B particularly BOOH. In adult ion,

tiiere 1H a number of raore United aonoenerp.et lc data

sets that are consistent with the present experimental

values (15).

2. Elastic Neutron Scattering irosa Sections

The differential elastic scattering cross sections

were Measured fro* O.J to 4.0 MeV. below £ l.i> MeV the

Incident neutron energy resolution was "»• 2U keV and the

Measurements were made at Intervals of "»• 20 keV. The

estloated uncertainties were 10 to 13 percent. Above

l.S MeV cross sections were determined at 1OO to 200 keV

incident energy Intervals with resolutions of 30 to 50

fceV and estimated uncertainties of 5 to 10 percent or 3

ob/sr, whichever waa larger. Factors contributing to

these uncertainties varied from measurenent to measure-

ment but were generally: 1) sanple counting statistics,

< 1 to 5 percent, 2) detector normalization procedures,

< 3 to 8 percent, 3) uncertainties in reference standards

of 1 percent for H(n,n) and 6 percent for C(n,n), and 4)

systematic uncertainties associated with geoactrical

factors (e.g., scattering angle determination) and multi-

ple event corrections collectively amounting to 1 to 3

percent.

The measured dlff -rential elastic angular distribu-

tions were least-square fitted with Legendre polynomial

series. The fitting procedures were based upon the mea-

sured values with the addition of a few 1W) deg. theoret-

ically deduced cross sections at higher Incident energies

in order to assure a well behaved extrapolation beyond

the neasured angular range. The results of the fitting

were generally consistent with "Wick's Licit" (16)> The

angle-integrated elastic cross sections, obtained fron

the fitting procedures were believed known to t> 10 percent

with the better accuracies corresponding to the higher

- I B -

energies"*-" 'ittey were generally consistent with the ob-

served total cross sections, as illustrated In Ftp,. 1,

particularly uer.onstrating an intermediate fluctuating

structure similar to the energy-average^tgiiavior of the

better-resolution total cross section results.

Energy-dependent structure was very evident in the"

differential elastic distributions, decreasing in etagni-

tude with increasing energy and approaching a smooth

behavior at 4.0 :ieV. below 1.5 MeV, these fluctuations

were so prcr.otmcea that it s?ss difficult to correlate

neasurecents natle with slightly different experimental

incident energies at.d/or resolutions or to ccnpare the

present results with those reporteci elsewhere. There-

fore the expert-cental differential distributions were

averaged over incident energy intervals of '- SO keV.

The results are suscarized in Fig. 2. txpresseo in this

forr. the distributions reasonably portray intersediate

structuie effects ami are r--ore cocparable with previously

reported results, bone of the latter comparisons are

shown in li?.. 3. lielow 1.3 MeV the present work is only

qualitatively consistent with that of t.orzh et al. (17),

Cox il'6) and halt and carschall (19). The differences

were attributed to the residual effects of structure in

the context of the experimental resolutions of the

various neasurenents. Kroc i.J to 4.0 KeV the present

results conpare reasonably well with those of holcqvist

and Wiedling (20), Tsukada et al. (21) .mo Mackwe et al.

(22). Where there are differences they are usually

within the respective experinental uncertainties, often

at lower energies and/or correlated with observed struc-

ture in the high resolution total cross section. An

example oi the latter effect is illustrated by the re-

sults near 1.8 MeV where there is a pronounced "bussp" in

the total cross section (See Fig. 1) which corresponds

-y-

Co the energy of an angular distribution measured in

the present work which differs fron results at slightly

lower energies reported in Kef. 20.

3. Inelastic Neutron Scattering Cross Sections

The energies of the inelastically scattered i;eu-

trons were determined fron measured flight tines and

flight paths and the known incident energy and verified

by the observed excitation of well known inelastic neu-

tron scattering processes in other nuclei (e.g., the

846 keV state in Fe). The accuracies of the excita-

tion energies determined in this manner were approxi-

mately 10 to 30 keV. Hie present results are compared

with previously reported values for Si, Hi and Tfi,

as summarized in the Nuclear Data Sheets (23), in Fig.

4. Some of the spectroscoplc techniques eisployed In

previous work are capable of determining level energies

with greater accuracy than the present ceasurements and

therefore the previously reported excitation values are

preferred for the interpretation of Sec. IV and evalua-

tion of Sec. V. Angle-integrated inelastic excitation

cross sections were deduced from the neasured differen-

tial values by least-square fitting a Legendre polynomial

series to the observed angular distributions. The esti-

raated accuracies of the resulting cross sections were

generally 5 to 15 percent fcr scattered-neutron energies

greater than 0.7 HeV. Lower energy scattered neutrons

were routinely observed but the corresponding cross sec-

tions were felt to be unreliable due to uncertain detec-

tor sensitivities and limited angular information. The

cross section results are sunurized and compared with

previously reported values in Fig. 5.

The observed levels at 1.156+0.015, 1.324+0.015 and

1.443+0.015 MeV were attributed to the first-excited

states in 62Ki(1.17 MeV), 6ON1(1.33 HeV), and 58Ni(1.45

MeV), respectively. The cross section magnitudes were

-10-

in general agreement with those obtaineu in the uirect

neutron rceasuretuents of Tsutiada et al. ill) and hoschunf,

et al. (24), Hodgers et al. (2!») , l*erey et al. (2f») and

Cranberj", ami Levin (27). The ap.reenent vitl: a nuisber of

results of (n;n',-y) measurements is not as satisfactory;

particularly where uncertainties in j-.anca-ray branching

ratios becoise a contributing factor (28,29,20,31). The

fluctuation in tiic cross section values, particularly in

the context of the prominent 1.45 JfeV state, was large

indicating tlie presence of an interraeniate resonance

structure. In such an environment, r.easurenents tnacie

vitli only slip.htly differing incident energies and/or

resolutions can give appreciably different results.

Furthermore, the structure evident in the total cross

section should be selectively enhanced in the individual

inelastic channels and preliminary results of detailed

(n;n',Y> studies !•>• ii. Snith support this precise (32).

similar structure is well known in sicilar inelastic

processes (e.g., the excitation of the &46 keV state in

^ F e ) .

The excitation of tme Z.libtU.lS and 2.235tU.U'iO

MeV states i>-ns pririarily attributeu to reported levels

in bl>:ii (2.16 and 2.28 MeV). In addition, there vas prob-

ably sore Rlnor contribution fron 2.05, 2.29 and 2.33

MeV states in M that vould not Stave been resolved from

the primary Mi contribution in the present experiments.

The measured cross section values were generally consist-

ent vith previously reported results, particularly those

of Tsukada et ai. (21).

Observed neutrons corresponding to an excitation of

2.449*0.03(1 MeV were attzibuted to contributions from the

reported 2.46 and 2.31 MeV states in i8Ki and OtJKi, re-

spectively. The resolutions of the present experiraents

would not resolve the two coriponents. The measured re—

-11-

suits are consistent vlth those reported by Boxchung et

aJ. (24) but possibly sotcewhat lower than the (n;n*,Y>

values of Kef. 31.

The observed excitations of states at 2.614+0.020

and 2./91+O.O3O MeV were well correlated with known levels

in 60Ni(2.63 MeV) and 58Mi(2.77 KeV), respectively. The

former are in good agreenent with the values reported by

Perey et al. (26). However, the present cross sections

for the excitation of the 2.77 MeV are not consistent

with those deduced from the (n;n*,y) measurements of Kef.

31 even considering the relatively large uncertainties in

the present work.

In addition to the above, neutrons were observed

corresponding to the excitation of states above 2.8 MeV.

These were not well resolved because of an increasingly

complex structure and the cross sections were relatively

uncertain. Therefore, these results Mere not interpreted.

IV. INTERPRETATION AND DISCUSSION

1. The Optical Model and Elastic Scattering*

The observed energy-averaged neutron total and elas-

tic scattering cross sections were examined in the con-

text of the optical aodel (33,34). Parameter selection

was based upon comparisons of measured and calculated

total and elastic scattering cross sections. The calcu-

lated values included compound nucleus contributions

determined with the Uauser-Feshbach formula (3) corrected

for resonance width fluctuation and correlation effects

(4). Over a large portion of the energy range of

interest, both total and scattering cross sec-

tions fluctuated by large amounts. Therefore, the aea-

sured values were averaged over t 0.2 MeV energy inter-

vals before Baking comparisons with calculated results

-12-

ami •ore emphasis was given to energies above * 2.0 MeV

wliere the fluctuatloos were less pronounced.

An Initial at tdipt to select optical pntep.cial para-

meters fro* X-square fitting to the observed elastic

angular distributions proved unrewarding. The descrip-

tion of individual distributions was generally good but

the resulting parameters were sharply dependent upon the

Incident energy due to the persistence of intermediate

fluctuations even in the 0.2 MeV energy average of the

measured values. Therefore, the potential was

subjectively selected frou cncurrent comparisons of

measured and calculated total and elastic scattering

cros£ sections. Two different potential models were used

as starting points for the calculations: 1) that of

Moldauer (35), primarily applicable in the lower energy

region, and 2) that of Uolmqvlst and Wiedling (20), more

suitable at higher energies regardless of reasonable para-

meter adjustment. The Holnqvist and Wiedling potential

was useful for the extrapolation of various experimental

results in the high energy region. Therefore, it was

accepted for use In the subsequent computations. The

parameter values are given in Table 1. The total cross

sections calculated with this potential agree within a

few percent with the experimental values at energies above

•v 2.0 MeV as illustrated in Fig. 6. The parameters were

not energy dependent and the introduction of such a depend-

ence as suggested, for example, by Engelbrecht and

Fiedeldey (36) led to some degradation in the description

of experiment. This was probably an artifact of the

particular potential and energy range since an energy de-

pendence is a characteristic of broader-scope studies.

Below about 2.0 MeV the calculated total cross sections

were somewhat larger than the energy-averaged experimental

results. This behavior is rattier characteristic of this

-13-

type of potential (relatively large real depth, "** 50

MeV, and narrow radius) in this Mass-energy region.

Improved descriptions of total cross sections In this

region are obtained using the potentials more of the

Moldauer font (relatively smaller real depth, % 45 MeV,

and larger radius). However, it is an area where large

fluctuations make quantitative comparison with an

energy-averaged model difficult and where data for

applications mist be primarily based upon experimental

values. Both types of potentials resulted in calculateda. -4

1-0 strength functions cf * 5 x 10 , consistent with

the values reported from resonance Measurements and

systenatlcs (37).

The calculated elastic-scattering cross sections

were sensitive to the cocpounu-nucleus contribution

throughout the range of the present measurements. This

contribution is enhanced by width-fluctuation effects

and reduced by resonance correlations. These opposing

corrections to the Hauser-Feshbach formula were estimated

using the approximations of ttoldauer (4) and the computer

code NEARREX (38). The results were sensitive to the

overlap parameter, Q, which was adjusted to obtain the

overall best agreement between measured and calculated

elastic and inelastic scattering cross sections. These

comparisons indicated a Q of 0.7 to 0.8 as illustrated by

the example of Fig. 7. This range is reasonable in

the context of the structure evident In the measured

quantities (e.g., total cross section). Using 0*0.75

the calculated elastic distributions generally compared

well with the measured results of the present work as

illustrated in Fig. 3. At the lower energies (y 1.5 MeV)

the fluctuations are large and some differences are to be

expected. At higher energies where the fluctuations are

smallest, the agreement with the present measured values

is good. The model was not explicitly adjusted to de-

-14-

scribe previously upcated elastic scattering results

at energies above 4.U MeV. However, the calculated

distributions were representative of Measurements as

Illustrated by the results at 6.0 and 8.0 MeV shown in

Fig. 3. More exact patataeterization can be obtained

at a given energy with detailed adjustment of parameters

but at the expense of the overall description. Indeed

some specifically tailored parameter sets reported in

the literature were found deficient in a broader energy

context. Calculated 14 MeV distributions were slnilar

to reported Measured values (39,40,41) with discrepancies

largely In the details of the diffraction patterns where

the experimental results themselves are ambiguous.

At these high energies collective vlbrational direct-

reactions probably contribute to the elastic processes.

These were estimated, using a coupled-channel calculation

based upon the above potential (42). The inelastic scat-

tering contribution was small at the energies of the

present measurements and not a significant factor In the

context of elastic scattering (less than uncertainties

associated with unknown level structures).

2. The Statistical Model and Inelastic Scattering

The inelastic excitation cross sections were calcu-

lated using the above optical potential and the liauser-

Feshbach fomula with corrections (3,4). The choice of

optical parameters was not explicitly influenced by

considerations of inelastic scattering but the selection

of the overlap parameter, Q, was Made In concert with the

cons; derations of elastic scattering as outlined above.

It was assumed that the elemental inelastic scattering

was entirely due to Ni and Kl as More than 94 percent

of the element consists of these Isotopes. The spectro-

scopic characteristics of these two isotopes are well

-15-

known to excitation energies above 3.0 MeV (see Fie. 4)

but at higher energies becone increasingly uncertain

with a corresponding unreliability of the calculated re-

sults. The region of uncertainty is generally above the

energy range of the present Measurements. The calcu-

lated results are sunurized and coapareu with the nea-

sured vtlues in Fig. 5.

The observed excitation of the 1.17 MeV state vas

attributed to scattering from Ni and not considered In

the present calculations. However, the Measured values

were approximately 15 percent of those calculated for the

1.33 HeV state attributed to Jtl as expected.

The observed 1.33 and 1.45 MeV states are similar

first-excited (2+) levels in ^Ni ami *8Ni, respectively.

Their calculated excitation functions are similar up to ^

2.2 HeV then becone different as varying channel competi-

tion sets in. The results of both calculations are quali-

tatively sinilar to the Measured values but there are

detailed discrepancies (particularly evident In the case

of the prominent 1.45 MeV state) which are attributed to

the fluctuating structure near thresholds (as noted in

Sec. Ill above). In view of these uncertainties, the

calculated results, largely based upon considerations of

neutron tots! and elastic scattering cross sections, were

judged acceptable. As expected, the calculated values

becone Increasingly larger than the Measured quantities

above 4.0 MeV due to OMisslon in the calculations of

unknown conpeting neutron channels.

The observed 2.15 (2+) and 2.2b (0+) HeV states are

primarily due to known levels in Ni with additional and

unresolved snail contributions fro« 2.05, 2.29 and 2.33

MeV levels in Hi. The calculated and Measured excita-

tion cross sections for the 2.15 MeV state are in good

agreement. The calculated results for the excitation of

-16-

che 2.28 MeV state are nailer titan Che Measured values

by an aaount consistent with the contribution fro* the

2.29 and 2.33 MeV states in 6 2M, not included in the

calculations. Indeed, the observed angular distribution

of scattered neutrons resulting froc the 2.28 MeV excita-

tion was anisotropic in the Manner characteristic of a

0* excitation but not to the degree Indicated by calcula-

tion assunlnj? contribution fron & single level. This

also would he expected fron socie additional contributions

from 62Ki.

The observed neutrons corresponding to the excita-

tion of a 2.40 MeV state were assured to be the SUB of58Mi(2.46 MeV,4+) and 6UNil2.51 MeV,4+) contributions.

Calculations based upon this precise gave results consist-

ent with the experimentally observeit cross sections of the

present experlnent to energies of % 4.0 KeV. At higher

energies the calculated results became Increasingly too

large, again probably due to the neplect of unknown cott-

petinp, neutron channels.

The neasurenents did not well define the cross sec-

tions for the excitation of the 2.63 KeV ami 2.77 MeV

states, however, calculated results baseu upon the pre-

nise of contributions fro* 60Hi(2.03 MeV,3+) and 58Ni(2.77

MeV,2+), respectively, were in reasonable agreement with

the experimental values.

The above calculated results were based upon a

spherical optical potential and the conpound-nucleus

nodel. However, the first excited states of the two

prominent even isotopes ( tfi and Mi) are attributed to

two-phonon vlbrational configurations (23,43). Therefore,

collective-direct excitations can contribute to the ob-

served scattering processes. This was esticiated

using coupled-channel calculations assuning m deformation

parameter, ti - 0.187 ant! a vibrational coupling of ground

-17-

(Of) and first excited (2+) states (44). At the energies

of the present Measurements the direct contribution was

not large as illustrated by the comparison of dashed end

dotted curves for the excitation of the 1.45 MeV state

shown in Flp.. 5. The anlsotropy in the scattered neutron

angular distributions predicted by the coupled-channel

calculations was not recognizable In any of the present

•easureMenta and generally of the order of the experinen-

tal uncertainties. Moreover, the possible effect is

•asked by the apparent fluctuations, noted above, and by

uncertainties associated with the physical nechanisns in-

volved in the coapound nucleus processes. The direct

component is a Major contribution and clearly evident at

incident energies well above those of the present experi-

ments. Examples are fount; in the cross section Magnitudes

and angular distributions associateu with the excitation

of the first (2+) states by 14 MeV incident neutrons as

reported by Stelson et al. (45), Clark et al. (46) and

KaMMerdiener (39). These experinental data at 14 MeV

were consistent with the results of the coupled-channel

calculations.

All of the above compound-nucleus calculations, for

both elastic and Inelastic scattering, ecployeo

the Hauser-Feehbach formula with the correction factors

suggested by Moldauer (4). The latter are recognized as

qualitative approximations, however. It la clear that

such correction factors appreciably Influence the com-

parisons of calculated and neasureu values and thus the

basic aodel selection. More definitive Model determina-

tion will probably require a better understanding of these

correction factors. Such is now being *oughttfor «x-

aaple, by Holuauer (47), kawai et al. (40) and

Weidenaniller (49). Wide application of these new physi-

cal concepts will require the developeent of practical

computational tools for e;:perlnent analysis.

-18-

V. THE EVALUATED FILE

The above experimental and calculatlonal results,

together with previously reported information, were

utilized to construct a comprehensive evaluated data

file in the KNDP/B format (b). The objective was to

make available the most recent Information In a form

suitable for applied use. This evaljation was confined

to enercles greater than 100 keV. For completeness, the

file was extended to lower energies explicitly using the

preliminary version of ENDF/B-IV formulated by M. Bhat

(6). In addition to the general elemental file, selected

Isotopic files were formulated where they referred to

specific reactions that are often employed on an lsotoplc

basis (e.g., in dosimetry applications). The elemental

file was constructed from these lsotoplc components where

appropriate. The derivation of the present file Is out-

lined in the subsequent text and the numerical values are

given in the Appendix. Throughout, attention was given

to both physical content and conciseness.

1. Total Neutron Cross Sections

From 0.1 to 0.5 MeV the data base for the present

evaluation was obtained fron Kefs. 2,51),51,52 and the

present work. Kef. 2 appeared to be of the best quality

and the nore cocprehensive therefore was given the prlcary

emphasis. A larp.e-scale graphical representation of these

data was assembled and points selected froc the Measured

values so as to give a clear representation of the re-

sults with a good degree of conciseness. This procedure

resulted in a very good description of the neasured

values. Above 0.5 MeV the present evaluation was based

primarily upon data from Ref. 14. The general character

of the structure and tlic energy-averaged Magnitudes of

that work were verified by the present aeasurenents and

those reported in Kefs. 15.53 ana 54. Data fron Ref. 55

-19-

tended to have a lower average magnitude and was not

used. The resolution of the data of Kef. 14 ap-

peared very good, and the energy scale was consistent

with the results of lsotopic neasurenents given in

Kef. 56. The evaluated file in this higher energy re-

gion was derived by the same point selection method

outlined above to 6.0 HeV. Above 6.0 HeV the data be-

comes smooth and the file was constructed froii energy-

averages of the treasured values over intervals of 25

keV or larger.

The results of the present evaluation are compared

with those of KNDF/B-IV in Fig. 8. Below energies of

approximately 0.7 MeV KNDF/B enploys a resonance-para-

meter description and the results are not directly

comparable with the point values of the present work.

Above 0.7 HeV the two evaluations arc 6inilar, though a

careful inspection indicates that the present file

gives a slightly inproved description of the fluctuating

structure with, particularly, higher resonance naxina.

Due to the sharp resonance structure over such of

the energy range of the file, error estimates are diffi-

cult. Undoubtedly, at some future date improved measure-

ments will result in larger rcaxina and lower minina as

suggested by theoretical statistical calculations (5).

However, it is unlikely that the energy-averaged magni-

tudes of the evaluated file will change by aore than 3

to 5 percent and, but for a few lower energy regions,

the extrena may not change by nore than 20 percent.

2. Elastic Meutron Scattering Cross Sections

The evaluated elastic scattering cross sections were

primarily ban»d on data from experiments to •* 8 HeV and

near 14 MeV. Theory was used to extrapolate and interpo-

late where necessary, particularly fran 8 to 14 HeV and

14 to 20 MeV. Below 0.3 HeV, the recent experinental

-20-

results of Zuhr (57) were given prinary emphasis.

They are consistent with the results of Ref. 12 and

the resolution was sufficient to define Intermediate

fluctuating structure. Fron 0.3 to 4.0 MeV primary

reliance was placed upon the present experimental

work supported by the results of Cox (18), Halt and

Barschall (19), Tsukada et al. (21) and Holnqvist and

Wiedling (20). Some of these experimental results

are compared in Fig. 3. Evaluated differential

cross sections at 5.0, 6.0, 8.0 and 14.0 MeV were con-

structed froQ the Measured values of Percy et al. (26),

Boachung et al. (24), holnqvist and Wiedling (20), Clark

and Cross (41), Kaaoerdlener (39) and Bauer et al. (40).

The experimental data base above 5.0 MeV was generally

available at slightly different incident energies. Mea-

sured values were combined in the evaluation when the

incident energies were within t 10 percent of a given

Median value. Generally the Incident energies were such

closer and an effort was made to balance high and low

energy results about the Mean.

The angle-integrated elastic cross sections were ob-

tained by least-square fitting a Legendre polynonial

series to the Measured values* The 0 deg. cross section

value was constrained to exceed the Minima set by

"Wick's Unit" (16).and ISO deg. values deduced fron the

«odel of Sec. IV, «ere Introduced to assure a well

behaved shape. The same Model was slightly "tailored" to

give good description of 8.0 and 14.0 MeV experimental re-

sults and then used to interpolate between 8.0 and 14.0

MeV and to extrapolate to 20 MeV assisting shape scattering

only.

The evaluated angle-integrated elastic cross sections

were consistent with other known partial cross sections

and the total cross sections up to about 4.0 MeV. Above

4.0 MeV the difference between total cross section, and

the elastic cross section and observed partial cross

-21-

sections defined the ccntinuwa inelastic cross section.

The final evaluated elastic cross section vas determined

by subtracting the observed nonelastic cross section

from the total cross section. This procedure is

necessary to achieve the nanadatory internal consistency

of the file. Unfortunately, it has the physically

consequence of reflecting nearly all the detailed struc-

ture of the total cross section to the elastic channel.

There is little alternative in the absence of high

resolution data in all channels ami with the requirement

of absolute internal consistency, lite final evaluated

result Is sutoaarlzed and compared with that of LNOT/B-IV

in Fig. 9.

The evaluated angular-dl6tributions of elastically

scattered neutrons are expressed as 4- coefficients where

dit 2w / 2 *C I u '

imo

and P£ are Legendre polynomials expressed in the center

of mass system. The coefficients are based upon experi-

mental values extrapolated by theory as outlined above.

They satisfy "k'ickcs Limit" (lb). The energy resolutions

associated with the angular distributions are "»> 50 keV,

i.e., much coarser than those of the anple-integrated

cross sections. However, the angular distributions do

show intermediate fluctuations as evident in the energy

dependence of the distributions shown in Fig. 10. The

absence of detailed resonance behavior of the angular

distributions nay lead to sorce problems in special appli-

cations -

The estimated uncertainties In the evaluated angle-

integrated elastic scattering cross sections are 5 to

10% up to 8.0 HeV ano near 14.0 MeV, regions where there is

-Tl-

experimental Information available. The uncertainties

nay be larger in the regions of theoretical Interpola-

tion and extrapolation (i.e., ».U>14.u MeV and > 14.0

MeV). The uncertainties in the relative angular dis-

tributions are qualitatively of the sarae magnitudes.

The file requires internal consistency, thus there is

generally a built-in correlation of total and partial

cross section uncertainties.

3. Inelastic Neutron Scattering Cross Sections

The evaluated inelastic scattering cross sections

are treated as discrete excitation functions froei

threshold to energies of 3.628 MeV. At higher excita-

tion energies the inelastic neutron process Is attri-

buted to a continuum of states with the emission of

both preconpound- and cosipound-nudeus inelastic neutron

spectra. These two types of Inelastic neutron processes

are dealt with In the following subtitles, A and B.

A. Discrete Excitation Cross Sections

The energetics of these contributions are based on

the spectroscopic values of Ref. 23 as defined in Table

2. The evaluated cross sections are compared with the

underlying data base in Fig. 3. The specific components

are as follows:

E - 1.172 MeV, 62N1

The evaluation is based upon the present experimen-

tal results and those of Tsukada et al. (21) and of Rogers

et al. (30). This experimental Information is for inci-

dent energies of - 3.0 MeV. At higher energies the evalua-

tion relies on theoretical extrapolation and analogy with

results experimentally determined for the similar first

excited (2+) states in Hi and ^Ni. The neutron emission

Is assumed isotroplc to 4.0 MeV and then becomes anlso-

tropic as direct reactions become appreciable. The degree

-23-

of anlsotropy is derived from model calculations as

discussed belov for the 1.33 and 1.45 MeV states. So

attention is given to the probable presence of

fluctuating structure. The latter assunptioix is an

over simplification but will probably have little

impact on oost applications of the file, the cross-

section uncertainties for the excitation of this state

are relatively large, 3O-5U2., but the absolute-un-

certainty Magnitudes are small,, - 20 mb.

Ex - 1.333 MeV, 6%1

The excitation of this state has been observed

experinentally to % b.O MeV and at -v 14 MeV in both

(n;n*) and (n;n',y) measurements. The evaluation relies

on experimental values interpolated with theory. The

approach to threshold from 2.0 MeV is based upon the re-

sults of Rogers et al. (30), Sluchaevskaya (31) and 1).

Smith (32). Primary emphasis is given to the latter.

They are relative values, nonaalized to neutron scatter-

ing results at £ 2.0 MeV, but are in sufficient detail

to give an Indication of the appreciable fluctuations

that oust be present. From 2.0 to B.O CteV the evalua-

tion is based upon the experimental values of the present

work, those of Uoschung et al. (24), 'i'sukada et al. (21),

Rogers et al. (30), Day (28), Scherrer et al. (29),

Rodgers et al. (25), Sluchaevskaya (31), ana Perey et al.

(26). The evaluation is extrapolated above 8 MeV using

theory adjusted to be consistent with the "*• 14 MeV experi-

mental, values of Kamerdiener (39) and of Stelson et al.

(45). The latter two sets of measurements represent the

composite excitations of 1.333 (60Ni) and 1.452 (58Ni)

states. The present experimental studies, supported by

other measured values, indicate that the neutron eniscion

is essentially isotropic below i< 4.0 MeV ano this is as-

sumed in the evaluation. Above 4.0 MeV the observed

-24-

scattered neutron distributions become increasingly

anisotropic (see for example the work of Uoschung et

al. (?*), Perey et al. (26), Stelson et al. (45) and

Kammerdiener (39)). These experimental distributions

were fitted with Legendre polynomial series. The

latter were smoothed and interpolated using coupled-

channel calculations and then used to provide the

angular distributions for the evaluation. Below t>

5.0 HeV the energy-averaged of the evaluated cross

sections were estimated to have an uncertainty of "v

15%. Above 5.0 MeV the estimated error becomes larger,

perhaps as much as 302 at 20.0 MeV. tlear threshold

the evaluation is deficient In describing the reso-

nance fluctuations and one may expect future high reso-

lution measurements to show fluctuations about the

energy-averageti values of as much as an order of magni-

tude.

EJJ • 1.454 MeV, 5 8 N i— — — — '— — — — — -—'•— eg

This state is the 2+, Ni, complement of the

slnllar 1.333 HeV state in Ni (see above). The data

base consists of the present measurements and those of

Taukada et al. (21), Rodgers et al. (30), Day (28),

Scherrer et al. (29), Rogers et al. (25), Sluchaevskaya

(31), Boschung et al. (24) and Perey et al. (26). In

addition, the composite excitations of the 1.333 and

1.454 MeV states at 14 MeV reported by Stelson et al.

(45) and Kamnerdiener (39) were considered. An indica-

tion of the partially resolved structure below 2.0 HeV

was obtained from the relative (n;n',Y) measurements of

D. Salth (32). Even above this energy, there is an

Indication of the persistence of unresolved resonance

fluctuations the definition of which is beyond present

experimental information. Therefore, the evaluation

follows an energy-averaged above t> 2,0 HeV. The

-25-

extrapolation to 20.0 MeV anil the treatment of emitted

neutron angular distributions were identical to that

described above for ttie excitation of the 1.333 MeV

state. The estimated error In the energy-average of

the evaluation Is XbX below 5.0 MeV increasing to as

ouch as 20-MZ at 20.0 MeV.

^ • 2.158 MeV and ^ - 2.28t> MeV, b0Ni

The evaluation is a subjective esticate of the energy-

averaged behavior of the cross section deduced fron the ex-

perimental results of the present work, those of Tsukada

et al. (21), Day (28) and Sluchaevskaya et al, (31).

These experimental results extend to *»» 4.5 MeV. The extra-

polation to higher energies Is guirieo by theory and aade

consistent with the combineu excitations of the 2.158 and

2.284 MeV states reported by Perey et al. (26). The esti-

nated uncertainty over the entire energy range is *v ± 202*

The neutron emission was assured to be isotropic for this

and all subsequent excitations.

^ - 2.459 MeV, 5 8Ki anil E x - 2.506 MeV, ^ N i

There is little experimentally resolved data on the

cross sections for the excitation of these two states. In

the present work, that of Sluchaevskaya et al. (31) and of

Boschung et al. (24) the cross sections are determined as

a composite. Perey et al. (2b) observed the excitation of

the 2.506 MeV and subsequent 2.625 MeV state in 6 UN1 as a

composite. Tsukada et al. (21) have reported the excita-

tion of the isolated 2.45V MeV and 2.506 MeV states at

only a few energies. Hot-ever, the J values of these ex-

cited states in both Mi and U± are reasonably well

known. Therefore, the present evaluation is based upon

the measured cross sections for the composite excitation

broken into the two respective components by a ratio

factor calculated fron the above Model. The results are

-26-

consistent with the available experimental information.

The uncertainty in the individual excitation cross

sections may be rather large (up to 50%) but the esti-

mated error in the composite is s&aller (t 20%) and it

is the latter uncertainty that will be relevant to most

applications.

^ - 2.b25 MeV, ^Hi

The available experimental information is fro* the

present work and that of Scherrer (29). Supporting evi-

dence are the results of Beschung et al. (24) and Perey

et al. (26) which include contributions from the 2.506

HeV state. This rather Meager experimental information

was extrapolated using theory to obtain the evaluated

excitation cross section. The result may have a large

error (30-50%) but this will be of little note in Host

applications due to the snail magnitude of the cross

sections.

1^ - 2.775 MeV, 58Ni

The evaluation is primarily based upon the present

experimental results extrapolated with theoretical esti-

mates. The result is very much larger than indicated by

the measurements of Kef. 31. The uncertainties in the

evaluation say be large (as much as two).

Eg - 2,901, 2.942 and 3.038 MeV, 58Ni

There is very little direct experimental evidence

dealing with these states. For this evaluation we rely

upon model calculations assuming the above potential and

the J values of Ref. 23. The calculationol estimates

should be qualitatively valid (± 302). In view of these

uncertainties, we treat the three levels as a single

composite state in this evaluation with a mean excitation

energy of 2.960 MeV.

-27-

E - 3.123. 3.1»4, 3.1*5, 3.2/0, 3.Jlo ana S.iVl HeV,—B «•• • • _ — • — «••— ^ _ M •»• *W

The crosa sections for the excitation of the

NI components liave been reported by Percy et ai«

(2b). Additional Measured values are given by

Boachung et al, (24). The individual excitation func-

tions have not been resolved. For this evaluation we

assuaw a oean composite excitation energy of 3.270 MeV

and use theory for the extrapolation of Measured values

particularly where associated with the excitation of the

3.264 and 3.42U MeV states in 5BNi. The uncertainties

in the resulting evaluated cross sections are estinated

to be £ 302.

Ex • 3.526, 3.531, 3.593 and 3.620 and 3.775 MeV, 58M1

and 2.5W,_3s.6l8x 1-670 and 2-232 MBV,_*J[,S1

The available experimental lnfomatlon is apparent-

ly United to the neasured cross sections for the corpo-hi I

site excitation of the Hi states reported by Perey et

al. (20). The present evaluation uses these Measured

Ni values and the theoretically-calculated excitationsCO

of the contributing Ni states to obtain the excitation

cross section of a "state" at an average energy of 3.62VMeV. The prinary uncertainty is in the calculation of

58the NI contribution. The uncertainty in the evaluation

is estimated to be - 30%.

The cross sections for the excitation of higher

energy states in Ni are available fron the experimental

neasurenents of Perey et al. (26). however, the larger

contributions from Ni are unknown and uncertainties in

.1 values nake calculations unreliable. Therefore, the

present evaluation is confined to discrete excitation

functions corresponding to states at energies of -v 3.7

MeV. higher energy excitations are treated as contlnuun

distribution!* as deacrlbcti beluw,

(he above discrete Inelastic excitation cross sec-

tions are compared wltli a nucber of those Riven in

KHDF/a-lV In fly. 11. The sue of discrete inelastic

cross sections ot the present evaluation is very slnllar

to chat of bSDF/B-IV below >.U :>V but tiiere are sore

appreciable differences between specific excitation

function*. Generally, the present evaluation tends

toward larger discrete Inelastic cross sections at very

hip.h energies (e.g., 10-20 HeV). This is a physically

acceptable representation of direct excitations which is

substantiated by experlturntal observation ami by theo-

retical estimates. These iiicit-uitcrp.y croa* section com-

ponents vill contribute to a iiaruer enission spectrum at

hljch incident eneiy.it:; than iiioicateti by the sinple

tenperature distribution.

b, Contlnuuw Excitation cross Sections

The evaluated contlnuun inelastic cross sections

extend froa the last discrete inelastic threshold (*.„ •

J.«.2b MeV) to 2U.U MeV. Tlie cross section naenituues

are the differences between the evaluates total cross

section and the sun of other idvntiflea partial cross

sections. Thus the coutlnuun cuf^cnenc say also include

otherwise unidentified partial cross sections. This is

unavoidable when file internal consistency is Mandatory

and all partial components aay not be fully {mown. The

uncertainties in the cross section ragnitudes are esti-

•ated to be ^ SV percent and are, of course, correlated

with those of other cross sections.

The neutron eclsslon speccrua was axsuaed to con-

sist of three components: 1) discrete neutron groups,

2) a temperature distribution due to coapound-nucleus

decay, and 3) a pre-quilibriua continuing distribution.

The first of these is defined in Topic A, above. The

-29-

second component was described by a Maxvelliaii tempera-

ture distribution (58) defined by

N(E) * K exp (-E/T)

where (2)

The third, pre-equilibrium, component lias been the

subject of recent study by Griffin (5V), Cline and

Blann (60) and others. The process is usually formulated

In the context of few-particle statistical Models describ-

ing the intermediate configurations between the initial

transitory particle excitation aim the final long-lived

compound nucleus. These pre-equilibriu* sodels success-

fully describe observed emission spectra. However, a

large number of uncertain parameters are involved thus

making preaictlons based largely on the models sonewhat

uncertain and difficult to apply in pragmatic evaluation.

As an alternative the present evaluation represents the

pr*-equilibrlum emission with a "hard" temperature dis-

tribution. Thus, the full continuum spectrum is given by

N(E) % A • E • exp (-t/TA) + B • E • exp (-t/TB> (3)

where (A) and (is) refers to compound nucleus and pre-

ei]uilihriuB contributions, respectively. The choice of

parameters is based upon experiueutal comparisons. The

results of Hathur et al. (61), Voiginer et al. (62) and

Perey et jl. (2b) primarily influenced the selection of

compound-nucleus (A) parameters. The selection of pre-

equilibrium (B) parameters were largely based on compari-

sons with the experimental results of Seeliger et al.

(63) and Kaanerdiener (39) and considerations of spectra

obtained in sphere transnission "bench mark" experiments

at 14 MeV (64). The compound-nucleus temperature ( T )

was assumed to have a <f E dependence with the propor-

tionality constant determined from experimental coopari-

-30-

sons. The pre-enuilibrlum temperature (1 ) was as-

siunea constant, a reasonable approximation in view of

other uncertainties. 'Itie finally selected parameter

values were:

Rel. Magnitude Teni>.(MeV)

LoKpound-Nudeus A - i.O T -0.334./ £A

(4)

Pre-equilibriun D - 0.075 T -7.U HeV

o

These values are consistent with the available experi-

mental information anu with cor.pounci-iiucleus paraceters

reported elsewhere (see, for exarple, Ref. 26 J.

All of the continuun distributions were step-wise

terminated at the inset of the discrete excitation con*

tributlons. This physically anomalous behavior is an

artifact of the transition between the two types of re-

presentation and should not effect most applications.

The evaluation assumes the contlnuurt neutron emis-

sion to be isotropic in the laboratory system. This is

reasonable in the context of coepound-nudeus contribu-

tions but a gross approximation of the pre-equilibrium

processes. The latter are characteristically peaked

forward (e.g., see Kamerdiener, Ref. 39). However,

quantitative definition of anisotropy from the presently

available experimental and theoretical knowledge of

scattering from nickel would be highly speculative and

not of appreciable value for many applications.

The present evaluated inelastic cross sections are

very different from those of KNDF/B-IV in the higher

energy region as illustrated in Fig. 12. The discrepancy

is nearly a factor of two at 14 HeV and above. This is

primarily due to larger contributions fron several partial

emission reaction channels in the present estimates.

Prominent among these is the (n;n',p+p,n*) reaction where

the present evaluation is auch larger than that of ENDF/b-IV

as discussed below. In addition, then are several re-

action channels in che present work that were not included

in ENDF/B-IV. With a well known total cross section ana a

reasonably known clastic scattering cross section these

various other partial crosft sections primarily Interact

with and reduce the inelastic scattering cross section.

As noted below, sone of these components are uncertain and

•ay be overestiuteu in the present evaluation. Conse-

quently, the present evaluated inelastic cross section at

energies of £ 14 MeV say be uncertain by as Mich as 25-502.

However, this large uncertainty rerains such sraller than

the discrepancy with the high energy inelastic cross sec-

tions of EKDF/B-IV. This difference nay have an important

effect on high energy applications such ms CTR blanket

studies.

4. Radiative Neutron Capture

The evaluation in generally based upon the data of

Kef. 65 to 72. Below £ O.i MeV the evaluation follows the

recent higlt-resolution results of Le Rigoleur et al. (65).

There is a small (y 20 keV) energy gap in the Le Rigoleur

et al. results near 200 keV which was bridged with a

speculative structure following the general data trend.

From 0.5 to 1.0 MeV the evaluation follows the energy-aver-

age results of Diven et al. (67) and it Is extrapolated to

higher energies following the Measured values of Poenitz

(72).

The energy average of the present evaluation is con-

sistent with that of Moxon (6b) to 1.0 MeV and reasonably

sinilar to the ENDF/B-IV values from 0.7 to 1.0 MeV.

Above 1.0 MeV, the present results tend to be sonevhat

larger than those of EHDF/B-IV. Tne structure in the

present evaluation at energies below 0.7 MeV is not direct-

ly comparable with that of liNDF/b-IV as the present work is

-32-

baaeit on direct experimental observation antl that of

ENHP/li Apparently on a resonance extrapolation uslnp,

ays tentacles.

It Is reaarkaMc that present experimental kncvl-

edge of nickel fast neutron radiative capture is so

sparse. This has been recognized ami work now In prog-

ress at Af.'L by Poenitz (72) is improving the situation

in the particularly uncertain region above several

hundred keV. Until these, and ainllar, new experi-

mental results become available in final font, the pres-

ent evaluation taist be considered tentative with uncer-

tainties of 20 percent or sore over Much of the energy

range. In addition, it Is expected that sore future

hif.h-resolution Measurements will show pronouncedly

larger fluctuations in the lower energy region <"v 1.0

HeV). This is particularly so as the available experi-

mental information in the structured region nay be in-

fluenced by scattered-neutron perturbations.

5. (n:X) Reactions58

Energetically possible (n;X) reactions in til,

Ml and Ni are sumtarised in Table 3. These proc-

esses were addressed in the present evaluation. In ad-

dition, there are possible contributions froo the

minority (£ 12 abundant) HI and Ni isotopes. Gen-

erally, the latter two isotopes were not given consid-

eration. The primary intent was an elemental evaluated

file, however, certain of the above processes are con-

nxmly employed on an lsotopic basis particularly in

dositnetry applications. In these Instances the present

evaluation includes a secondary lsotopic evaluated file

in addition to the primary elemental file. Both files

are given in the ENDF/B format.

Subsequent sections deal with the specific (n;X)

reactions in Table 3.

-33-

A*The present evaluation considered contributions from

the 5BNi(n;2n) anu b0Ni(n;2n) reactions as defined in the

subsequent paragraphs. Both of these reactions have rela-

tively higher thresholds than those associated with the

few-percent-abundant TJi, b Si and Ni. Therefore, in

addition to the major contributions, the evaluation intro-

duces a very small "tail" extending to the lowest threshold;

7.954 MeV ( Ni). The neutron emission spectrun is approx-

imated by a temperature distribution of the fora N(E) t •

exp (-E/T) where the energy dependence of the temperature

is given by T - 0.25 /EH}. This is a qualitative estimate

based upon systematics and represents a sonewhat different

spectrum than given in tNUF/b-IV.

The isotoplc and elemental evaluations are compared

with those of ENDF/B-IV in Fig. 14. Over ouch cf the

energy range the present evaluation is t 15% lower cnan

that of EHDF/B-IV. This is probably not a significant dif-

ference. The uncertainties in both evaluations are at

least as large as this difference due to the very uncertain

knowledge of the Ni(n;2n) process (see below).

The

This reaction has a Q - -12.203 MeV. 57N1 has a half

life of 36 hours and decays via electron capture and H+

emission (73). Most reported measurements have Involved

counting annihilation gammas and there are no particular

problems associated with measurement of the reaction

cross section via this technique.

Measurements have been made over the entire range

from threshold to 20 MeV with a concentration of values in

the range 14-15 MeV. There are obvious discrepancies in

several of the data sets. The available data were divided

into two categories. One included those sets which ap-

peared reasonably consistent in magnitude and in the

-34-

energy dependence of tiie excitation function. In this

category are Included the data of Presrwood and Bayhurst

(74), Paulsen and Liskien (75), Bornsan et al. (76),

Clover and tfeigoid (77), Rayburn (78), Cross et al. (7»),

Bradlitc and Fink (80), Barrall et al. (81), Fink and

Wen-deh-lu (82), Paul and Clarke (S3), Strain and Ross

(84) and Temperly (85). The second category consisted of

data sets Which were examined but rejected because of

apparent inconsistencies with data in the first category.

Selection and rejection of data sets were subjective and

based on consideration of normalisation, energy depend-

ence and experimental factors which govern credibility.

Included In the second category were the data of Rayburn

(86), Jeronyiao et al. (87), Preiss and Fink (88), Purser

and Titterton (89), Csikei (9U) and Csikai and Peto (91).

Three data sets (Refs. 74-7b) cover essentially the en-

tire range from threshold to 20 MeV. The data of

Prc\itwootl and Bayhurst (74) appear consistently high

while that of Borman et al. (76) are consistently low

when compared with the data of Paulsen and Liskien (75).

The data of Paulsen and Liskien was the most influential

In this evaluation. The present evaluation is compared

with the category one data base in Fig. 15.

The l^iinj^n1.)^ Reaction,

There is apparently no experimental data available

on this reaction. Estimates at 14 MeV based on statis-

tical theory, N-Z systematics, empirical formulae and

data from neighboring nuclei are often used and three

evaluations of this sort have been reported. L. Jekl

(92) gives a value of 359 nb. and Body and Csikai (93)

reported a value of 408 nib. at 14 MeV. Pearlstein (94)

computed o _ , at three energies and for a fissionn,«n

neutron spectrum with the following results:

-35-

E n (eV)

13 .i14.115.1fission spect.

We use the values of Pearlstein

a , (nb)

1562954090.034

for 13.1, 14.1 and

15.1 MeV, then assume that o , , • 600 ab at 20 MeV.

The qualitative rational for this choice is that the

(n;2nf) cross section for 58Ni is * 50% larger at 20

MeV than at 15 MeV and the Q-values differ by only •»-

0.8 MeV.

B. The (n;3n*) Reaction

All of the contributing reaction Q-values are nega-64tive and of large magnitude (the smallest is Ni -

-16.501 MeV). Moreover, the reaction thresholds for the

prominent Isotopes Ni and Ni are above 20.0 KeV.

Therefore this process was not incorporated in the pres-

ent evaluation.

C. The (n;p) Reaction

The present evaluation constructs the elenental

(n;p) cross section from the Ni(n;j>), Ni(n;p) and

Ni(n;p) components. Two possible additional contribu-

tions are the Ni(n;p) and Ni(n;p) coriponents. Both

of the latter were ignored due to snail isotopic abun-

dance and lack of experimental data. These omissions

should have only a small effect upon the elemental cross

sections. The derivation of the Isotopic components is

discussed in detail in the subsequent paragraphs. The

results are graphically summarized and compared with

ENDF/B-IV in Fig. 16. The present elemental evaluation

is slightly larger than that of ENDF/B-IV (% 5%) and

does not show as much structure. The uncertainty asso-

ciated with the evaluation is estimated to be - 10% or

20 mb, whichever Is larger, to energies of 14 MeV. The

-3b-

The agreement with the prior fci>H>F/tt-lV values is gener-

ally consistent with this accuracy estimate excepting

those regions where tNOF/ii-IV shows considerable struc-

ture (see discussion below;.

The i O u p l ^ C o Jteact ion_

The Q-value of this reaction is +U.3V!> MeV.

Various levels in Co are populates. The laost coraaonly

discussed of these is the 9.1i hour isomeric state at

0.0249 keV and the ground state vhich oecays via g+

emission* and electron capture to levels in Fe up to an

excitation of I.b7 MeV (95). The reaction is veil

suited to study via activation techniques. The evalua-

tion is inclusive of contributions fran isoneric and

ground states.

This reaction is widely employee in reactor dosi-

netry (96,97) because of the low "effective" threshold and

because of the convenience of gaca&a counting. Consequent-

ly, there is not only a wealth of experiitental data avail-

able, but also a number of evaluations (e.g.. Kefs. 96-99).

The present evaluation gave primary attention to the ex-

perimental values. Because of the volune of data avail-

able, it was decideu to be more selective than might

otherwise be the case. The oata seiecteo cet the criteria

of being reasonably consistent with the average of all

data sets. Greater weight was given to data sets which

covered a wide energy range anu exhibited reasonable

energy dependence. The compilation of Lisfcien and Paulsen

was utilized to deduce the general shape of the crass

section between 1 and 20 MeV (1UU). This compilation

includes most work through 19b7. between 1967 and the

present, there have been several measurements as reported

in CINDA (101). The two nost significant new data sets

are from the wozk of Paulsen and Widera (99) and from Smith

and Meadows (102).

-'7-

The «iata sets which nost strongly influenced the

present evaluation are plotted In Fij,s. 17 and la.

They are those of Saith and Meadows (102)v Paulsen and

Mldera (99), Meadows and tthalen 1103), Debertin ana

Koesle(104) and Barry (1U5). Other data sets were

either rejected because they deviated too far froit the

average or vere given less veight because they provided

no new information or vere iu nargiual agreement with

the cajority of previous values. This was particularly

true for data In the 14-15 MeV region where an inclu-

sion of all available data would not substantially con-

tribute to the evaluation. These OMissions were judged

to have little effect on the evaluation. A curve was

constructed through the selected data sets and the eval-

uated cross sections were derived fro* the curve.

For £ < 1 HeV, only the data fro* Ssith and Meadous

(102) and froB integral reactor Measurements sited light

on the cross section. The integral data has been distilled

and evaluated by HcElroy sod co-workers (9b,97) and leads

to -*- 3 x 1U~" barn for E^ t> 0.5 KeV. The Integral aeasure-

•ents give no details of the excitation function, KcKlroy

and co-workers have assuned tiiat the Ki(n;p> Co cross

section Is a constant fraction of the total crosa section

In this region. The data of Salth and Meadows extends down

to 0.44 HeV. The two lowest energy points at 0.44 and O.W

MeV have broad resolution and large errors* However, these

data are consistent with an average cross section of t 2.8

x 10 barn. This is in good agreenent with the general

trend of the McElroy et al. results In this region mo we

assume that the cross section is approximately a constant

of 2.8 x lO""6 barn for LR - U.1-.65 HeV. There M y be

structure in this region but there is not enough inferaa-

-38-

tlon available to determine its nature. From U.l.5 MeV

to 1 MeV, a smooth curve vas drawn through the data of

Smith and Meadows. This data indicates a lower "effec-

tive" threshold than previously assureu (e.g., see Kefs.

9fe,97).

In tiie region t « 1.0-0.0 MeV, the evaluation was

primarily influenced by the data of Paulsen and Uidera

(99), Smith and Meauovs (102), Meadows and Whaien (103)

and Barry (1U3). The data of Temperly in the region

3-3. S MeV is in reasonable agreement with the primary set

in overall piagnitude, hut does not exhibit a sinilar

energy dependence (8i>). The same can be salu for the

data of Conzalez et al. (1Kb; and Van ioef (107). The

data of ivakai et al. in consistent with the prirary

set, but is of poor resolution and has larf.e errors (lUi>).

The data pf Konijn and Lauber (Io9) deserves particular

attention because of the influence it apparently had on

tiie evaluation by liresesti et al. (V8) and the LNUF/B-IV

evaluation. These data exhibit large fluctuations in the

region 'l.b-i.H MeV vtiile the average energy dependence is

in reasonable agreement with the present evaluation.

Snith and Meadows (102) measured the cross section with

better resolution ami observed sor.u structure but the

fluctuations were not nearly as larp.e as observed by

Konijn and Lauber. This discrepancy renains unresolved.

He have accepted the data of Smith ant. Meadows in prefer-

ence to that of Konijn and Lauber in this evaluation.

Kron b-b MeV, the uata of Pauisen and Wicera (99),

harry (105), i)ebertin anu Koesle (104) are in reasonable

apreer.ent and adequately define the cross section. The

data of barry seens consistently higher tlian that of

Paulsen and Widera, but the results apree within the

stated error limits. The region free, tt-13 MeV Is devoid

of data, so ve have estirtateii the shape of the cross

-39-

section with a curve which interpolates in a smooch

manner.

1'he magnlttuie of the cross section ana its energy

dependence in the region 13-10 MeV is based on the work

of l'aulsen and hidera (V9) and Harry (lob). We have

taken cognizance of the multitude of data points in the

vicinity of 14 MeV. Much of these data consists of

single-energy measurements with large error bars. Un-

fortunately, there are discrepancies ol as mich as a

factor of 10 between several of these data sets. The

data of Temperly (US) provide six data points in this

region which exhibit a reasonable energy dependence, but

otherwise are systematically higher than the data of

Paulsen and Widera and of tfarry.

For the region 10-20 MeV, only the cata of Borraan

et al. (110,111) and of Jeronyro et al. (87) are avail-

able. The data of Jeronyeo et al. gives cross sections

which appear far too sxaall aiiu were not considered in

the evaluation. The data of uorman et al. are consider-

ably higher than that of Paulsen aim Widera (9V) ana

liarry (105). We have enuloyeti the general energy de-

pendence of the data of liortnan et al. in this evalua-

tion, but normalized to the results of Paulsen and Widera

and of liarry.

The resultant evaluated curve ana the data which

most strongly influence*! the present evaluation are

shown in Figs. 17 and lb.

Jt

The Ni(n;p) reaction produces Cite active daughter

^ C o . The (Rvalue for this reaction is -2.040 MeV.

There are two prominent activities in Co. The ground

state has a half life of 5.24 years and generates the

1.17 and 1.33 MeV gacxia rays familiar to users of

-40-

gaisma-ray detectors. The 58$. 6 keV exciteti state of Vo

is an isoner with T..^ " 1O.35 min. The isoner cross

section ratio o /a is of interest in nuclear structurem g

studies. For taost applications (dosinetry, heating and

damage) the total cross section is Important. This can

be measured by waiting for all isomeric activity to die

and then measuring the 5.24 year ground state activity.

Measurements have been cade of the isoner cross

section ratio. Paulsen and Kidera (V9) obtained a value

of 0.53 * 0.07 barns at £ R - tt.19 KeV and 0.52 ± 0.0b

barns at 14.0 MeV. A raeasurecent by Vrasad and Sarkar

(121) yields a value of 0.025 i O.UUb barns for the

10.35 rain lsor.er excitation cross section at h - 14.bn

MeV. Assuming an isorcer ratio of "»• 0.5 it would seen

that this value is too small by more than a factor of

two.

Measurements by Allan (116,120) and March and

Morton (118) v-ere made using photographic eculslons.

The emulsion measurements for E * 14 MeV indicate thatn

protons froo the (n;p) reaction correspond to a nuclear

temperature of ^ 1 MeV.

Experimental measurements define the cross section

reasonably well In the energy region K * 5.O-19 MeV.

At lower energies (E - 2-Xb MeV), there is a conspic-

uous absence of microscopic data.

We have relied on the evaluation of Slum and

McElroy for E -2-7 MeV (92). The lower-energy cross

sections were deduced by unfolding activation data froc

various reactor spectra. Their evaluation agrees well

with some of the microscopic data available at E » 5.67

MeV. Data from Liskten and Paulsen (112,113,114,115)

cover the energy range £ * 5.6-19 MeV quite thoroughly.

We have relied heavily on these data since no other

measurements cover as wide an energy range. The avail-

able data base indicated an "S-shape" structure in the-41-

region 10-12 KeV. No physical justification for such a

"bump-dip" coula he identified, therefore, the- present

evaluation assur.es a sRootio energy dependence rather

similar to the naxlnun in tie Ui(n,p)~* Co reaction.

The naxioitia spread of the Neasurrts values iron the eval-

uation in this region la - 2 standard deviations. The

usual array of i 14 MeV single .>ata points is available.

The data from Allan (lib), LevkovsKij et al. (117),

March and Morton (118) ana Storey et al. (114) are in

reasonable agreement with the work of Liskien anti

Paulsen, Measurements at -- J*i MeV by Allan (12U) and

Croa6 et al. (7y) yieicieu values which appear Coo large.

The present evaluation in conpared with proninent

data sets in Fif.. 19.

This reaction produces Co which has a 1.63-hour

half life and enits a- and Y-ray.s. Measurements of this

cross section should not be particularly forbiddinp ex-

cept for the low abundance of I<i in natural nickel.

In any event, the experimental data are United.

Van Loef (107) has neasured the (n,p) cross section

at 3.3 t 0.2 KeV ana obtained the value 3 * 1.5 vi>.

•Jiere are various fission spectrun and pile measurements

viilch were not used In this evaluation. The only renaln-

ing data are at E "v 14 MeV. All of these aeasurenents

are via activation. Blosser and haniiley (122) report

o • 91 mb at 14 MeV. Cross et al. reported a value ofnp ^

1U3 ± 10 id> at 14.5 MeV (7V) and later at 14 MeV measured

a value of S3 tab (123). Levkovskij et al. report a value

of 98 i lo nib for E n - li MeV (117). Valter et al.

(124) report a value of bb nb at 14 MeV. These data are

insufficient to define the shape of the (n;p) excitation

function. However, we note Cuat tiie Q value of this re-

action Is -0.5 MeV and differs by only % 0.9 HeV from the

Lit L O

ij-value for Ni(n;p) Co. Neglecting matters such as

conpetition fron octier decay channels, we constructed

and "evaluated" cross section curve which Is qualita-

tlvely like the ;«i(n;p) curve but noraalizeu to pass

through the Van Loef point at i.i MeV anu the available

14 MeV data. We accepted the suggested value of Sti tab

Cor 14 MeV given by Pal et al. (125) in generating this

curve. The evaluate*, cross section is shown the curve

in Fig. 20.

The 2Ni(njp2 fto Reaction_

The Ni(n;p> reaction leans to Co which has a

13.9 min. ground state half life. There is also a 1.31

rain, isoner. The only available information on the

(n;p) cross section is at £ i 14 MeV where there are

several measured values. The activation rceasurer.ents are

by Levkovskij et al. (117) (21 ± 3 mb at 14 MeV), Cross

et al. (123,125) (24 ± 6 Kb at 13 MeV and 39 cib at 14 MeV)

and Valter et al, (124) (22 mb at 14 MeV). The measure-

ments by J. t. Strain (S4) (10b mL at 14 MeV) and Preiss

and Fink (88) (2.0 t C.5 «b> for the l.M min. isor.er and

3.3 i 0.02 nb for the 13.9 Bin. ground state at 14.» MeV)

sees discrepant. We assure a total (n,p) cross section

at 14 MeV which is an average of values fron Refs. 117,

123,125, namely 26 ni>, and reject the values frop. Kefs.

B4 and 88. Kor conparison, we have the theoretical value

from Gardner and Kosenblun (12b) of 39 nb at 14 MeV which

is in reasonable agreement with our choice. Since the

fragmentary evidence indicates this reaction is sirilar

to that in other nickel isotopes and the natural abundance

is small, the process was not considered in the evaluation.

1). The (n;a) Reaction

All isotopes of nickel can contribute to this process

at energies of a few MeV. however, the experimental infortna-

-43-

Cion is very fragmentary and apparently lirtited to58... t»0,,. , 62... 62,... . , , , ,

Ni, Ni and M . f.i has a low eleciental abun-

dance and was icnored in the present evaluation shown

in Fir.. 21 • The cross sections of the present evalua-

tion are 25-JOi snaller than those of ENDF-IV and ap-

proach threshold in a different manner. Moreover, the

present evaluation may be too large if some of the

theoretical-systematic estimates given below are correct.

These are large discrepancies but can be expected in view

of the marginal data base available to both evaluations.

The uncertainties are disturbing in view of the wide use

of high-nickel alloys in radiation environments giving

rise to materials-damage problems.

This reaction has a ((-value of +2.B9 MeV. The prod-

uct nucleus, Fe decays lOUi by electron capture to the

ground state of Hi. There is insufficient energy avail-

able to reach any excited states of Mn, consequently the

2.4 year half-life decay (73) produces only X-rays. The

large positive ({-value and the relatively large number of

accessible states in Fe virtually Insure that the reac-

tion cross section will be significant and the resultant

a-particle spectra complex. Therefore, accurate measure-

ments of the reaction cross section, inclusive of all

final states in Fe are very difficult to make.

In principle, It should be possible to utilize acti-

vation and low-energy photon (K -v 6.5 keV) detection

techniques to measure the electron capture X—rays. Ap-

parently this has not been done. The United available

data for this reaction deal with direct detection of the

alpha particles.

Weitman et al. have measured the yield of helium

produced by irradiation of natural nickel samples (127).

For a fission spectrun most of the helium production is

-44-

hH 55due to the Ni(n;ot) Fe reaction. Mass spectrographic

techniques were used to detect the helium. The objec-

tive of the measurement was to study swelling effects.

The authors calculated on "effective" microscopic cross

section for E » 1 MeV of 4.S x IV" barn. No errorsn

are quoted for this result, but it must be kept in mind

that this derived value is dependent upon the shape of

the cross section excitation function in the region of

the fission neutrons and this function is essentially

unknown.

Several measurements have been made of the a

spectra for 14-15 MeV neutron bombardment of Ki.

These measurements were not able to distinguish alpha

particles from (n;n',a) and (n;p',a) reactions. Slinn

and Robson measured the cross section for excitation of

the ground state of Fe and deduced the value 1.0 t

0.3 nb at £ - 15.7 MeV (128). Spira and Robson made

similar but more detailed measurements at E « 14.6 MeVn

(129). They deduced a cross section of 1.4 ± 0.4 rob

for excitation of the ground state of Fe and 4.4 ±

1.0 mb for excitation of the 1.332 + 1.412 MeV excited

states of Fe. In addition, they estimate a cross

section of 7.b ± 2.0 tub for production of a particles

with E > 14.5 MeV (corresponding roughly to the excita-

tlon of levels in Fe up to 3 MeV). In this work, the

contributions from higher-energy states were neglected

as the authors were explicitly interested in the excita-

tion of discrete low-lying levels in order to study

certain aspects of nuclear structure theory. This limi-

tation makes the data of little value for applications.

Seebeck and Herman have made direct-particle detec-

tion measurements on the Ni(n;o) Fe reaction at 14.0

MeV (13U). Their apparatus was designed to have a

greater sensitivity to low-energy alpha particles than

-45-

the measurements described above. Various techniques

were employed to discriminate aj-.ainst noise ami to re-

ject background. In addition, they oeasureo the cross

27 24section for the Al(n;a) Na reaction and obtained a

value of 0. 119 i U.ulU barn which agrees well with re-

suits from activation experiments. For the M(n;u) Fe

reaction, they deduce a cross section of 0.113 • 0.016

barn after correcting the data for the J Ni(n;n',a) reac-

tion.

The results described above more or less exhaust the

available data on the reaction, so we turned to theory for

guidance in generating an evaluated curve. Gardner ami

Yu-Wen Yu conducted a study on the basic trends in (n;a)

reaction cross sections for Z » 6 - 30 nuclei (131).

Statistical calculations were used to predict the relative

(n;a) reaction cross sections for 14.5 MeV neutrons and an

empirical equation was developed to predict the absolute

cross sections. Comparison was made with measured values

wherever possible. No data were available for the58 55

Ni(n;a) Fe reactions, but the value calculated by these

authors is 0.25b barns at 14.5 MeV. Buetner et al. carried

out statistical calculations for various threshold-reaction

cross sections including the i«'i(n;a) Fe reaction (132).

The excitation function which they generated increases

nearly linearly from approximately zero at "v 5.0 MeV to ">>

0.37 b a m at £ 14 MeV. Between 14-10 MeV the cross sec-

tion levels off and begins to decrease. The shape of the

excitation is similar to that of the 9Co(n;a) Mn reaction

for which considerable data are available (100). Such

qualitative comparisons are a last resort since they can be

so readily influenced by other factors such as 0-value and

behavior of other decay-channels from the compound nucleus.

The available theoretical information may not be very

convincing. However, one fact in common is that these

-46-

calculations indicate a larger cross section than one

deduces from the data of beebeck anu iiorronn (130).

In iraking tlie present evaluation, it was decided

to rely on the available li.ita, sparse as they are, in

order to deduce the magnitude of the cross section.

The data of Weltman et al. provide a point at •*• 1 MeV

(127). The cross section nay be non-zero at lower

energies and possibly even significant for thermal

neutrons, but lacking, data, we assumeu that it decreases

linearly to approximately zero below 1 MeV. At 14.0 MeV,

we chose the value of 0.113 barn reported by Seebeck and

ltorman because the agreement of their results for27 24

Al(n;a) Na with activation values is convincing (130).

The shape of the cross section at other energies was

estimated by comparison with tiie results for the

Co(n;a) Mn reaction, taking qualitatively into account

the differences in (j-values (U« +0.3 MeV for the latter

reaction). The A!i(n;a) Fe cross section is assumed to

reach a naxinium in the vicinity of 12 MeV ana to decrease

at hi flier energies where the uMi(n;2n) reaction competes

strongly.

Our evaluation Is in j-.ooii agreement with a sinilar

curve generated by Meyer (133) except below 2.U wiiere

our results are biased toward larger values by the data

of Weitrcan et al. (127). Meyer was guinea by the statis-

tical calculations of briksson (134) at I « j anu ID MeVn

in the generation of his evaluated curve. The results

are compared with the meaper experimental data in Fig. 22.

TI»e. l^iinjLoi5!1^ 3P* ^^il^L*S.*SL1iPl.*S)^Lel ReactionsThere is only one experimental measurement avail-

able, that of .Spira and Kobson (129). They measured the

14 MeV cross section for the (n;a> reaction to the ground

state of Fe and obtaineu 4.3 t 2 tub. lncludinp o's

-47-

with enerpy L. > 14.'j IteV the cross section was raiseda

to i.b ± 2 ob.

Lacking data, we resort to ttieory ami are af.nin

facetl with a confusing picture. Garuner anu Yu (131)

have used the statistical rodel to calculate the (njn)

cross section at 14.it >!eV. 'they obtain o • 90.8 mb.

iiuetner et al. (132) have performed itinilar calcula-

tions for the (n;a) and (n;nja) reactions and obtained

results rising from threshold to '»• til) mb at 14-16 MeV.

This Is reasonably consistent with the Gardner anu Yu

estinate. however, Schniut (135) questions the norr.al-

lzation used in the calculations by buetner et al. and

suggests Chat the calculations may overestimate the

cross sections by a fact of *»• 7. If so, the estimates

of Buetner et al. are siiiilar to the single measured

value of Spira and Kobson (129). There obviously Is a

large uncertainty in these cross sections. This evalu-

ation accepts the theoretical estimates of Kefs. (131)

and (132) as they appear to be raore consistent with Che

magnitudes encountered in the Ni(n;u) processes. The

possible error of nearly an order of magnitude is ep>-

phasized. It nay amount to as much as *»» 20 nib at 14

MeV in the elemental cross section.

l h£ ^Jiiiniar^Fe Reaction_

The daughter Fe has a 44.0 day half life and two

microscopic measurements have been reported. Levkovskij

et al. (117) report a value of 17 ± 4 mb at 14.8 MeV

while Yu and Gardner (.136) report a value of 22 ± 3 mb

at 14.1 MeV. Gardner and Yu (131) have also computed

the (n;a) cross section at 14 MeV uslr.p a semi-empirical

formula (prior to measurement) and obtain 20.b mb in

good agreement with experiment. The above indicates

that, in view of the isotopic abundance, this cross sec-

tion will make a negligible contribution to the evalua-

tion and thus it was omitted.

E. The (n;a.n*) Reaction

The lowest threshold for this reaction is 0.401 MeV

( Ni). There is some very fragmentary information

available as outlined in the discussion of (n;a) processes.

The present evaluation includes a (n;a,n*) component

estimated from the Ni component alone as illustrated in

Pig. 23. The uncertainties in this estimate may be very

large (50 to IQ'JZ). The neutron emission spectrum is

assumed to be a soft "temperature" distribution of the form

used for the (n;2n) process. There is no comparable

ENDF/B-IV component.

fr". The (n;p,n*) anti (n;ri) Reactions

Thresholds for (n;n,p'+p,n') reactions are all high,it

above 1 8.0 MeV. The present evaluation is based entirely

upon contributions from Ni and Ni,estimated as out-

lined in the subsequent sections. Contributions from the

remaining Isotopes should be small as the abundance Is a

few percent or less and the thresholds are generally above

t> 10.0 MeV. The resulting isocopic and elemental evaluated

cross sections are outlined and compared with that of

ENDF/B-1V in Fip,. 24. The present evaluation is ouch

larger than that of ENDF/B-IV ana it may still be too

small as the very fragmentary information about the Ni

contribution may have resulted in a small estimate. Meas-

urements which led to the present evaluation may have in-

cluded erroneous (n;d) contributions. However, this would

likely be a small perturbation, both evaluations are un-

certain by rather large amounts, but probably much less

than the discrepancy between the present work and that of

ENDF/B-IV. The neutron emission spectrum was assumed to

be a soft "temperature" distribution of the form used for

the (n;2n') process. This Is only a very qualitative

estimate and gives no consideration to the differences

between spectra from the (n;n',p) and (n;p,n*) processes.

-49-

Such distinctions are not warranted in view of the

qualitative nature of the estimate.

The (n;d) reaction was estimated following a method

analogous to that described above. It consisted of only

Ni and Ni contributions. The available information

is very marginal and the present evaluation, shown in

Fig. 25, must be considered little nore than qualitative.

However, the cross sections are small and should have

little effect for most applications. There is no compar-

able ENDF/B-IV (n;u) file.

ihf. i8NiiniI\l.£+E.ILli5Z.c£ £nd_ f^ilniMi^Co ReactionsCO CO """" ~ ~ ~ " ""*

The Ni(n;d) Co reaction has a t^-value of -5.962

MeV while the breakup reactions 58Ni(n;n',p+p,n')57Co

have a higher (J-value of -ti.177 MeV. Weak binding and

barrier penetration considerations are responsible for

the fact that deuteron emission does not compete strongly

with breakup. In all instances, Co is the final prod-

uct nucleus. Co decays with a half life of 272 days to

Fe via electron capture. Consequently, activation

techniques can be utilized to measure the cross sectiono , , ,, The fraction due to deuteron emission can-non ,p+p,n +dnot be distinguished from the breakup fraction by this

method. There is a source of error in activation measure-

ments if no correction is made for the M(n;2n) Ni

(c.frf

make.

(c.frf) Co contributions. This correction is not hard to

The distinction between the Nl(n;n',p)57Co and

Ni(n;p,n') Co reaction is one of reaction dynamics and

should really be looked upon as separate exit channels fcr59decay of the compound nucleus Ni. The difference in

dynamics leads to differences in the neutron and proton

energy spectra which may have important consequences

-50-

In so far as applications are concerned. In tiie absence

of measurements the decay fractions for these channels

Is determined by compound-nucleus calculations. A few

calculations of this nature have been made for 14 MeV

neutrons, but the results leave much to be tiesirea.

We first consider the available data fror. activa-

tion studies. The results of barrall et al. (til).

Glover and Uelgold (77), Fink and Lu (82), Temperly (85),

Cross et al. (79), Cross and Clarke (137) and nranlitt

and Fink (80) are reasonably consistent. The activation

data of Purser and Titterton (8V) and Jeronymo et al.

(87) yield cross sections which are rcuch snalier. With

the exception of the data of Jeronymo et al., the above

measurements are all in the region 13-15 MeV.

There have been various measurements involving de-

tection of the charged reaction products. Many of

these utilized nuclear emulsion techniques, i.'ithout

exception, the cross sections derived fron these oeas-

urenents are low. Included in this group is the work

of Alvar (138), Allan (116,120), Kumabe and Fink (139)

and Glover and Purser (140). The data point of Allan

(116) was included in the evaluation because it came

closest to the activation values. The rest were re-

jected. Statistical calculation of the (n,d) reactionCO

on Hi by Lu and Fink (141) indicates a cross section

of 0.01 barn at E « 14.4 MeV. Uebertin and Koeslen

measured the deuteron spectrum for this reaction at 22

MeV and deduced a cross section of U.0235 ± 0.0U4 barn

including contributions from transitions up to ^ b MeV

excitation In the final nucleus Co (104). Statisti-

cal calculations by Buetner et al. (132) indicate a

cross section of t< O.U06 barn for h - 14.1 MeV.n

This sparse experimental and theoretical evidence is

-51-

sufficient to conclude tliat the (n;il) contribution is

a snail perturbation to the breakup components. Our

evaluation is based costly on qualitative estimates

with the results shown in Fig. 26.

Since the (n,d) contribution is snail, the activa-

tion data is essentially due to the (n;n,p+p.n') com-

ponents. Ke selected a value of 0.55 barn at 14.i MeV

as being representative of the experimental data. The

data set of Jeronyno et al. (t>7), while apparently dis-

crepant in normalization, is the only one which covers

the energy range 12-20 MeV, A curve was cirawn

through the data of Jeronymo et al. and then renorcsalized

by a factor of 3.i3 so that the curve would pass through

the selected 14.5 MeV value of U.5"J> bam. The shape of

the excitation function near threshold retrains a Matter

of speculation.

The statistical calculations of the (n;n{p) and

(n;p,n') contributions by Lu and Fink yielded a value of

2.5 at 14 MeV for the ratio a , fo , (141). The be-n,n .p n p nhavior at other energies is unknown. However, the present

evaluation approximates this spectrum with a single

evaporation distribution following the procedures used

for the (n;2nr) reaction. In Che absence of definitive

experimental results this estimate nust be considered

qualitative. The above evaluation and respective oata

base are illustrated in Fig. 27.

l h £ l°l'ilnil[il5lc£ and l°i«i(ninl,p+p_,n'JL^Co KeacitlonsThere is very little information available on these

two reactions. Colli and lori (142) pleasured the oiffer-

ential cross section for the (n;d) reaction at an angle

of 140 deg. (28* opening angle) and E - 14 MeV. For

the ground state transition they obtain — « 1.9 (+102)

-52-

mb/sr. The ground state group is strongest, but from

the appearance of the deuteron spectrum, there are un-

resolved levels corresponding to excitations up to 3

MeV. It is estimated that ~ for H^ £ 3 MeV

(E, > 4 MeV) is -v A mb/sr. It Is difficult to esCi-d•ate the integrated cross section of the basis of the

limited data. Assuming isotropy we obtain a , *»• 50 mb.56 55 n

There is evidence based on Fe(n;d) Mn angular distri-

bution Measurements by Colli et al. (143) that the

assumption of Isotropy is poor since the distributions

exhibit the characteristic forward peaking of the direct

pickup mechanisn. Thus, a . "*- 50 ab is almost certainly

an overestimate.

Data on the (n;n',p) reaction have been deduced by

peeling off the (n;p) contribution from nuclear emul-

sion measurements. Chatterjee (144) reviewed the 14

MeV data on (n;p) and (n;p,x) reactions as of 19b4.

There are apparently no newer results. The values re-

ported by Chatterjee are: a - 60 * 12 BL (from<v n*«P

Allan (120)), * 6i> mb (fron March ana Morton (lib) and

59 ± 9 nib (from Allan (116)). There is also a 15e

differential scattering value of -£• , £ 25.9 ± 5.2 mba.t n;n p

(from Colli (145)). Calculations by liuetner et al.

(132) of the (n;n',p)cross section for E - 14-16 MeV

show that it increases rapidly from 12 eb at 14 MeV to

t> 120 mb at 16 MeV. If tills is true, then the experi-

mental data must be very uncertain in this region.

With the above evidence, evaluation must be a

speculative and qualitative. We assume a 14 MeV (n;d)

cross section value of 30 mb and the shape of the sanecu

reaction in Ni, adjusted to the correct threshold. We

follow the same procedure for the (n;n'»P+P»i>>) reaction

using a 14 MeV normalization of 65 mb. These are rough-53-

estimates which nay be In error by factors of 2 to 5.

However, the effects on application are probably snail

as the cross sections are not larp.c- ana the isotopic

contribution is small.

G. (n;t) Reaction

The thresholds for this reaction in both the promi-

nent Isotopes are above 11.0 MeV. The cross sections

should be smaller than those of the (n;d) reaction

(already small). Essentially no experimental informa-

tion is available. Therefore, this process was omitted

in the present evaluation.

H. (n;2p) and fa;3lle) Reactions

Both of these processes have relatively lov thresh-

olds in Ni(t< 6.5 MeV). They are experimentally essen-

tially unknown and are probably similar to the (n;d)

cross section, (I.e., snail). Therefore, they were also

omitted.

I. (n;2p.n')» (n;p.2n*) and (n;p.a) Reactions

The first two of these have thresholds of t> 15.0

MeV. The lowest (n;p,a) threshold is £ 6.5 MeV. Little

is known about any of these processes and the cross sec-

tions are expected to be small. Therefore, they are not

included in the present evaluation.

J. Photon Production

The photon-production evaluated cross sections were

a composite of three contributions: 1) from neutron

capture, 2) from (n;n',Y) reactions, and 3) and fro*

high (> 4.0 MeV) neutrons aj per the following.

Ph£tm»_Production

The spectrum of capture gamma-rays at themal

neutron energy was taken from Ref. 146. The spectrum

was assumed not to vary with incident neutron energy.

While this assumption is obviously incorrect, no better

prescription is known. The gamma-ray multiplicity was

assumed to vary with incident neutron energy according

-54-

to the relationship:

M(En) - M(Th)*(En

where M(E ) Is the multiplicity at incident energy £n»

M(Th) Is the multiplicity at tliennal neutron energy

and Q Is the Q-value of die reaction.

Photon Production from tiie (n,n'fY) Reactions for En< 4. HeV

As outlined in Section V.3.A, discrete excitation

functions are given for (n;n*,Y) reactions for levels up

to 3.628 HeV. Several of the "states" are mixtures or

combinations of levels fron Hi and Ni which could

not be resolved experimentally. Direct measurements of

photon production are reported in Refs. 147,148 and 149,

Only Ref. 149 reports data for incident energies less

than 4 MeV. The Raima-ray production cross sections from

1 to 4 MeV reported in Ref. 149 presented the data in .25

MeV bins from .75 to 2 MeV and in .5 MeV bins for photon

energies - 2 MeV. In order to conserve energy between

the excitation functions for neutron inelastic scattering

and photon production for incident energies less than 4

MeV, level schemes and branching ratios were adopted for

5 8N1 and ^ N i from data provided in Refs. 23 and 150.

Because some levels could not be resolved experimentally

the adopted level schemes and disintegration nodes are

sonewhat artificial. The assumed structure data are

presented in Figs. 28 and 29 which can be compared with

Fig. 4. As a check against the experimental data, the

total photon production cross section at the upper end of

this energy range (i.e., 4 MeV) was compared with the

measured values reported in Ref. 149. It was found that

the line spectra obtained as described here agreed

within experimental error with the measurement.

-53-

_Photon_Prqduct^qn .Cross. jSectioiis_and_S[>e£tra_4_s_0_-

E - 20 MeVn

The experimental data reported in Refs. 147,148

and 149 are in substantial agreement where they over-

lap. Since Ref. 149 covered the entire energy range

the values for the cross section and spectra are based

on the data of that reference, liecause of a low energy

cut-off at 0.75 MeV, two lower groups were added from

0.25 to 0.5 MeV and from 0.5 to 0.75 MeV with a value of

0.13 barns for the first of these and 0.26 barns for the

second.

£omparison_with KNUF/Ji^IV MAT 1190_

The aain difference between this evaluation and

that of MAT ll'JO is in the energy range froc; 1 to k

MeV incident neutron energy. The ENDF/B-IV data are based

on Ref. 149 from 1 to 20 MeV while the data presented

here are based on the same reference but frost 4 to 20

MeV. The reconciliation of inelastic scattering func-

tions and photon production data from 1 to 4 MeV described

above was not done in the KNDF/B evaluation.

VI. CONCLUDING REMARK

The total neutron cross sections of elemental nickel

were determined at intervals of a keV fron 0.25 to 5.0 MeV.

The experimental values confirm the e^erpy-averajred magni-

tudes of previously reported high resolution measurements

at lover energies and give new definition in the few-MeV

range. The differential elastic neutron scattering cross

sections of nickel were measured from a 300 keV to 4.0 MeV

with sufficient resolution to portray intermediate fluc-

tuating structure. The cross sections for the inelastic

neutron excitation of eight states to energies of 2.ti MeV

were determined for incident neutron energies up to 4.C

MeV. The experimental results were described reasonably

-56-

well by an optical-statistical model including correc-

tions for resonance width fluctuation ami correlation

effects in compound-nucleus processes. The latter

correction factors were significant and the interpre-

tation was limited by uncertainties in their calculation.

Contributions due to direct collective excitations were

estimated by calculation and found to be snail. They

could not be identifier in the present experimental

results obtained at energies of - 4.U MeV.

The present experimental ana calculational results

together with those reported in the literature, were

used to construct a comprehensive evaluated neutronic

file in the ENWformat. This evaluateo file extended

from 0.1 to 20.(1 MeV and was extrapolated to thermal

energies using the values previously defineu in

KNDF/B-IV. The present evaluation and that of LNDF/tt-lV

are substantively different in certain areas.

-57-

Ki.Fi.KhM,I.S

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-63-

Table 1

aOptical Model Parameters

Vb - 50.80 MeV, R* - 1.198 F, Ay - G.bb F

WC - 9.25 MeV, Re - 1.204 F A - 0.484 F

Vd - 8.0 MeVso

a) These parameter values are identical Co Chose ofRef. 20. Their use in the present work involvescompound-nucleus correcCions as described in Chetext.

b) Saxon form.

c) Sacon derivative form.

d) Thomas Spin - orbit form.

e) Radii are expressed in form R"R • A .

-64-

Table 2

Excited "Levels" Contributing to Discrete

Inelastic Neutron Excitation

Cross Sections

Level E (KeV)

1.172

1.333

1.454

2.158

2.2U6

2.459

2.506

2.625

2.775

2.960

3.270

3.628

Eth(MeV)

1.192

1.355

1.479

2.195

2.324

2.500

2.548

2.670

2.822

3.010

3.325

3.6&9

1

2

3

4

5

6

7

a9

10

11

12

-65-

Table 3

Sumcary of (n;X) Reaction Thresholds (in HeV)

Reaction

<n;2n')

Cn;3n»)

(n;p)

(n;p,nf)

(n;d)

(n;t)

<2;2p)

(n;3He)

(n:a)

(n;a,nf)

(n;2p,n)

(n;p,2n')

(n;p,o)

58Hi

12.415

22.S62

0

8.319

b.036

11.265

6.O71

6.599

0

6.319

14.451

19.895

6.430

6°Ni

11.579

20.731

2.074

9.692

7.430

11.703

10.488

9.33K

0

6.401

17.186

20.329

9.367

b2Ni

10.770

18.717

4.511

11.302

9.041

11.580

14.460

12.375

0.442

7.136

2.022

20.790

10.502

-66-

FICURK CAPTIONS

Fig. 1 Total and elastic scattering cross sections of elenental

nickel. The present experimental total cross sections are

indicated by a solid curve (below l.i MeV) and circular data

point? (above 1.6 MeV). The angle-integrated elastic scat-

tering cross sections are indicated by square data points.

The dotted line indicates the evaluated total neutron cross

section described in Sec. V of the text.

(Neg. No. llb-235?)

Fig. 2 Differential elastic scattering cross sections of

elemental nickel. The present experimental results, averaged

over 30 keV resolution increments, are Indicated by circular

data points. The curves indicate the results of fitting

Legendre polynonial series to the Measured values.

(Hep,. No. 116-2360)

Fig. 3 Comparisons of selected differential elastic scattering cross

sections of the present work with previously reported values

and vlth the results of •oriel calculations. The present ex-

perinental values are Indicated by circular data points;

those of Ref. 17 by D , Ref. lo by A , Kef. 19 by + , Kef. 20

by X , Kef. 21 by O , Kef. 22 by • , Ref. 24 by I« and Kef. 26

by X . The indicated incident neutron energies are those of

the present results (in MeV). Some of the previously reported

values nay Aitier In incident energy by 5-1U percent. The

results of model calculations described in Sec. IV of the text

are Indicated by curves.

(Neg. No. 116-2470)

Fig. 4 Excited structure of 5BNi, ^fci and 6<£Ni. Previously reported

values, as suonarlzeu In the Nuclear Uat« Sheets (23), ere

shown for each of the isotopes. The results of the present

experiments are noted by the boxes at the right of the diagram

where the width of the boxes qualitatively indicates the ex-

perimental energy definition.

(Neg. No. 116-2164)

-67-

Fiftc b Inelastic neutron excitation cross sections of nickel. The

corresponding excitation energies (in MeV) and contributing

Isotopes are noted. The present experimental results are

indicated by solid data points. Other (n;n*) and (n;njY)

experimental results are referenced as follows: A »21,4~»

30, X -24, S> •IS, t -29, X -25, Z - 31 and Y - 2b. The

solid curve indicates Che evaluation described in Sec. V. of

the text. The results of statistical model calculations are

noted by the dotted curves and, when Inclusive of direct-

reaction contributions, by dashed curves.

(Neg. No. 116-2705)

Fig. 6 Comparison of Measured and calculated total neutron cross

sections of nickel.

(Neg. Ho. llto-27Ub)

Fig. 7 Comparison of Measured and calculated differential cross

sections for the elastic scattering of 3.5 MeV neutrons from

nickel. The measured values are indicated by data points.

The calculated results are noted by curves obtained using

the Indicated values of the overlap parameter, 0.

(Neg. No. 116-2707)

Fig. tt Comparison of the present evaluated nickel total neutron

cross sections with those given in EKDF/B-IV.

(Nep>. Ho. 116-2329)

Fig. 9 Comparison of the present evaluated elastic neutron scattering

cross sections of nickel with those given in ENDF/B-IV.

(Neg. No. 116-2710)

Fip.10 Evaluated elastic scattering distributions normalized to a

constant elastic scattering cross section of one barn.

(Itep. No. 116-2712)

Fig.11 Some comparisons of evaluated discrete inelastic neutron ex-

citation cross sections. The present evaluation is indicated

by solid curves ana that of ENDF/B-IV by dashed lines.

(Nep.. No. 116-2713)

Fig.12 Evaluated inelastic neutron scattering cross sections. The

results of the present evaluation are indicated by solid

curves. In addition the total inelastic cross section given

-68-

by ENDF/B-IV Is noted.

(Nep.. No. 126-2711)

Fig.13 Comparison of evaluated radiative capture cross sections of

nickel.

(Net;. No. 116-2709)

Fig.14 Evaluated (n;2n*) cross sections of nickel. The isotopic and

"NAT" values are from Che present work. The ENDF/B-IV values

for the natural element are also indicated.

(Hep,. No. 116-2704)

Fip.15 The (n;2n') cross sections of Ni. The experimental values

are from Kefs. 75-U4 and the smooth curve is ti.e present

Isotopic evaluation.

(Keg. No. 116-2191)

Fig.16 Comparison of tUe present evaluated (n;p) cross sections with

those given in ENDF/B-IV.

(Keg. Ko. 116-2703)5fi

Fig.17 The (n;p) cross sections of Ni below 6.0 MeV. The experi-

mental values are discussed in Sec. V of the text and the

curve indicates the present evaluation,

(teg. Mo. 116-2190)CO

Kip.18 The (n;p) cross sections of Ki over the entire energy range

of the evaluation. The experimental points are discussed in

Sec. V of the text. The curve indicates the present evaluated

results.

(Neg. No. 116-21U9)

Fig.19 The (n;p) cross sections of Ni. The experimental results

are discussed in Sec. V of Che text. The curve is Che present

evaluation.

(Nep.. No. 116-2393)

Fig.20 The (n;p) cross sections of ° Wl. The notation is Identical

to that of Fig. 19.

(Neg. No. 116-2394)

Fig.21 Comparison of the present evaluated (n;a) cross sections with

those given in ENDF/B-IV.

(Neg. No. 116-2702)

-69-

Vii;.22 .'leasurrii and evaluated (n;u) cross section of Ni.

(Nep. Mo. llb-2207)

Fij-,.23 Evaluated (n;nja+a,n'> cross sections of nickel.

(Nep.. No. Ilfc-2o9y)

Fip.24 Comparison of evaluated (n;n",p+p,n') cross sections of

nickel.

(Neg. No. 116-2701)

Fig.25 Evaluated (n;d) cross sections of nickel.

(Me|>. No. llb-2700)

Fif>.2to Evaluated (n,d) cross sections of Mi.

(Net;. No. 116-2209)

Fig.27 Measured and evaluated (njn'p+p.n1) cross sections of Ni.

(Nep. No. 116-22UU)

Fif.2tf Level scheme of Ni used In the ganna-ray production evalua-

tion.

(Nef,. No. 116-7516)

Fig.29 Level scheme of Ni used in the parana-ray production evalua-

tion.

(Nep,. No. 116-7517)

-70-

APPENDIX

NUMERICAL EVALUATED DATA FILE IN THE ENDF/B FORMAT

-A-

c u. -

am xm <c »r » aj<s r- tore »

j »

z in

(Tt 2 —

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2.t6000*3.i:4100*

3I61.100*4 .79000*5.4'inOO*2 .60600*l.OUOOO-O.OOQOO*5.94154*1.24300*2.o?Q00*4 ,30800*6.&3Q00*8,7'JOOO*9.66P0O*5.94154*1.29200*2.25700*5,?3Q00*2,33000*3.01000*3.29U00*3,33000*3.94000*4.74000*4.96000*5.15000*5.63000*5,69000*7.13U00*2,80620*1,00000-

04450144413444

4^44444445014444441333A444444444445

0.00000*5,81<326*6,t)Q800-1,00000*7,50000"0.00000*5.00000-5,00000-5,00000-0,00000*5,00000-1.500JU*1,50000*1,50000*1,50000*5,00000-1.5000U*1,50000*1.50000*1.50J0U+1.500UO*5,00000-2,64700-l.OOOJO*6.5J0U0-O.OQOOO*S.OOOiJG-5.000110-5.000UO-5.000UO-5 ,CO0l)0-5,bOOOO-0,00000*5,00000-1,50000*1,50000*1,30000*1.50000*1,50000*5.000UG-1,50000*l.SOOiiu*5,00000-1,50000*5,00000-1,5000b*1,50000*3,97000-1,00000+

5555

121314141515

0cli

100

1 1.1819C* 41 1.40219* 31 3,30210* 30 11 6,23000- 1o e.20000- i0 1,06000* 0J 6.33UO0- 1U 7,20000- 11 9,00000* 00 1,44000* UU 3.57000* 00 1,31000* 00 2,03000* 00 4,76000* U1 1.29000* 01 0•j 1

1 00 01 2,50210* 31 6.52140+ 21 7.91400+ 11 3,92430+ 21 3.12140* 21 6,92140* 20 11 fc.OlQOO- 10 6.34000- 10 6,23000- 1C 1,90000* 00 6,20000- 10 6,40000- 11 9,00000- 1J 1,27000+ 00 1.90000+ 01 1.05000* 00 9,60000- 11 1,66000* U0 9,20000- 10 6,90000- 12 05 1

16222 a91102

33

1023

102

1.16170+1,40000*3.30000*

2.30000-2.20000-4.60000-3,30000-1.20000-8,40000*8.40000-2.57000*7.10000-1,43000*3,76000*6,90000-

2.50000*6.50000*7,70000*3.90000+3.10000*6.9CCO0*

1.00000-3.40000-2.8000C-7,00000-2,20000-2.40000-3.00000-2.70000-7.00000-4,50000-3,601)00-1,06000*3.2UOO0-2.90000-

908

1734

11711

5933

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1 00 20 184 2.14000* 03 2.14Q00* 03 2.14000* 00 722 6.00000- 11 6.00000- 11 6.00000- 12 6.00000- 11 6.00000- 10 6.00000- 11 6.00000- 1n l.GOOOO* 01 6.00000- 1U 6.00000- 10 1.00000* 01 6.00000- 10 11 00 20 363 2.14000* 02 2.14000* 01 2.14000* 02 2.43000* 02 2.14000* 02 2.14000* 00 843 6.00000- 12 6.00000- 12 6,00000- 11 1.20000* 01 6.00000- 11 6.00000- 11 6.00000- 11 1.00000* 01 1.20000* U1 6,00000- 11 6,00000- 10 6,00000- 11 6.00000- 11 6.00000- 10 1

l o

0.00000-o.oooor-iO.nOOOG'

000303000

120.00000* 0O.flOOCO* 0o.oconc* oO.OFOOO* 0o.ncooo* o0.00000* Cn.ooooo* o0.00000* 00.00000* 00.00001* o0.00000* CO.CPOOO* 0

0

c06

O.OCOOO* 0P.OUCOO* 00,00000* 00.OOOOO* 0O.TOOOO* 0O.IM'OOP* 0

140,00000* COaCCOOO* 0

c,ocono+ oO.GOOOO* 00.0300C+ 00,00000* 0P,0(,000* 00.00000* 0

o.noooc* oO.ObQOO* 0O.OL'OOO* 00,00000* 0O.onGOQ* 00.0UOOO+ 0

00

2628

28 145126 145128 1.45128 145128 1«5128 145128 145126 145l28 145128 1451

1 00 0

26 215128 215128 215128 2l5l2e 215126 215128 215128 215128 215126 215128 215128 215128 215128 215128 215128 215128 215128 215128 215128 215128 215128 215128 215128 215128 215128 215128 215128 215128 215128 215128 215128 215128 215128 215128 215128 215128 215128 215126 215128 215128 215128 215126 215128 215128 215128 215128 215128 2151

60616263646566676869707172737475767779798081826564856687686990919293949596979899

1001C11021031041051P61071081P911C111112113114115116117118119

-A-2-

0.U3000*6.13958*4,60000*3,d5000*5.3ri000*9.35U00*6,13953*7,60000+2,60640*1,00000-O.uOOOO*6.33782+1.38000+3.32000*6,33782+9,52000+

0 6.50000-1 0.C0000+3 5,00000-4 5.0000U-4 5,00000-4 5.UO30U-1 0.00000+4 5,0P00ii-4 1.40000-5 l.UCOOO*o 7.5<juoa-1 O.OOOOO*4 5,00030-4 5,00030-

O.OOOOC*

101 1.70?10+1 2,52140+1 1,02140+I t,2b210*

i 1,75600+25101 ii. 02140 +1 <i, 52140 +0

003 1,70000*2 2,50000*2 1.00000*3 2.25000*12 1.75000*C1002 6,00000+2 9,50000*

224

3 2.14000* 02 2.14000* 02 2.14000* 03 2.14000* 00 62 6.00000- 10 11 00 20 122 2.14000* 02 2.14000* 0

60

04

O.rncOO* 00.01)000+ 0O.r'UOCO* 0O.0COOC* 0

1000p2001

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3 1,50OQ0* 0 7,16000+ 0 6.18000* 0 1.00000* 0 0,0000"* G

0.00000+ ii2.SJ000+ 10.00000+ C

4l.COOOO- 5l.COOOO- 24.48205- 21,05684- 12.49196- 15,07596- 11.38552+ o3.2o699+ 07.7D338+ C1.61642* 14.28J02+ 11.(0991+ 22.16484+ 25.10458+ 29.94738+ 21.29155+ 31.29201+ 31.29245+ ?1.7622<+ i2.25480+ 32.25631+ 32,25685+ 3

2.25802* 32.26022* 33.43410* 34.20081* 35.52782+ 35.52931+ 35.52985+ 35.53032+ 35.53101+ 35,54488+ 36,63353+ 36.63954+ 36.89001* 36.S9046* 36.69147* 38.09744+ 3

0.00000*5.81826*0,00010*

1.54136*1.23943*9.95200+

GGG

36

8.69263*3.36*364*5.15/44*6.C1B59+7.92497*7,65670+7.79-303*7.7H46 +7.53*65+

6,85466*

6.5R936+6,53948*6.1856U*

5,77058*5.76200*5.77213+5.77367*5.77543+».32657 +3.91428+2,526/1*2.52513*2.51297*2.52069+2.52197+2,50846*1,36066*1,36159*1,36236*1.35231+1,35486+4.08794-

2 1,00000- 4I 2,53'JGO- 2u 5,96561- 20 1.4J666- 1) 3,31683- 10 7.82091- 10 1.84413+ 00 4.34836+ C'1 1.02532+ 1U 2.41765+ 10 v,70070* 1C 1,22199* 2u 2.&6143+ 2l» 6,17654+ 20 1,29104+ 30 1.291/9+ 3J 1,29214+ 30 1,29266+ 30 2,2'J226+ 30 2.25551* 30 2.25653+ 30 2,25701+ 30 2.25747+ 30 2,25649+ 3SI 2,27907+ 33 3,77751+ 3J 4.57079+ 30 5,52352+ 30 5.52953* 50 5,53liJl* 30 3.53047* 3J >,53143* 30 5,86555+ 30 6,66930+ 30 6,8-3979+ 30 6,89015+ 30 6.89068+ 30 6,89216+ 31 3,41520* 3

09903

5.40526* 11.06757* 19.66070* 06.99970+ 06.56901* 0O.26S20* 08.10475* 07,96347* 07.90035* n7,83644* U7,77190* 07,69007* C7.51756* 07.20132* o6.59i)76* C6,58961* a6.56942* 06.569U7* G5,76245*5.77bb5+ 05,76245+ 05,75590* 05.75V7Q* P5,77515* 05.76C65* 04.47216* 03,51196* fi2,52570* 02,52425* 02,51620* C2,52025* P2,52129+ o2.19632* 01.36200* 01,37145* ft1.35549* l'1.35297* G1,35498*

G03

25261,00000- 33,36743- 27.94022- 21.67226- 14.41470- 11.04096* 02,45454* C5.78767* 01.36470* 13.21789* 17.58763* 11.62648* 23,63514* 26,22097* 21.29134* 31.29166* 31.29230* 31.29342* 32.25376* 32.25596* 32.25668* 32.25715* 32.25769* 32.25919* 32.34554* 34.01358* 35.02767* 35.52899* 35.52978* 35.53015* 35,53069* 35.53218* 36.88784* 36.88932* 36.83985* 36.69031* 36,89100* 36.90005* 3

0

c2526

22.24026* 11.02679* 19.4062C* 06.S351C+ 06,46184+ 06,21627* 06,0587b* 07,95240+ 07.B7770+ 07.P1620+ 07,74574* 07,64579* 07,42403* 07.C1173* 06,59026+ 06.5P965* 06,56906* 06,58675* 05,7«H3* 05.77703+ o5.7773U+ 05.7794fl+ 05.76716+ 05.77565* 05.7C741* 04.17C74+ 03,36576* 02,52597* 02,51204* 02,50879* 02.52103* B2.52111+ 01,36079* 01.36043* 01.36235+ 01.35084+ 01.35559+ 0

28 215126 215128 215126 215128 215126 215128 215128 215126 215128 215126 215126 215128 21512e 215128 215128 2151

2 00333

1.34975+ 01.52*74- 1 8,61219* 3-7,50730- 3

262828282628 328 328 328 326 328 326 326 328 326 326 326 328 328 328 328 328 328 328 328 328 328 326 328 326 328 3282626282*328 328 328 328 328 328 328 328 3

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3-6.6b963-3-o.iCtiao-4-1.27509+4-2.11620*4-2.50210*4-3.5212J*4-3.62V20+4-3.77610*4-3.63700+4-3.63590*4-4.45960+4-4,13470+4-2.77279*4-1.49600+4 9,3c400-4 1,42340+4 3,82:JUO-4 O.709U0-4 6.534U0-4 6.173C0-4 5,75130-4 5,90600-4 4.2871)0-4 3.97300-4 4,37nuO-4 6.101C9-4 3.95400-4 2.412C0-4 2.958U0-4 1.27100-< s.i4ooa-4-^.06000-4-6,70000-4-6,86000-4-J.7bliiO-4-1,i5aoo-4-1,06700-4-1,13-bUO-4-3,983&9-4-;.59564-4-7.16701-4-6.50350-4-6.96900-4-9,13610-4-fj,32H09-4-8,18210-4-1.13fc66+4-2.86358*4-2.11391*4-3.66<Jt4-4 6.313S5-4 5.54177-4 5,36370-4 5,40327-4 3,35265-4 1,12483-4 7,19950-4 7,60250-4 1.29427-4 2.8C530-

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