NO. TATÜA-R-9QA7-F

TITLE

Development of improved procedures for evaluationof neutron cross sections for reactor neutron dosimetry

FINAL PKPORT FOR THE PERIOD

1977-10-O1 - 1980-02-29

AUTHOR(S)

Herbert Vonach

INSTITUTE

Institute für Radiumforschung und KernphysikViennaAustria

INTERKATIONAL ATOMIC ENERGY AGENCY

DATE June 1980

/7

Final Report on Research Contract 2047/R1XRB

Evaluation of the Cross-Sections for the Reactions19F(n,2n)18F, 31P-(H",P)31Sl', 93Mb(n,n')33mNb and103Rh(n,n')103mRh.

Institut für Radiumforschung und Kernphysik der

Universität Wien

Chief Scientific Investigator Prof. Dr. H. Vonach

March 1979 - May 1980

Table of Contents

AbstractI. IntroductionII. Use of theoretically calculated cross-sections in the

evaluations11.1. General Procedure11.2. Details on the model calculationIII.The 19F(n,2n) reaction1I1.1. Experimental data base111.2. Evaluation and results thereof

31IV. The P(n,p) reactionIV.1. Experimental data baseIV. 2. Statistical model calculationsIV.3. Evaluation and results thereofV. The 93Nb (n,n')93mNb reactionV.1. Experimental data baseV. 2. Statistical model calculationsV.3. Evaluation and results thereofVI. The 103Hh (m1 )103mBh reactionVI.1. Experimental data baseVI.2. Statistical model calculationsVI.3. Evaluation and results thereofVII. Derivation of the relative correlation matrices

- 13 -and relative excitation functions or measurement« relative to

abstract

The cross-sections for the four important neutron dosimetry

reactions 19F(n,2n)18F, 31P(n,p)31Si, 93Nb(n,n»)93mNb and103Rh(n,n*)1O3mRh were evaluated in the neutron energy range

from threshold to 20 MeV.

For the F(n,2n) reaction the evaluation could be based entirely

on experimental data; for the reactions P(n,p) Si and103Rh (n,n')103inRh large gaps in the experimental excitation

functions and large discrepancies between the existing data

made it necessary to supplement the experimental data by cross-

section calculations and to give about equal weight to the ex-

perimental and calculated cross-sections. For the Nb(n,n') "1Nb

reaction the evaluation had to be based entirely on

the theoretically calculated cross-sections.

All data sets were critically reviewed and obviously erroneous

data sets were disregarded. If- necessary, the data were re-

normalized in order to take into account adjustments in

corresponding standard cross-sections and decay schemes.

The cross-section calculations were performed using the statisti-

cal model of nuclear reactions allowing for precompound

processes in the first reaction step and errors of the cal-

culated cross-sections were estimated from their sensitivity

to the various input parameters'.

Cross-section values were evaluated for energy groups between

0.1 MeV and 1 MeV wide, the width depending on both the slope

of the excitation functions and the density of the available

data.

For each evaluated cross-section also an uncertainty (on a

1a confidence level) was derived taking into account

the errors given by the experimentalists, the general con-

sistency of the experimental data and the estimated errors

of the theoretically calculated cross-sections. In addition

relative correlation matrices were derived for each evaluated

excitation function describing the correlations between the

uncertainties of the cross-sections at different energies .

The correlations between the cross-section uncertainties

for different reactions were found to be negligible.

The results of this evaluation as well as those of Ref. 1/

will be combined with the ENDF/B-V doslmetry file into an

international neutron dosimetry file by the nuclear data section

of the IAEA.

J

nI« Introduction

In order to satisfy the increasing demand for neutron

cross-section evaluations providing also information on the

uncertainties of the evaluated data and their correlations,

the authors recently developed procedures for deriving values

of the diagonal and, at least approximately, also of the non-

diagonal elements of the covariance matrices of the evaluated

cross-sections and applied these procedures to four neutron

threshold reactions chosen for their importance in fast

neutron dosimetry /1/.

In continuation of this work four more threshold reactions,

the 19P(n,2n)18F, 31P(n,p)31Si, 93Nb(n,n')93mNb and

Rh(n,n') Rh reactions,were evaluated using the general

procedures outlined in Reference 1 •

The reactionswere chosen in close cooperation with the

nuclear data section of the IAEA. Just as in the case of the

reactions.evaluated in Ref. 1 reactions not yet contained in

the ENDF/B dosimetry file, but also requested as important

for dosimetry purposes especially by European users, were

selected. ,,••'• - • • ' ' ' 19 18,For the reaction F(n,2n) F the experimental data were

sufficient for an evaluation based exclusively on measured

cross-sections, for the other three reactions, however,

the situation was much worse and it became necessary to give

considerably more weight to theoretical cross-section

calculations than in the evaluations of Ref. 1.19Thus for th« reaction F(n,2n) th« «valuation was per-

1 - 2 -

formed exactly according to the rules described in R ef. 1,

chapter II, for the other three reactions the experimental

data were processed also as outlined in Ref. 1., however,

in addition theoretical cross-section curves were calculated

and included into the evaluation.

The uncertainties of the calculated cross-sections as

well as estimates of their correlation coefficients were

derived from calculated sensitivities of the cross-sections

to changes of the various input parameters within their admissible

limits. This whole procedure which has not yet been used in

Ref. 1 is described in detail in chapter II.

- 3 -

II. Use of theoretically calculated cross-sections in evaluations

II.1. General procedure

II.1.1. Use of statistical model calculations as independent

source of information in addition to the experimental

data base.

Already in the evaluations of Ref. 1 statistical model cal-

culations were used to fill smaller gaps in the measured

excitation function (e.g. the region of O - 2 MeV above

threshold in the Cu(n,2n) and Zr(n,2n) reactions).

In these cases, however, rather accurate cross-section measure-

ments existed over most of the energy range and therefore

the parameters used in the calculations were adjusted to fit

the known part of the excitation function and by these con-

straints a rather accurate estimate of the cross-sections

in the unmeasured region became possible. Of course in this

procedure the theoretical values are not independent of the

measured values but highly correlated with them.

This procedure is appropriate if at least a considerable part

of the excitation function is known more accurately than it

can be calculated at present considering the uncertainties of

the input parameters of nuclear reaction model calculations.

If, however, the quality of the experimental data is com-

parable or worse than that of cross-section model calculations

the quality of the evaluation will be improved considerably

if theoretically calculated cross-sections are used as a second

independent source of information. The set of calculated cross-

section values with estimated 1o uncertainties and correlation

- 4 -

coefficients B Kis added to theexperimental data and

used in the further evaluation procedure in the same way as

the latter to derive the evaluated group cross-sections

and their variances and covariances.

In this procedure the calculated cross-section

values have to be completely independent of the experimental

values, that is they have to be calculated from our best

choice of input parameters like optical model or level density

parameters without any attempt to fit them to the experimental

data. Of course cross-section data other than for the reaction

to be evaluated may and will have to be used as a guide in

these choices e.g. only such optical model parameters will in

general be admitted, which reasonably reproduce the observed

total and non-elastic cross-sections.

The uncertainties Ao(E.) and the correlation coefficients

B „ of the calculated cross-section values can be estimatednnK ,from the sensitivity of calculated cross-sections on the

various input parameters and the accuracy with which these .

parameters are known.

If we assume that the calculated cross-section values °caic(Ej)

are functions of n input parameters p^ • • • Pn which are

known with uncertainties Ap1 ... Apn, the uncertainty

i8

'calc1 iI ..P1) t(Üf

i (E ) \ca^-c * .Ap lOpn

Fn/

1/2

- 5 -

whereby the quantities 5 - A p will in general be derived from"m

the changes in cross-sections if all parameters except p are

kept fixed and only the parameter p in question is changed

by the estimated amount Apm from its most probable value.

Likewise the covariances <Ao , (S.).Aa , (E.,)> of the cal-

culated values have to be estimated. The uncertainties of the

calculated cross-section values for different energies

are certainly correlated to a rather high degree due to the

very fact that most parameter changes result in an increase

or decrease of,the whole excitation function.

For any two energies E. and E., this covariance can be estimated

as: - - '--•

<&'calc(Ei)A<Icalc<Ei'»=

'calc'V

With the results of equation(H.'l)and(lL.Z)the relative correlation

coefficient B.

as

(II.3)

.UIl

, .., (see Ref. 1, p. 10) can be calculated

Bnn' • ;kk '

<Agoalc(Ei}'

k - k' « index characterizing the particular set of cal-

culated cross-sections.

By averaging over all pairs of energies E. and E.,, one

finally gets the quantity B ^ characterizing the average

degree of correlation between the cross-section values at

- 6 -

different energies.

Of course a considerable amount of information is lost

in this averaging procedure, but if the calculated cross-

sections are evaluated together with the experimental ones foe which

only such average correlation coefficients B . can be esti-

mated the more detailed information available on the covariance

matrix of the calculated cross-sections can not yet be utilized

at present.

In cases where the theoretical cross-sections are the only

available source of information of course the values S- ,calcare identical with the evaluated group cross-sections and the

covariance matrix is given by equ II.2).

Correlations between the calculated cross-sections for different

reactions and between the calculated cross-sections and the

measured cross-sections will in most cases be very small and

will be neglected in all cases.

The described method of evaluation using calculated cross-

sections as a completely independent additional source of

information will be used whenever the experimental data base

is insufficient especially in the following cases.

a) If no reliable experimental data exist.

b) if only one data set is available; as discussed in Ref.1

(p. 133) especially for the case of the Zn(n,p) reaction

taking just one data.set may lead to a dangerous underesti-

mation of the uncertainties of the evaluated group cross-

sections .

c) if the uncertainties of all experimental values are about

equal or larger than the uncertainties achievable in cross-

section calculations (20 - 30%).

- 7 -

In the present work the above procedure was used for the93Nb(n,n')93inNb evaluation (case a).

II. 1.2. Use'of statistical model calculations in conjunction

with an accurate cross-section value at one energy

In many cases there are no experimental data in a

large energy region (e.g. 1O - 2O MeV) except for

one small energy range usually 14 - 15 MeV where rather

good cross-section measurements are available, which are far more

accurate than the theoretical values computed according to Il.1.1.

In such cases thei ciost accurate information on the excitation

function can be obtained by jointly exploiting the theoretical

and experimental information in the following way:

1) An evaluated cross-section and its uncertainty are calculated

according to the standard procedures for the one accurately

measured energy group.

2) A tL- *;. tical excitation function is calculated using cur best

a priorichoice of input parameters as described in the pre-

ceding section.

3) Due to its rather large uncertainties this excitation

function will in general not exactly agree with the experimen-

tal group cross section derived in step 1. Thus the input

parameters will be slightly modified (within their known un-

certainties) in 'order to fit the theoretical curve to the one

measured group cross-section and that excitation function is

used as evaluated cross-section. Of course this procedure is

not unique as in general the necessary adjustment can be

achieved by variation:, of a number of different parameters

- 22 -

- 8 -

resulting in a number of slightly different excitation

functions .

However, as yet we found that in all cases investigated

up to now, these adjustments were very small and con-

sequently the choice which parameter to adjust was not

critical.

4) For calculation of the variances and covariances of the

evaluated group cross-sections, however, we must not

use equation (II.1 ) -(H. 3) , but have to take into

account the constraints on the parameter space imposed

by the condition that we do know an accurate cross-section

value at one energy. This is dene approximately in the

following way:

Input data to the calculation are the one known group

cross-section °exD(E.«)

the matrix of uncertainties

its uncertainty Aaexp(E4) and

'-

according to IZ. 1.1.

Within the limits of - Ap1 any linear combination of

variations of the parameters is permissible, provided the

resulting uncertainty A°caic(E.j) does not exceed Aoexp (*••})•

A band representing the permissible uncertainty range for

the excitation function is therefore generated by displacing

the excitation function by applying parameter variation Apnj) at E. byand replacing it to within the limits of

simultaneously applying a fraction of a second parameter

variation

- 9 -

(II.4) °optimum calc*Ei

ApP

Ap

condition: £ < 1 and

(II.5) - °calc

This can be done to a sufficient precision by some 1O

suitably chosen combinations n;m. As "calculated excitation

function" the center value of the generated band is given,

the uncertainty is taken equal to the width of the band.

Covariances are calculated as given by formula (II.2 ),

but taking now the combined variation of each pair n;m

as one parameter variation in the sense of formula (II.2 ):

(Apn + f*Apm) 4 Apn,

- 10 -

II.2. Details of the model calculations

All calculations were performed using the computer code STAPRE

/2/. This code serves for the computation of energy-averaged

cross-sections for particle induced nuclear reactions with <several

emitted particles and gamma-rays under the assumption of sequential

evaporation. For the first evaporation step preequilibrium particle

emission is included and treated on the basis of the exciton

model; for the equilibrium part the width fluctuation corrected

flauser-Feshbach formula is applied. For the further evaporation

steps only the usual Hauser-Feshbach formula is used. Y-competition

was accounted for from the second compound nucleus on , for the

Tfc(n,n') Tto calculations at low energies even- fro» the first compound nucleus en

Jh general, the following input parameter« are used as our best a priori choice:

a) Optical Model Parameters:

Neutrons: As all cross-sections are rather sensitive to the

choice of the neutron potential, for each case all available

potentials are investigated for their fit to total and especial-

ly non-elastic cross-section, and strength function and a choice

is then made as discussed with the individual reactions.

Protons: Becchetti-Greenlees /3/ for A>4O

a-particles: Huizenga-Igo /4/

b) Level densities: The back-shifted Fermi gas model is used,

with the parameters- of DiIg et al. /5/ assuming values of

the spin cutoff parameters corresponding to the full<

rigid body moment of inertia. In the «xciton »odel part,

the particle-hoi« stat« densities ar« calculated with a single

particle stat« density g obtained fro« th« F«rmi gas

«-parameter as g- A a. However, no pairing correction«

were used for the particle-hole state densities.

- 11 -

c) Precompound matrix element: Energy and mass dependence Is

taken according to ref. 6, the value of the constant FM is21 —1adjusted so as to give a value of approximately 5.1O s

for the transition rate from 3 to 5 exciton states at 21 MeV

according toGadioli et al. /7/.

d) Particle emission rates in preequilibrium stage /7/

e) Y-competition: For E1 radiation the energy dependence of

the y-decay width according to the giant dipole resonance

model of Axel /8/ was used. For the other multipolarities

(M1, E2, M2, E3, M3) energy independent y-strengthUfunctions

were used. An overall normalization of the y~ray trans-

mission coefficients was obtained by adjustment of the

total s-wave neutron radiation width at the neutron binding

energy to an experimental value r~.

f) Discrete levels in all residual nuclei were used up to the

highest excitation energies for which reliable spin and parity

assignments exist. Unless otherwise indicated this in -

formation wat. taken from Nuclear Data Sheets.

This general choice of parameters was used for the cases of93Nb(n, n')93mNb and 103Rh(n, n')1O3*Rh. For the 31P(n, p)

reaction, however, use was made of the extensive evaluation work

of B. Strohmaler /10/ and the parameters found to give a best

fit to all neutron induced reaction on phosphorus were used.

F - 13 -and relative excitation functions or measurements relative to

different standards were reported in one paper, the paper was

split into its two parts for further processing and correspon-

dingly there appear two entries in Tab.HI.I.for such papers

(Bormann 67, Bormann 65, Nagel 66).

Detailed examination of the above measurements resulted in

rejection of 7 measurements for the following reasons:

Picard 61 and Picard 63: identical with Picard 65

Picard 65: Relative excitation function did not allow ad-

equate renormalization due to strongly deviating

shape«.

Strohal 64: Shape of excitation function disagrees strongly

with all other data.

Nagel 65: superseded by Nagel 66

Shiokawa 68: deviates by more than 6 standard deviations from

average

Rayburn 61: deviates by ybout 8 standard deviations from

average

The cross section data from all accepted measurements are

summarized in Table XZI.2. The table lists all cross section

measurements in order of increasing neutron energy. For

each data point the following quantities are listed:

the average neutron energy and the energy spread (half-width

at half maximum) of the neutrons used for the measurement, the

uncertainty of the average neutron energy, the cross section

values and errors as given by the authors, an indication

which renormalization procedures have been applied to both

cross sections and errors according to general'rules of R«f. 1,

section II and finally the renormalized cross section values

and errors. The renormaiized cross section values are also

shown in Fig. IIX.1. The uncertainties in the average neutron

- 14 -

energy E centr. not given in most papers were either estimated

from the experimental conditions as described in the papers

or in a few cases obtained by communicating with the authors.

As indicated in Table III.2. cross sections and errors were

partly renonnalized according to the general procedures out-

lined in Ref.1. section XI. If not specially indicated in

Tab. III.2., the following standards were taken:

a) Decay scheme as given in Table of Isotopes. As there have

been no significant improvements to these data for many

years, no corrections had to be applied for such changes.

b) Reference cross sections for the reactions Fe(n,p),

^5Cu(n,2n) and 235U(n,f) from the ENDP/B-IV file.

An estimated error of 5% has been assigned to such reference

values and included in the final error of the renormalized

cross section.

In the following cases special corrections had to be

applied instead of or in addition to the procedures specified

above:

Pasquarelli 67: The systematic errors in absolute beta-counting

using fixed solid angle and rather thick samples

due to self-absorption and scattering are probably

at least 5%, therefore the total error given

in the paper seems unrealistic and was increased

to 6%.

Vonach 68: cross-section was renormalized to Al (n,o) re-

ference cross-section of 112.0-1.4 mb according

to the precision measurement of Vonach et al./28/,

which

- 15 -

appears at present more accurate than the. ENDF/B

values

Chatterjee 69 and Csikai 67: cross-section was renormalized to

Cu(n,2n) reference cross-sections from the

evaluation of Tagesen et al. /1/.

Bormann 67: Bormann gives mutually inconsistent results for

measurements with two teflon sample thicknesses.

Only the results of the measurements with the thin

sample which suffers less from scattering effects

were used. In addition his errors (only statistical)

were increased by quadratic addition of an assumed

3% error for scattering effects from the rather bulky

target construction.

5 relative excitation functions have been renormalized to the

"preliminary evaluated excitation function" (absolute data points

only, see /1/, p. 4).

The «normalization factors R and errors/4R are:

Ref.Rayburn 62

Bormann 65 A

Bormann 67 A

Vonach 68

Bormann 67 B

R.727

.886

.413

49.34

.769

(%)3.15

3.02

0.79

2.42

2.31

- 16 -

In the energy region from threshold to 12.6 MeV there is only

1 data point available, however from theoretical considerations

the general shape of the excitation function near threshold should

follow to a good approximation!

O1 (E) « const, «r (E -

6 additional points, referenced Vonach 79, have been added, by

extrapolating the low energy end of the evaluated excitation

function according to formula (III.1) , including a smooth

continuation of the errors.

- 17 -

»H O IM PJ 1-* "O 8 8 m n n n n « n S S 2 * K "*M PJ n *-i T*

t M

£ s!

S m- S•o T

§ iI P

g §

L. SSo

N M K ID w O «

i §

S iff C

. i l•; - f -

*4 «» *4

i i

- ; c ü =• 3 3 0 =

5 g

-^

I S S

S u ~ ~ =IH 5 -I U Ul

n n n n

- 31 -

- 18 -

CROSS SECTION ( 10 flBl

ro

i en

9 Q 4

(n2'"" 2m22oig OT 2 moo t. 01 oi 3Ji-ItD mm — \J0120) l" m BB 01 M OB ff) Ol 01 01 U)

PO

t i i

- 19 -

References to Table III.1. and Fig. III.1.

Paul 53: E.B. Paul and R.L. Clark, Can J. Phya. 31 (1953) 267

Ashby 58: V.J. Ashby et al., Phys. Rev. 111 (1958) 616

Brill 61: U.D. Brill et al., Soviet. Phys. Doklady 6 (1961) 24

Rayburn 61: L.A. Rayburn, Phys. Rev. 122 (1961) 168

Picard 61: J. Picard et al., J. Phys. Rad. 24 (1963) 813

Cevolani 62: M. Cevolani and S. Petralia, Nuov. Cim. 26 (1962) 1328

Rayburn 62: L.A. Rayburn, Proc. Conf. on Direct Interactions and

Nuclear Reaction Mechanisms, Padua 1962

Strohal 64: P. Strohal et al., Phys. Lett. 1O (1964) 104

Bormann 65: N. Bormann et al., Nucl. Phys. 63 (1965) 438

Nagel 65: W. Nagel and A.H.W. Aten jr., Physica 31 (1965) 1O91

Picard 65: J. Picard and C.F. Williamson, Nucl. Phys. 63(1965)673

Nagel 66: W. Nagel, Thesis, Univ. Amsterdam 1966

Bonaann 67: M. Bormann and I. Riehle, Z.f.Physik 2O7 (1967) 64

Csikai 67: J. Csikai and G. Peto, Acta Physica Hungarica 23 (1967)87

Menlove 67: H.O. Nenlove et al., Phys. Rev. 163 (1967) 13O8

Pasquarelli 67: A. Pasquarelli, Nucl. Phys. A93 (1967) 218

Shiokawa 68: T. Shiokawa et al.,.-J. Inorg. and Nucl. Che» 30(1968)1

Vonach 68: H.K. Vonach et al., Proc. Conf. Neutron Cross-Sections

and Technology, Hahington 1968, p. 885

Chatterjee 69: A. Chatterjee, Nucl. Phys. and Solid State Phys.

Symp., Roorke (India) 1969, Vol. 2, p. 117

Crumpton 69: D. Crumpton et al., J. Inorg. and Nucl. Che».31(1969)1

- 20 -

Mogharrab 72: R. Mogharrab and H. Heuert, Atomkemenergie 19

(1972) 107

Robertson 73: J.C. Robertson et al., J. Nucl. En. 27 (1973) 531

Ryves 78: T.B. Ryves, P. Kolkowski and K.J. Zieba, J. Phys. G. 4

(1978) 1783

- 21 -

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- 24 -

III»2. Evaluation and results thereof

The intermediate (column 5) and final result« (colunn 7, 8

and 9) of the evaluation procedure according to Ref. 1. ,

chapter II,step« 4 and 5 are listed in Table III.3. The final

results are sunmariied again in Table III.4.

As there is no evidence'for strong cross section fluctuations

for this reaction« the energy group size has been chosen mainly

governed by the availability of data points, up to 12.4 HeV it is

the identical repetition of the extrapolated data points, to

14 MeV the group width of .4 MeV has been chosen to ensure at

least 2 independent data sources per group, to 15 MeV there are

sufficient data to allow the reasonable minimum (due to neutron

energy spread) of .2 MeV, and finally up to 2O MeV a group width

of 1 MeV is sufficient and adequate in view of the few data and

the smooth course of the excitation function.

Fig. III.2. shows the final results and the previous

evaluation of Lapenas /9/. Above 14 MeV our values are

15% lower than Lapenas1 predictions. This is Mainly due

to the Inclusion of some recent precision measurement»

(Robertson 73, Ryves 78) not yet contained in Lapenas'

evaluation.

B B

O o 0 o n

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- 25 -

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U. B • • • p • • w« «M M v •• M * N M M M M M M M M <««MMMM(M*.*>M n»rv«o^r - — —u N ft *«(* n n M 00*4 *<Q e*«p«««(«< N«<««N«4*« ptoK«*««oo4in*« r i C M M x r ^ o ^ xK n n nn n n n nnn nrt Ani^nnn n n n n n n « f tnnnnn««» n n r a n n n r a n

* • * w ID * *« Q »«w » »»p P» <• • «4 •*• n n n •»<*«• «•«••»is.'ioooons« - 8 s? s s i :.: ES «hsR SKBSBS $..!»1(111«K& • • • • • • * « * « • « • * • » • • • « • • « • • « • « • • • • • • »•« o r. »• ax »«too-o

M x M M M N M *' » fc ü 5 S C M n » M M M N ( M < * «n nnnnnn «vnvwcn«« *

? & » o ON o ^ *• ooo ov o o-• o v n ofe^nn*» O O R M M O O O O N O O O O B M N O ooovcxn N « £»- i- N M Mixe on N O N o r v n N S V M n onrinvoSSo-« oööoo-irj-c ococ-cu u* o M SN V N O " "•» nN O N O A O M N M M J I N N isfc». Sn-ön ».n n*nod-«vv V Q M V T Ji- KW ö ö N O o o M MOM NN M N n n M . OM. O M M i i n O M M M ^ N O M n n v N M V M M t C N Ü M B11 Ul **

X -n M i§O M MN V <0 • N M «N M « ttm N K « M n nM M M N M i M N N n n n n w N O

W » N » »W» »in«»-o

a» R R *K * M n 4*K

x W

*• 9

J *5 t ? S 8 8 8 ?^ Z M M M M N N N? r

»-O

Nn

8N

rinvninn •«•«N*«»»-nnnnnn nnnnnn

N S

n n

O O O O O M• v v v v v v

SV

MMMM NNNNNNNn V V V v n

V V V V V V V V V V V V V V V V V

N VV V

L

r - 26 -

~n e

M M « n N » M M < « N X M M M f <• <• N p • M n n n n n n n nSSSSSSSSSSSSSSS

nnift vn nin -OM

S0 11

i Sen

IU HM MM »••••«•<»•< «Nnn *NMM«N«NNnriNMNiMn MN nnnn r4nnn-*Mn NM

5 Sn

M U

nnnnnn - N N K N N N N N N N N K T V NMv4 *«*4*4*«*4*4*«««*f*«**««**«*««4 «4«<*«««««««««*l«4«4«4M*4v4

S S

- 40 -

L__

i2S *

I ,I 8

i s.I &i

i Iini S

IL*

r

s a

s .K9 . N

•fc • '«

^2 I

SsS828 3J2S*

m-Kn nnp>n jo

523 8<88f

- 27 - \

- 41 -

r - 28 -

TABLE ».M, 19 F <N»2N>

EVALUATED GROUP CROSS-SECTIONS

GROUP-ENERGY X-SECTIONCMEV3 TO

11.0011.4011.6011.8012.0012.2012.4012.8013.2013.6014.0014.2014.4014.6014.8015.0016*0017.0018.0019.00

CMEV3

11.4011.6011.8012.0012.2012.4012.8013.2013.60 1 - -

14.0014.2014*4014.6014.8015.0016.0017.0018.0019.0020.00

CMB3

0.201.262.454*086*098.5012.2720.4128.8134.9040.8743.0446.0847.1051.4457.4668.7577.1983.8183.47

ERRORCMBa

0.040.160.300.50 .0.741.030.543.021*531.240.770.800.880,762.062.341.001.681.231.73

ERRORCX3

21.512*812.312.3

• 12.112.14.414.85.33.61.91.91.91.64.04.11.42.21.52.1

- 29 -

CVI- .

C

OO

LOj

CVJ

ID LA «• K» ' OJ

IfU Ol ] NOU33S SS(KP

- 43 -

r - 30 -

IV. Tho 31P(n,p)31Si reaction

IV. 1. Experimental data base

To establish the data base, a literature search has been per-

formed in two steps.

a) Two very comprehensive compilations, namely CINDA

up'to Supplement 79 (1 Oct. 1979) and the threshold reaction

compilation EANDC 95 "U" (Feb. 1974) have been used as

index to existing literature.

b) The most recent editions of some journals most likely to

contain relevant publications have also been semrhal up to March 1980.

The original papers have1 been looked up, whenever available

checking simultaneously that references cited therein were

already contained in the literature list. The most important

information on the 16 experiments found in this way is

briefly summarized in Table IV.1. Columns 1 to 7 give the

energy range of the experiment, the number of cross-section

measurements within this range, the method used to detect

either the induced activity or the particles produced in the

considered reaction, the method used to determine the neutron

flux, the first author and date of the respective paper and

the reference number used furtheron In the compilation.

In case the cross-section was measured relative to some other

cross-sections it is indicated whether this reference cross-

section had been taken from an earlier own absolute measure-

ment of the authors, in which case the measurements were also

considered as absolute measurements, as discussed in Ref.1,

II.1., Step 1.

- 31 -

Detailed examination of the above measurements resulted in

rejection of 4 measurements for the following reasons:

Allan 61: The measured proton spectra even if corrected

for (n,np) processes give only the sum of (n,p )

and (n,pn) cross-sections

Hassler 62, Prasad 71 and Pasquarelli 67:

Cross-sections deviate by 4, 14 and 1O standard

deviations (as given by the respective authors)

from the main body of the data

The cross-section data from all accepted measurements are

summarized in Table IV. 2. The table lists all cross-section

measurements in order of increasing neutron energy. For each

data point the following quantities are listed: The average

neutron energy and the energy spread (half width at half

maximum) of the neutrons used for the measurement, the un-

certainty of the average neutron energy, the cross-section

values and errors as given by the authors, an indication

which renoxmalization procedures have been applied to both

cross-sections and errors according to the general rules of f,ef. 1

section IZ and finally the »normalized cross-section values

and errors. The renormalized cross-section values are also

shown in Fig. IV. 1. In on* case (Metzger 48) where both

absolute cross-section measurements and the determination of

a relative excitation function is reported in one paper, the

paper was split into its two components for further processing

and correspondingly there appear two entries in Table iv.1. for

this paper.

- 32 -

The uncertainties in the, average neutron energy ER centr.

not given in most paper« were either estimated from the

experimental conditions.as described in the papers or in a

few cases obtained by communicating with the authors.

As indicated in Table IV.2. cross-sections and errors were

partly renormalized according to the general procedures out-

lined in Ref.1., Section II.

If not specially indicated in Tab. IV.2. the following

standards were taken:

a) Decay scheme as given in Table of Isotopes. As there have

been no changes to these data for many years no correction

had to be applied for such changes.i

b) Reference cross-sections for the reactions Fe(n,p) and2 •to"°U(n,f) from the ENDF/B-IV file. An estimated error of

5% reap. 3% has been assigned to such reference values and

included in the final error of the renormalized cross-

section.

In the following cases special corrections had to be applied

instead of or in addition to the procedures specified above:

Kantele 62: Cross-section was renormalized to Cu(n,2n)

reference cross-section from the evaluation of

Tagesen et al. /1/

Metzger 48: (absolute cross-section measurement at 30 NeV)

Cross-section is normalized to sum of H(n,ao)

and N(n,p0) cross-section. These cross-sections

do show a strong resonance structure just around

3 MeV. This fact together with the rather ill-

defined neutron energy distribution used in the

- 33 -

measurement necessitates an increase of the

assumed error of this measurement to 27%.

Morita 58, Ricamo 51, Cuzzocrea 59 and Lüscher SO:

Errors were increased by quadratically adding 5% for

systematic errors to the purely statistical errors

given by the authors.

Metzger 48: (measurement of relativ« excitation function)

Errors were increased adding 7% quadratically

to the purely statistical errors given by the

authors.

Renormalization of the relative excitation functions Metzger 48,

Lüscher 50, Ricamo 51, Morita 58, Cuzzocrea 59 and Grundl 67 hasi

been executed following the general procedure outlined in

Ref. 1 , p. 4. However one faces the special situation, that

only one absolute excitation function is available, complemented

by 6 single point measurements, mainly around 14 MeV.

Most of the relative excitation functions however cover only a

small energy range, but exhibit strong structure. By adjusting

the relative excitation functions to follow the absolute measure-

ments over the widest possible energy range, an acceptable agree-

ment can be achieved in the ranges 1.5 to 3 MeV, 3.9 to 4.9 MeV

and 5.2 to 10 MeV. Onresolvable discrepancies, leading to enlarged

uncertainties of the evaluated excitation function, remain in

the ranges 3 to 3.9 and 4.9 to 5.2 MeV.

The following renormalizatlon factors R and respective

uncertainties R have been applied:

- 34 -

Ref.

Metzger 48

Luescher 50

Rlcano 51

Morita 58

Cuzzocrea 59

Grundl 67

R

.78

.89

.31

1.05

.90

.98

AR (%)

2.0

5.0

5.0

3.0

2.0

10.0

The large uncertainty assigned to the last renormalization is due

to a slight deviation in the general shape.

- 35 -

U 8 §K . N N

M N m" » " • « "n » R v

H O Z WM N * B

I 3 < i

U

IX £ * a i •^ .t " * _

* <w • * * * * *

i l g I l i a l s

4.hz

tL

n

x

Ui UlM M «

s i :

i s

UiT

B)H

i S E

0 o n o e1 "3 * . .* B B » «

8 0. M

* *

3i

Mu g R S

- 49 -

- 36 -

COS

O.•x

C

P-

CVI

CM

tnVlH

OO

U)

CSI .

<n

OO

rs.

10

LO

CM

18U OI J MOI103S SS(KO

- 50 -

r - 37 - r

COs

CL

PL.

• • I. K-"

«D

"*".+,**•

ft*

X

}+ rvj tz

l SU Ol l HOI133S SS(KiO

- 38 -

LO

CL-N

C

-

M M-M-

-M--M-

M ". X-M • • SiIiSiSi

O+MX4O4X

*• m CM —

(flU 01 I HOI133S SS02I3

Kt

CL-X

C

- 39 -

->-

-**.*

CM

01

U)

LO

H 6'

^BlSUKM IOC«»»•u) . B

Bl! )MU.i

M 4 X e » B » « Q «

l l

IiU Ol J HOIiOBS SSO»

Ol

l l

U)

U)

- 40 -

References to table 3Y.1. and fig. IV. 1.

Metzger 48: F. Metzger, F. Alder and P. Huba, HeIv. Phys.

Acta 21 (1948) 278

Luescher 50: E. LOscher et al., HeIv. Phys. Acta 23

(1950) 561

Ricamo 51: R. Ricawo, Nuov. Cl*. 8 (1951) 383

Forbes 52: S.G. Forbe«, Phys. Rev. 88 (1952) 1309

Paul 53: E.B. Paul, R.L. Clark, Can.J. Phy». 31 (1953)267

Grundl 58: J.A. Grundl, R.L. Henkel and B.L. Perkins,

Phys. Rev. 109 (1958) 425 •

Morita 58: S. Merita, J. of Phys. Soc. Jap. 13 (1958)431

Cuzzocrea 59: P. Cuzzocrea, 6. Pappalardo and R. Ricano,

Nuov. Ci». 16 (196O) 450

Allan 61: D.L. Allan, Nucl. Phys. 24 (1961) 274

Hassler 62: F. Hassler and R.A. Peck jr., Phys. Rev. 125

(1962) 1011

Kantele 62: J. Kantele and D.G. Gardner , Nucl. Phys. 35

(1962) 353

Grl*aland 65: B. Gr!»eland, E. Kjellsby and J. Vines,

Phys. Rev. 137 (1965) 878

Grundl 67: J.A. Grundl, Nucl Sei. and Eng. 30(1967)39

Pasquarelli 67: A. Pasquarelli, Nucl. Phys. A93 (1967)218

Prasad 71: R. Prasad and D.C. Sarkar, Nuov. CM. 3A

(1971) 467

Robertson 73: J.C. Robertson et a., J. Nucl. Bn. 27(1973)531

- 41 -

N N N N N N N N N N N ( V N N h - N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N

!HUHiHHH*Hi3ttiHKHH***$

« znzn <«as o *enoee

8"

u e e o e e e e o o e f t » « e e » e « < > « e o * e e e o e o « * * * o e « « » * » 0 « o * e * * * e e e o e e

N N N f « C i n N N N f t N c t ( ( l w ( c * ( t w N N N N N N I M N N IN N N N N N N n M M Nt N M

L_

- 42 - f

"

i K NNN IS.NN K NtS, h. rofoN N N N N N N N N N N N N N N N N N N N N

; ri -.

ciX

t

EW eooo«*oooooeoooooeo*o*oooo«*oo?>oooooooooooooooooo«ooooooooo

i9 u o e o o o o o o o « o o e e o o o o e ö o e « o o o o e o o * o o o o e e o e o o o o 0 o o e o < > o

SS«

r - 56 -

L__

- 43 -

N N N N N N N N N N N N N N N N N N N N N N N N NNNNNNNNNNNNN NNNNNNNNIxN

•; r o -< n IH « « n » « •- •• •<» « N « » •< n •< n •«« »» M « x •• « M « « •« n n •<« M » MMMM«n«<H»*«»-<v«M«M

» s§I ¥

eeeee4»o*e* **««o****«o»«eee

S«

r - 57 -

- 44 -

Is

N

I V N N N I V N K N N NN N N N N N N N N NN NN NN NN N NNN

* s

.; ri 2

rnnnnnnnn-««««N-*«n«<«n-««>«

SHSS85SSSsS!HHjcu oeo«oooooooo*«o*»*oo*ooooooooo*ooo

i iiO ••••••••••« oe*

n 3ü eoeoooooooooooooooooooooooooooooooooooooooooooooooooooooooo

IgIZ"

r - 45 -

E u

•

; ri -

Ii

5

Ii!

J I I -S«« A B * ««•«««»«««« U^ A Wl»•N Z •««« mm.mm+m Ci

sstge ü

iiiii

I w N H

- 59 - l

- 46 -

IV. 2. Statistical Modal Calculation«

A* apparent fro« !able IV.2. and Ug. IV. 1. there are no

experimental data in the energy rang«« 10-14 and 15 - 2O

MeV, whereas «OM rather accurate measurements do exi«t

in the 14 - 15 NeV range.

Therefore the evaluation in the 10 - 2O MeV neutron energy

range was done by means of statistical Model calculation«

with parameter« adjusted to reproduce the weighted average

of the experimental cro««-«ection« from 14.5 to 15.5 NeV.

Table IV. 3. li«t« the input parameters»chosen. These para-

meter« are al»o«t identical with the par • chosen by

Strohmaier /10/ in the simultaneous evaluation of all

neutron-induced reactions on P and therefore well

established. The information in the discrete levels was

taken from Bndt et al. /11/ as was done in Mf. 10.

Table IV. 4. lists the admitted variations of the various in-

put parameters used for the error estimate and Table IV.5.

lists the cross-sections calculated with these perimeter

change«.

Therefrom the uncertainties of the calculated values were ob-

tained according to the procedure! described in section II.1.2,

The calculated cross-section values and their uncertainties

are given in Table IV.«.; they are also included in Table 3V.2.

- 47 -

Tabla IV.3.

!•!•t of input paraMatara uaad for tha calculation of

tha 31P(n,P)31Si racitation function.

Paranatar value

FM

DD

6OO MaV3

2OOO MV

0.50 NaV

0.75

Laval dancity paraMtar« for

"P a

A31P a

4

31Si.

A

28Al.

A

30Si.

A30AIa

A27Mg a

A

3.20 NaV '

- 2.50 NaV

3.00 NaV"1

• 1.5O NaV

3.00 NaV"1

- 1.50 NaV

2.95 NaV'1

• 4.50 NaV

3.00 NaV'1

- 3.00 NaV

2.75 NaV'1

- 4.50 NaV

2.25 NaV'1

- 4.50 MaV

- 48 -

Transmission coefficient«

n Potential obtained by coupled channel« optical Model

fit to n scattering data on 31P /1O/

p Hani Melkanoff /12/

a Ruizenga et al. /4/

- 49 -

Table IV.4.

List of parameter variations studied for deriving an error

estimate of the calculated cross-sections for the31P(n*p)31Si reaction.

Variation Mr. Variation

Constant FM for precompound matrix element

reduced from 6OO to 400 MeV3

a(31P) increased from 3.OO to 3.40 MeV-1,

simultaneously

A(31P) increased from - 1.5 to - O.6 MeV

a(31Si) increased from 3.OO to 3.40 MeV~1,

simultaneously. .31A( Si) increased from - 1.5 to - 0.6 MeV

Neutron transmission coefficients of Percy

and Buck /13/ used instead of those of

Ref. . 1O

Proton transmission coefficients of Percy /14/

used instead of those of Hani et al. /12/

- 50 -

5

IIfl1

II

in T-

T- IHm o

n «N <OO>O

W OB •» »* X» OK M * IS. i-i N. IS. OB *-• n Otnnninnto ~i

z NO ONOu nn<rn«r.««Tio<h<0N-anin<r

rt CKON-OO»NO QK NN

N •«• < n »> ID »> N o « » o» at » <o on »KJ NWi-IfJION

T^ Z WK ODNrt

NO«r N ow NO wooM Z NN NCBOB »O-CS «K OOOfli-l i-i N

-ONOB CK Ort N <tn-ON«9 OKO- - - - - - -

- 64 -

- 51 -

Table IV.6.

Final remit« of the model calculation« fitted to the

14 MeV experimental data for the 31P(n,p)31Si reaction.

ENEROY .

8.849,87

10,9011,9412,9714.0015.0316.0717.1018.1319.1620.20

X-SECTIONCMBJ

142.81148.57139.58123.01107.4093.9482.9173.6965.9959.3353.6648.81

ERRORCMBJ

17.9116.0212.6010.778.164.792.143.214.906*126.787.07

r - 52 -

IV. 3. Evaluation and results thereof

For the energy region from threshold to 1O MeV the evaluation

was based entirely on the experimental data and carried out

according to the procedures described in Ref. 1 , for the

10 - 20 MeV range the calculated values according to sections

IV.2. were used. The intermediate (Column 5) and final results

(column 7, 8 and 9)of the evaluation procedure according to chapter

II, step 4 and 5 of Ref. 1 are listed in Table IV.7.for the

experimentally covered energy range. The final results for the

whole energy range are summarized in Table IV. 8. The energy

group size was chosen as 0.2 MeV in the steeply rising part

of the excitation function from threshold to 4.8 MeV and around

1 MeV for the flatter part above that energy.

It has to be emphasised that the given group cross-sections

are only meant to be cross-section! averages over the respective

energy groups. At any particular energy the actual cross-section

may deviate significantly due to crocs-section fluctuations.

Fluctuations of the Bricson type with "periods" of about SOkeV

and considerable amplitude are to be expected especially in the

energy region below 1O MeV due to the relatively small number of

effective reaction channels contributing to the (n,p) crocs-

sections.

In Vlg.3V.2a and 2b our results are compared with the earlier

evaluations dn SAMDII-CCC1128 /15/, OKDL-DFM226 /15/ and

BMDL-78 Mat. 7821 /16/. As apparent all previous evaluations

exhibit rather strong structure in the cross-sections below

6 MeV which obviously corresponds to the structure found by

- 53 -

Cuxzocrea 59. However, if on« also .includes th* results of

other author« which did not find thi» resonance structure

(see Fig. ZV. 1.) th« discussed structure disappears to larg«

«xt«nt. Essentially th« «valuation in th« 3 - 6 H«V rang«

is largely a question of judgement between some rather dis-

crepant and old data set«. Mew measurements are therefore

urgently needed in this energy rang«. In th« r«gion froa

6 - 14 MeV we are in reasonable agreement with all peerions

evaluations. In the 14-20 HeV range our evaluation lies about

in the Middle between the older evaluations /15/ which see«

to have neglected precoBpcnnd effects and th« recent Liver-

more evaluation /16/ which apparently somewhat overestimates

these effects.

L

- 54 -

i

S 8

1g*

fi

»-

s- ee eoeeeoeooooo

N N N N N

* s

- 55 -

ZU

rS wF

fcl

Z «

Zi88

N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N nn

L_

r - 56 -

E > x

£ H

: u« TU

n n n n n n n n n n n n n n n n n n i « M n n n n n n n n i n n n n n n

- 70 -

- 57 -

S„ a• K *i- r n

i i

• • .t-fö"

I. xI )

8 .i slZ xn xt)

s•n

g S s I i

M TU

iS tt 533335315SRRRS^P: SJtCC ^SSS SRRSSRR«n nnnnnnnnnnnnnnnn nnnnn

*

|§ ^ ipsspppisHi tmt im %$un mmi #m minJ5SSSJ

SSEEJ^

- 58 -

!lZu R•

N

g S S S 8 S 2 S 2 £ £ g* • • » • • • » * o N •> N • n• n » * - r

* n oi § § i• * • •n o « o

v o o o o o» 5 o 5 o ov o o o o o•4 O O O O O

nH

i

U.

Q

iCCg

§ g* •K 8

r» x n2 « 3 B N * !fn n ix x nS 8 J ? S S

S 5 § I 2 5* * * * * *S S ? R S 8

O X H x MNQ N N N NnxO N N « n N n N (M M NSRSR R U i U U U SSRS -R-ES S S S S S

uc *njP9S ^fiäß1^ *"S SSS SB"» ^i* ^ N « M N « N xonnn » •• o » »uu SoVnn nnnnx wn Ann nv«n n* v n t« o ••»••»• ••••••• K •* <• n »i

x • •

w^ «W N N V ) **•• «f4NN W «• N CV^ O » «ONO »N»« m M n •« •* N

iig m m nn m ^ s iSSS SRR ftm ftf5 R 8 i S8888 R S 8

ü.

«4n

p SSSSS 8R8$g =5t =I u

SlSS fctg ? J t SSSS 55JRIS fc S 2 S 8••••*! +*•% o « n **** 2S5Z5 3 ^ 5 £ £

8n

S S K S K• * • * n « N • IK

- 59 -

TABLE JP*. 31 P (NfP)

EVALUATED GROUP CROSS-SECTIONS

GROUP-ENERGYCMEV]

1.401.802.002.202.402.602.803.003.203.403.603.804*004.204.404.604.805.206.007.008.OO9.5010.5011.5012.5013.5014.5015.5016.5017.5018.5019.50

TO CMEV3

1.802.002.202.402.602.80 •-3.003.203.403.603.804.004.204.404.604.805,206.007.008.009.5010.5011.5012.5013.5014.5015.5016.5017.5018.5019.5020*50

X-SECTIONCMBJ

1.5227.48010.21327.50341.04962.70561.98659.96572.24466.28471,53687.34285.941

••: 98.466101.887121.157125.035126.971141.649

; 132.566138.908143.502137.987122.101106.95991.85483.34974.36366.73860.17154.54149.743

ERRORCMB3

0.5320.8962.5213.3602.1052.7453.8336.4186,5535.0205.3444.1754.8845.9824.305 .6.3589.5567.2789.9189.0378*4948.61312.457

. 10.6918.1283*4841.4943.2404.9566.2076.8917.205

ERRORCX]

34.912.024.712.25.14.46.210.79.17.67.54.85.76.14.25.27.65.77.06.86.16.09.08.87*63.81.84.47.410.312. 614*5

- 60 -

tau oi i Holloas ssoao

- 74 -

- 61 -

(Vl

CD(Vl

(n

oo

rs

i i •__

LO

Kl

tn

co

rx

u>

LO

(Vl

J j

IffU Ol I MOI103S SSOU

- 75 -

- 62 -

V. The 93Nb(n,n')9311Nb reaction

V.1. Experimental data base

To establish the data base, a literature search has been

performed in two steps.

a) Two very comprehensive compilations, namely CINOA

up to Supplement 79 (1 Oct. 1979) and the threshold reaction

compilation EANDC 95 "U" (Feb. 1974) have been used as

index to existing literature.

b) The most recent editions of some journals most likely to

contain relevant publications have also been acarchefl up to March 1980.

The original papers have been looked up, whenever available

checking simultaneously that references cited therein were

already contained in the literature list. The most important

information on the 7 experiments found in this way is brief-

ly summarized in Table V.1. Columns 1 to 7 give the energy

range of the experiment, the number of cross-section measure-

ments within this range, the method used to detect the con-

sidered reaction, the method used to determine the neutron

flux, the first author and date of the respective paper

and the reference number used furtheron in the compilation.

Detailed examination of the above measurements resulted in

rejection of 4 measurements for the following reasons:

Morgan 67, Williams 69 and Buchanan 71:

preliminary reports on the experiments described

in full detail in Williams 75 •

- 76 -

- 63 -

Roger« 71: reported relative gamma-ray production cross-

sections differ strongly from all other measure-

ments r probably because of the much poorer

quality of the gamma spectra which are apparent

from the figure in the paper.

As indicated in Tab.V.1. the data given in all the papers93m

are not the cross-sections for formation of the Nb

isomer itself but partial y-production cross-section« from

which the isomer production cross-sections can be derived.

This was done in the following way:

Following the decay scheme of van Heerden and Mc Murray /17/

whose (n,n'Y) data have both the best energy resolution and

the highest sensitivity for detecting weak -»—transitions,

the Y-transitions with energies 656.4, 779.4 and 2123 were

assumed to be the only transitions feeding the isomeric level

from the excitation energy range below 2.5 MeV. Therefore

the sum of these 3 gamma production cross-sections plus a

(relatively small) contribution due to the direct population

of the isomeric level by inelastic neutron scattering is given

as the formation cross-section for "üb in Table V.2.

The latter contribution had been taken from the cross-section

calculation described in the next subsection. In case of

the production cross-sections for the 656.4 keV y-transition

there exists the additional difficulty that in the measure-

ments of Gtfbel et al. /18/ and Williams /19/ this gamma-

ray was not resolved from a noch more intense 653.4 keV

- 64 -

gamma transition. In these cases the observed 653.4 + 656.4

peaks were divided approximately into their two components

using the intensity ratios of van Heerden /17/ who had been

able to experimentally separate the two peaks.

The cross-sections for formation of ^Jb derived in this

way are given in Fig. V. 1. The errors given in the figure

are those calculated fron the errors given by the authors

for the corresponding ganma transitions and an assumed 25%

uncertainty for the calculated cross sections for direct popu-

lation of the isomeric level by inelastic neutron scattering.

As apparent fcom the figure there is a large discrepancy bet-

ween the data of van Heerden and Williams on the one hand

and the data point of Göbel which is about SO % higher than a

reasonable extrapolation of van Heerden's excitation curve.

This would at first sight indicate that the measurement of

Göbel et al. /18/ should be rejected. Comparison of the

spectra of Göbel with the spectra of van Heerden for

En • 2.53 MeV, however, shows that the relative Intensities

of the various gamma peaks agree rather well and that the

difference is due to a difference in the absolute

cross-section scale. In order to decide which of these scales

is most probably correct we have calculated in all three

experiments the total inelastic cross-sections .

by adding up the production cross-sections for all

gamma transitions feeding either the grotand or the isomeric

state, in Fig. V.2. these total inelastic cross-sections are

compared with those derived from direct detection of the

n- 78 -

- 65 -

inelastically scattered neutrons /20, 21/ and from sphere

transmission measurements /22, 23/. As apparent front the

figure the inelastic cross-sections derived fron GObel's data

agree well both with the results of the inelastic neutron

scattering and of the sphere transmission Measurement*,

whereas the cross-sections derived from the other (n,n'-r)

experiments are considerably lower. Thus at present the data

are extremely inclusive as which of the data sets should be

renormalized and therefore no renormalisatious could be

performed. Summarizing the experimental situation it can be

said that only in the energy range of about O.9 - 2.7 MeV

there are experimental data at all and that these data have

large errors of about - 3O% which is about as large

as the uncertainty of model calculations. Thus we decided not

to use the experimental data at all but to base the evaluation

on the cross-section calculations described in the next sub-

section only.

- 66 -

i B B B I S

FV O

i I

s § s iS Ä Ä t

U

g O g

g g i i Iz t * *

i i i i i i il i S S I S i

X X X X X X X K

H H ife fe b * feH i il» M N M N N

g ? R fe S *M M M N M O

l

L

- 67 -

—X-

-X-

-X-

.— K W IN

3Sxo+»

-Q

•X«

IO

LO

law ooi i MOU33S ssoao

l - O - 1

Cl - H - 1 O

I - >-— »

I - G>

I - M - 1 O

I - fr - 1

X O

t 4

I * * *i i 11• < O X O f r +

•••M

IW

L

- 69 -

Reference» to Tabue V.l. and Figure v.l.

Morgan 67: I.L. Morgan, Progress Report Texas Nucl. Corp.,

OBO 2791-26 (1967)

William« 69:' G.H. Williams, Wash. 1136 (1969) 2O2

Göbel 70: H. Göbel et al., Z. Physik 24O (197O) 43O

Buchanan 71:P.S. Buchanan, Progress Report Texas Nucl. Corp.,

ORO 2791-32 (1971)

Rogers 71: V.C. Rogers, Nucl. Sei. Eng. 45 (1971) 297

Van Heerden 73: I.J. van Heerden and W.R. McMurray, Z. Physik 26O

(1973) 9

William 75: G.H. William, Thesis, Univ. of Texas 1975

- 70 -

Mn ID WO M g O S <>N P Q Op n

CD NOtn >mn NIK »NM « B NM M VMM MVMMMMMMM

- 84 -

- 71 -

(D u n nnnninnininininnnnnin n2 K nnnnnnmnnnnmnnnnn

i- in in n n in » n CN w <\.

M O O O O O O O O O O O O O O O O

ULJ oo>o>o-^o-Hcv i in -Hvo-m(Nooo-cu ro IM r. r.itMo«oin*-n!NrMN(M»<-iIK r» PJ r» PI r» N •< Ci3K=I ii« MZ O Ui Z>h-

tC

x

a,*H C O O O O Q O O O O O O O O O O Cg ^ P J ^ C O ^ H J f c ^ O O O V C M ' C f J w f r ' Ca o o* r^ w »H HI •* o w to * n •« o in *-t oneu ^ o O w C M O ' - t W N f O T H f r N X J ^ w r gAC tnL-minin^TMf-jfjf-j-f'H-H-H'M^Ul

,KUJ U

H;i;i2^ p;*oii£ !i. g K K U • K: KO! U3U ZO

u£u.

Sa: o o o o o o o o o o o cO^ o o o o o o o o o o o c"a S mrv o r>to« KTCBMI

> OOO O§ 000in» N

u ki

s: LJ o o o o o o o o o o o o o o o o o

. uu«uo JB <Ü- UI J

«

3 kj ö CO Ö O O O O O O O O O O O O O

£io o S e w E S oO K U K K OKKu t; 5o a UU) u cj u

UKUUU4E UUzu) esB KmI J uiüi»•ngS^gÜSg!uSü m""° ""^S u ui ü u ü ü

<n a « t «c «uu

- 72 -

V. 2. Statistical model calculation»

Statistical model calculations were perform«} for the whole

energy range from threshold to 2O HeV. In addition to the

general description of the calculation procedure given in II. 2.

the following details of these calculations have to be mentioned.

93A. ) Nb level scheme used for the calculation

For the accuracy of the Hauser-Feshbach calculations at low

energies it is very important to use as much as possible

detailed information on the level structure, spins/ parities,

and v-branching ratios up to as high excitation energy as

possible. Thus the spectroscopic information to be used

as input for the model calculations is to be critically

discussed.

As the basis for our calculation we have chosen the level

scheme derived by van Heerden /17/ from high resolution

(n,n'Y) data. Considering the quality of the spectra and

the fact that spectra were measured at 26 incident neutron

energies between 0.7 and 2.5 MeV it seems highly improbable

that levels were missed below 2 MeV excitation energy.

Additional levels at 1.29,1.364, 1.572, 1.71, 1.775MeV found in

charged particle reaction /24/ were not included. Considering

the accuracy and energy resolution of the charged particle

spectra there is no convincing evidence that these levels

are really different from levels of similar energy found

- 73 -

in fef. 17 and there is strong evidence against the existence

of such additional levels from the fact that no corresponding

Y-transitions were found in the (n,n'y) reaction.

Thus level-energies up to an excitation energy of 2.2 MeV

and branching ratios were taken without changes from Table 2

resp. Fig. 2 of Ref.17 . Concerning the spins and parities

some of the assignments of Ref. 17 had to be changed for the

following reasons. The spin assignments of Ref.M are primari-

ly based on the comparison of the measured excitation functions

with Hauser-Feshbach calculations and do not take care of the

restrictions imposed on the spin assignments by the y-decay

characteristics of the levels. As it can safely be assumed

that all observed y-transitions are of either E1, Ml or E2 type

the maximum spin difference between any two levels connected by

y-transitions is two units for levels of equal and.one unit

for levels of opposite parity. Application of this rule to the9 3level and decay scheme of Nb leads to the following

consequences:

a) A unique spin assignment 5/2~ results for the 8O9.8 keV

level from observed decay of the 1947.4 keV level to

both the 11/2+ 978.6 keV and the 8O9.8 keV level, for the

spin of the 1947.4 keV level the assignment has to be changed

from 5/2 to 7/2+.

b) As the levels at 16O2.8, 1686.1 and 2171.1 (all

assigned as 15/2+ in ref. 17) all exhibit y-transition

to the 9/2+ ground-state their spin values have to be re-

duced to 13/2+.

- 74 -

c) As the level at 2162.2 keV decays to the 978.6 keV

11/2 level its spin assignment has to be changed from

17/2+ to

d) The observed decay of the 1914.7 keV level to the 13/2+

949.6 and 9/2+ 1O82.3 keV levels is incompatible with the

spin assignment 5/2 in Ref. 17 and the assignment has to

be changed to 9/2 or possibly 13/2 .

For all levels where the spin assignments had to be changed

by one unit the new Hauser-Peshbach cross-sections are

higher than those for the spin assignments given in Ref. 17

and also higher than the measured cross-sections. As, how-

ever, the total calculated inelastic cross-section exceeds

the measured one by about 2O% (see Table 1 of Ref. 17 ) these

discrepancies are not unreasonable; as can be seen also for

sane of the levels, for which the spin is well known from Coulomb

excitation experiments, the experimental cross-sections are

well below the calculated values. Accordingly we have for

our calculation adopted a spin value of 3/2 for the 686.8

and the 1369 keV level and 7/2 for the 1483.1, 1499.4 and

1679.6 keV levels assuming that it is more probable for the

calculated cross-sections to be higher than the measured values

than to be lower. Only in case of the 1914.7 keV level

there remains a genuine discrepancy, the observed y-production

cross-sections being much smaller than the calculated ones

for all spin values permitted by the observed gamma decay

model.

The level energies, spin and parity values and branching

ratios used in the calculations according to the above con-

- 75 -

siderations are summarized in Table V. 3. Up to the 1296.8

keV level the spin and parity values are certain. For the

higher levels it cannot be excluded that for a small fraction

of the levels the right spin values have been missed by - 1

unit and the sensitivity of the calculated cross-section to

such uncertainties is investigated in the calculations

and included in the error estimates of the calculated

values. The parities of some of the higher levels are com-

pletely unknown (see Table V.3.) and arbitrarily one value

had to be selected for the calculations which, however, are

rather insensitive to these parity choices.

- 89 -The cross-section data from all accepted measurements are

- 76 -

B.) Neutron optical potential

In order to choose optimum transmission coefficients, a series

of the usual global neutron potentials as well as several

optical potentials fitted individually to neutron scattering

data on Nb were investigated for their fit to nonelastic /17,

18, 19, 20, 21, 22, 23/ and total /25/ cross-sections up to

3 and 15 MeV, respectively. The potential given by Delaroche

et al. /26/ turned out to reproduce the experimental values

for these cross-sections best. Moreover, due to the procedure

of determining the optical potentials parameters used by the

authors of Ref. 26 good fits to the s- and p-wave neutron

strength functions and the potential scattering radius are

also warranted. A comparison of the calculated (n,2n) excitation

function and the neutron production spectrum at 14 MeV bom-

barding energy to experimental data compiled in Ref. 27

confirmed our decision.

The parameters used for the final calculations, the con-

sidered parameter variations, the results of these parameter

variations and the final model calculation result, that is

calculated cross-sections and their errors according to the

results of the parameter variations (section II.1.2.) are

listed in Tables V. 4. - 7.

- 77 -

Table V.3 . Level scheme for Nb used in the statistical

model calculations.

Level Nr. Energy Spin Parity Branching ratios

g.s.12

34

56

7

8

9

1O

11

12

1314

1516

1718

1920

O

30.4

686.1

743.7

808.4

809.8

949.6

978.6

1082.3

1296.8

1315.3

1334.3

1369

1395

1483

149O.7

1499.4

1546.0

1602.8

1665.2

1679.6

9/2

1/23/27/25/25/2

13/2

11/2

9/2

9/2

5/2

17/2

3/2

5/2

7/2

17/2

7/23/213/2

3/2

7/2

+

1OO%

1OO%

+ 1OO%

+ 1OO%

1OO%

+ 1OO%

+ 1OO%

+ 34%

66%

+ 49%

25%26%

81%

19%

+ 100%

+ * 1OO%

+ * 1OO%

- * :81%

19%

+ 100%

- * 1OO%

+ 1OO%

+ 17%

57%

19%

7%

+ 100%

+ * 19%50%31%

—•*• g.S.* 30.4

•»• g.S.•* g.S.-»• 3O.4

-»• g.S.->• g.S.

•*• g.s.•»• 743.7

•»• g.S.+ 743.7

+ 978.6

+ 743.7

-»• 808.4

+ 949.6

-f 8O9.8

-* 809.8

•*• g.S.* 8O8.4

* 949.6

-»• g.S.+ 686.8

-»• g.S.-»• 949.6

+ 978.6

-*• 1082.3

f 743.7

+• g.S.* 743.7

* 1315.3

Level Nr. Energy Spin

- 78 -

Parity Branching ratios

21

22

23

24

25

26

27

28

29

30

31

32

3334

1682.6

1686.1

1728.1191O.41914.7

1947.4

1949.6

1963. 3

20O1.92018.82117.4

2153.4

2162.2

2171.1

7/2 . +

13/2 +

3/2 +

7/2 - *

9/2 +

7/2 +

5/2 +

13/2 +

17/2 +

3/2 + *17/2 +5/215/2 +

13/2 +

28%

48%

24%

26%

41%

33%

1OO%

100%

38%

62%

44%

56%

37%

34%

29%

32%

9%

11%

48%

1OO%

1OO%

100%

100%

1OO%

7%

42%

51%

* g.S.

•*• 743.7

-y 978.6

* g.S."*" 949.6~* 978.6

-»- 1O82.3

-> g.S.

•* 949.6

-* 1082.3

* 809.8

+ 978.6

* g.S.

* 808.4* 743.7-»• g.S.-* 949.6-»• 978.6

-> 149O.7

-»• 949.6

-*• 809.8* 1490.7* 30.4

^ 978.6

-*• g.S.* 949.6

* 978. f

*)No information exist« on parity of level. Arbitrary one

half of theie level« was given positive and negative

parity, respectively.

- 79 -

Table V.4.

Table of input parameters for calculation of the Nb(n,n') 10Nb

excitation function.

Parameter

FM

DU

Used value

23O MeV3

130 meV

O

0.25 MeV for

0.5O MeV for

1

6.34 MeV

6.34 MeV

Level density parameters for

"Nb

93Nb

93Zr

90Y

92Nb

92Zr

89Y

a

A

a

A

a

A

a

A

a

A

a

A

aA

11.98

- O.76 MeV

11.46 MeV"1

- O.4O MeV

12.31 MeV"1

0.81 MeV

9.40 MeV"1

- 0.31 MeV

10.OO MsV"1

- 0.55 M*V

10.87 MeV"1

1.16 M*V

10.30 M«V"1

- O.5O MeV

- 80 -

Transmission coefficients

n Delardche et al. /26/

p Becchatti et al. /3/

a Huizenga et al. /4/

L

- 81 -

Table V.5.

List of parameter variations studied for deriving an error

estimate of the calculated cross-sections for the93Nb (n,nf) 9310Nb reaction.

Variation Nr. Variation

3

4

5

6

7

8

10 *

Total s-wave neutron radiation width at

neutron binding energy increased from

13O to 3OO meV.

Constant FM for precompound matrix ele-

ment increased from 23O to 4OO MeV .

a(94Nb) increased by 1 MeV~1

a (93Nb) increased by 1 MeV~1

A(93Nb) reduced by O.5 MeV

a (92Nb) increased by 1 MeV*1

QOA (Nb) reduced by 0.5 MeV

Neutron transmission coefficients of Wilmore

Hodgson used instead of those of DeIa-

roche

Reduction of nuclear moment of inertia

from 1OO to 5O% of rigid body value

(r0 - 1.25 fro)

Spin of levels at 1.369, 1.395, 1.483,

1.499, 1.680, 1.910, 2.019 increased by

one unit,parity changed.

- 82 -

11* Spin of levels at 1.369, 1.395, 1.483,

1.499, 1.68O, 1.91O, 2.O19 reduced by one

unit,parity changed

Only one half of the resulting change was considered as 1 a

error and has been catalogued in Table V.6.

i &

- 83 -

VOt

OlH

3

m

•s

O•H4^id•Hh(O>hO)-P$

IIS1!

l(O

AtU

caO

•H-PUO)nUn2U

0t

C*C

I

n w v c o x w n i n o D - i i ' } ' C W O - ' C N r o c j x x - e - ' C O - x o « v n v D - o - - c v r > j u : o ' c * o : p 5 xX CCi • • • * • • • • • • • • • • • • « • . • . • • • . . . » , » . • . . . . , . ,"* o x n a x K « o «<o o- o- a O N « in » n w r» n N Cj r-; u x 5 S ;-. i.-,v «•' * " S — x 2

-» x x C ) C-i CV <M ri N CJ N M N PJ C-J P-J CJ N N CJ T-.' CJ CJ X —

v i ^ ccnocp ioo i^ßconccc i f t i f tO jn in inL^L^n inc inn in iß i . ' co^ - . ' i t oC OI"" u 1 ' « H ö ~ n £ N N b c i n r i « « ö " ö ^ m N * < ö « R i r i « » K » £ « V M ' ' ; K c j c : i - x— —! w « ro n w m n cj rj cj CJ cj cj N CM cj c; cj -<

> c o o o p o o o <

c, IU

C C O O C C O O O O C O O C O C O C C O O O O O C C C O C O C C C C O p O O C

tt • • •

u ' - t M x N c j n n n w w n n N C j c j n n r M C J N n c j r Ü M C . ^'

oococoococoooocoocooooooecccccccccoooooflj « * . . . . . . . . « « • • » • • » • • • • . . . . . . . . . . . ^'. * . . ,u "«wos^ino-c jNOOOO-ceiN-onT^ronwncjc jn iSotocc inJw.CvTifJc jxxx « x cj cj n n n n cj N cj cj N cj n cj N cj cj cj N cj cj«

O C O O O O O O O O O O O O C O O O O O O O O O C O C C O C O C O O O O O O C

• C r w N N S * *

X X - I N cj n n r o n n N c j c

oooooooooocoooocooooooooooooocooeoooooc^ I a V O S W M C O W - O 1 C P - W r ) X X V V N O - C o W O J W - O V C N ^ - N - C n CJ x r— ~ —

" *"" x x x C J N N W n C M n N C J C J C J N N N n N C J C J H C J x x '

n oeoopooqoeooooopoooooopooooooopoeooopqoa

8 ocooooooocoococcooooooeeoeecooococcccoO - O - W — i m O x - O - O N O O - V x C N N C I W O C O m O - N N N O - ^ - O V N - C V - O W C O V N

n p p o e p o o o o o p o o o o o o o o e o o o c o o p p o o o o e e o o p o oOJ

CJ *Ul

ttU

It-

COe>

- 84 -

Table V. 7.

93Final results of the model calculations for the Nb (n, S

reaction « final evaluated group cross-sections.

EVALUATED GROUP CROSS SECTIONS

GROUP-CMEV3

0.140,400.660.911.161.411.671,922.172.432.682.933.183.44.3.693.944.194. 454.704.955.205.465.715.966.226.857.868.879.8810.8911.9012.9113.9214.9315.9516.9617.9718.9819.99

•ENERGY X-SECTIONTO CMEVD

0.400.660.911.161.411.671.922.172.432.682.933.183.443.693.944.19

. 4.454.704. 955.20 •5.465.71 .5.966.226.857.868.879.8810.8911.9012.9113.9214.9315.9516.96 .17.9718.9819.9921.00

CMEU

3.1517.4037.8090.00110.30152.80195.30222.60274,60302.20308.80304.00296.50286.70276.30266.00256.70248.70242.20237.30233.90231.80230.50229.80229.70229.00224.90200.80131.1082.5055.4041.8034,3029.5025.9022,9020,5018.4016.70

ERRORCMBII

2.. W4.1218.0143,6249.7547.6245.1642.3946.8040.6743.0446.5548.9551.81o3» *JQ54.7554.8054.3853.6652.8452.0751.4251.0350.9750.7851.3152.1350.6941.6933.0027.3023.8021.4419.5217.6616.0314.5113.1912.06

ERKORC%3

90. 023.747.648.545.131.223.3.19.017.013.513.915.316.518.119.420.621.321.922.222.322.322.222.122.222.122.423.225,231.840,049.356.962.566,260. 270,070.871.772.2

L.

- 85 -

V.3. Evaluation and results thereof

As already discussed the calculated values are adopted as

evaluated group cross-sections in the Nb(n,n') 111Nb case

for the whole excitation function. Thus the final evaluation

result is already given in T able V.7. In addition these values

are shown in Fig. V.3.

- 86 -

1

§

-Q . If O/ B!

E <->Kl ,

x—v I— s 10

f~""~ °- "u

" CC

•— tu

_Q x

~^~en

•

•

1 '— X —

B

— X —

• XI

.

_

' x

x

x •

X •

"

'

xv X

„

''•kj

"

,

«f Kl

KX

"

V J

CVI

C3OJ

en«F-4

CD

CiUO*"*

LO*•*

.

W^

t— »

^ * ' '

2LDfyUBB

LU

OO

rs

i n\,O

LO

^." *

_-».

C^J

. XX V _-

I I ^^

C V ) - O

18U 001 ] MOI133S SSOaO

- 87 -

VI. The 103Rh(n,n' Y)103mRh reaction

VI.1. Experimental data base

To establish the data base, a literature search has been per-

formed in two steps.

a) Two very comprehensive compilations, namely CINDA

up to Supplement 79 (1 Oct. 1979) and the threshold reaction

compilation EANDC 95 "U" (Feb. 1974) have been used as

index to existing literature.

b) The most recent editions of some journals most likely to

contain relevant publications have also been searched up to March 1980.

The original papers have been looked up, whenever available

checking simultaneously that references cited therein were

already contained in the literature list. The most important

information on the 6 experiments found in this way is

briefly summarized in Table VI.1. Columns 1 to 7 give the

energy range of the experiment, the number of cross-section

measurements within this range, the method used to detect

either the induced activity or the particles produced in the

considered reaction, the method used to determine neutron

flux, the first author and date of the respective paper and

the reference number used furtheron in the compilation.

In two cases (Santry 74 and Barnard 78) the papers report

essentially on two different experiments for determination

of the 103Rh(n,n')103mRh cross-section using either different

techniques for detecting the reaction or for determining

the neutron flux. In these cases (as indicated by two entries

- 88 -

in !'able Vl.1. the papers were split into their two parts, which

were treated as independent data sets in the further evaluationI

procedure.

Detailed examination of the above measurements resulted in

rejection of 2 measurements and partial rejection of a third

measurement for the following reasons:

Kimura 69: reported excitation curve deviates strongly from

mutually agreeing excitation functions of Santry 74

and Barnard 78 and Paulsen 78

Nagel 66: value deviates by 4 standard deviations from

average of the other values.\

Santry 74: At energies above 6 MeV thefre exist serious dis-

crepancies within the results of this work, cross-

sections determined using the DD-source reactions are

about 25% higher than those measured using the TP-

reaction, the lower results being in agreement with the

recent work at Geel (Liskien 80). Moreover the very high

cross-section values found in Santry 74 in the neutron

energy range 7 - 10 MeV could not be reproduced with any

calculation using reasonable input parameters. Thus it

seems that that part of the measurements of Santry 74,

which used the OD-reaction in the neutron energy range

6 - 1 2 MeV is systematically in error probably due to

the influence of parasitic low energy neutrons. There-

fore all cross-section measurements of Santry 74 based

on the DD-reaction were rejected for neutron energies

above 5.5 MeV.

- 89 -The cross-section data from all accepted measurements are

summarized in Table VI.2. The table lists all cross-section

measurements in order of increasing neutron energy. For each

data point the following quantities are listed: the average

neutron energy and the energy spread (half width at half

maximum) of the neutrons used for the measurement, the un-

certainty of the average neutron energy, the cross-section

values and errors as given by the authors, an indication

which renorns<?.lization procedures have been applied to both

cross-sections and errors according to the general rules

of Ref. 1, section II and finally the renormalized cross-section

values and errors. The renormalized cross-section values are

also shown in pig. VI.1. The uncertainties in the average

neutron energy E centr. not given in most papers were either

estimated from the experimental conditions as described in the

papers or in a few cases obtained by communicating with the

authors.

As indicated in Table VI.2. cross-sections and errors were

partly renormalized according to the general procedures out-

lined in Ref. 1 , section II.

If not specially indicated in Tab. VI.2. the following

standards were taken:

a) Decay scheme as given in Table of Isotopes

b) Reference cross-sections for the reaction 32S(n,p) from

the ENDP/B-IV fi .e. An estimated error of 5% has been

assigned to such reference values and included in the

final error of the renormalized cross-tection.

In the energy range 13.4 - 15 MeV the mor« accurate results

from the precision measurement of Vonach /28/ for the27 24Al(n,a) Mg reaction were used for renormalization j

of the ENDF/B-IV values. This applies to Pazsit 72.

- 90 -

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- 93 -

References to Table VI.1. and Figure VI.1.

Nagel 66: 'W. Nagel and A.H.W. Aten jr., J. Nucl. En. A/B 2O

(1966) 475

Kimura 69: I. Kimura et al., J. Nucl. Sei. Technol. 6 (1969) 1

Pazsit 72: A. Pazsit and J. Csikai, Sov. J. of Nucl. Phys. 35

(1972) 232.K

Santry 74: D.C. Santry and J.P. Butler, can J. Phys. 52 (1974)1421

Barnard 78: E. Barnard and D. Reitmann, Nucl. Phys. A3O3 (1978)27

Paulsen 8O: A. Paulsen, H. Liskien, Nucl. Sei. En. (in press)

Pazsit 75: A. Pazsit et al., J. Applied Rad. Isotopes 26 (1975)621

- 94 -

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- 97 -

VI.2. Statistical Model Calculations

As apparent fron Table VI.2. and Fig. VI.1. there are no

accepted experimental data in the energy range 7 - 1 4 and

above 17 MeV, whereas there are three independent mutually

consistent measurements resulting in a rather accurate average

of 304.3 i 16.8mb for the group cross-section for the 13.5 - 14.5

interval. Therefore the evaluation in the 6 - 13.5 and 15 - 2O

MeV neutron energy ranges was done by means of statistical

model calculations with parameters adjusted to reproduce the

experimental value in the 14-15 MeV range.

Table VI.3. lists the input parameters chosen for this purpose.

The neutron optical potentials of Igarasi et al. /29/ was used

for generating transmission coefficients because compared to

various global potentials this one is superior in reproducing

the total cross-section between 2 and 15 MeV /25/

simultaneously with the 103Rh(n,n1)1O3mRh cross-section in the

low energy «6 MeV) and 14 MeV range. The decay scheme of Ref.

3O was used to describe the discrete levels of Rh up to

an excitation energy of 1.293 MeV and the remaining parameters

were given standard values as described in section II.2.

Table VI.4. lists the admitted variations of the various input

parameters used for the error estimate and Table VI.5. gives the

cross-sections obtained with the varied parameters.

Therefrom the uncertainties of the calculated values were derived

according to the procedure described in section II.1.2. The

calculated cross-section values and their uncertainties are given

in Table VI.6.; they are also included in Table VI.2.

- 98 -

Table VI.3.

Table of input parameters for calculation of the103Rh(n,n')103mRh excitation function.

Parameter Used value

FH

DO

Ieff/Irigid

195 MeV3

165 meV

O

0.5 MeV

1

Level density parameters for

104

103

103

1OO,

102

102

99

Rh a

A1Rh a

A

Ru a

A

'Tc a

A

Rh a

A

'Ru a

A

'Tc a

A

14.00 MeV"1

- O.75 MeV

14.4O MeV"1

- 0.23 MeV

12.69 MeV~1

- 1.08 MeV

13.5O MeV"1

- 1.00 MeV

14.00 MeV"1

- O.75 MeV

13.01 M«V"1

0.48 MeV

12.64 M«V"1

- 0.36 MeV

- 99 -

Transmission coefficients

n Igarasi et al. /29/

p Becchetti et al. /3/

a Huizenga et al. /4/

- 103 -

Table VI.4.

List of parameter variations studied for deriving an error

estimate of the calculated cross-sections for the 103Rh(n,n1)1O3mRh

reaction.

Variation Nr. Variation

3

4

5

6

7

8

9

10

Constant FK for precompound matrix ele-

ment increased from 195 to 275 Me\r.

Total s-wave neutron radiation width

at neutron binding energy increased from

165 to 250 meV

a (104Rh) increased from 14.0 to 15.O MeV"1

a (103Rh) increased from 14.4O to 15.40 MeV~1

A (103Rh) decreased fron - O.23 to - O.98 MeV

a (102Rh) Increased from 14.O to 15.0 MeW~1

A(102Rh) decreased from r O.75 to - 1.25 MeV

Reduction of nuclear moment of inertia .

from 1OO to 5O% of rigid body value

(X0 - 1.25 fm)

Binsize DU reduced from O.5 to O.25 MeV

Neutron transmission coefficients of

Perey and Buck u*«d instead of those of

Igarasi.

~1 - 101 -

O O O OC O O O O

OC C O O O O O O O O O O O-

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nnmoVlo

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- 115 - l

- 102 -

Table VI.6.

Tina! results of the model calculations fitted to the 14 MeV

experimental data for the Bh(n,n') Rh reaction.

ENERGYCMEVD

6,067.078.089.0910.10.11.1112,1213.1314,1415.1516.1617,1718,1819.1920.20

X-SECTIONC MB 3

1164,001146.001112.001092.00972.40689.70494.10373.20295.40241,30203,20177.30159,80148.00139.10

ERROR

96.98113.52125.82127.2389,2155.2347.7234,1416,5038.9338.2736.2734.0031.9029.86

l- 103 -

VI.3. Evaluation and results thereof

For the energy region threshold - 7 NeV the evaluation was based

entirely'on experimental data and carried omt according to the

procedures described in Ref. 1 }for E * 7 - 2O MeV the calculated

values of the preceding section were used. The intermediate steps

(column 7, 8 and 9) flat the experimentally covered energy range

threshold - 7 NeV are given in Table VT.7. The final results for

the whole energy range are summarized in table VI.8.

In figure VI.2. our results are compared to the previous eva-

luations of Lapenas /9/ and Butler and Santry /31/. As apparent

our evaluation is in good agreement with the previous ones below

about 6 MeV whereas there is a discrepancy of about 2O% in the

6 - 1 2 MeV range. This is due to the fact that the older

evaluations are essentially reproductions of the cross-section

data of Santry 74, whereas we decided to reject these data

for the reasons discussed in section VI.1. and decided to

rely on our statistical model calculation described in

section VI.2.

- 117 -

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n« -< (n -o o nno» »oo n o o ».rMVCD^*4Q IsnÖ« OMO CDinON0-CMM-O(MO I - )OOO « O- O n CM O •

fr- N «- *• N oo i- *- »- fr- (••»~ in *•»~ +• r- t-«-1- t- ^ t- »• i-, t-1- t-NnCMWtVCBvHN N » O W N W C M T CO^fMHrWN TO VH N K &• O*

(X rs m - r « e o « » c r f r N N »»T *-o« » v « r > * n t y < » r n < K n n m v n n r< IK i m t»i*><-4t&o-rä tf»»N>*H »*o**n **WT n*««4O »-»^ONTNift »»^-ino-wr«« ISNMWN^ o-inoc«-o-« s -o s; r. rx«-cN<or<. N O O O a<oo o- e- »- «K oo>oo*-9>oo ooooo-ooo e o o c o o o o -* « r. -<

I O O O O O O O O OOO»OOpO O Q O p OOO> O M 6 0 O P T O < C O N

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n* K»* n n n i n « r w -

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n » I O N » - o M »v H O N D - C M 4 T O O C M M > v 4 vHpvHv / OCM*•ONV5-ON N-O-ON-OK NBBO S -C»

Is

O O O O O O

- 106 -

CD

O

t»

N

N

n o o o o0 0 0 0 0 g

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Ö O Ö Ö Ö

n•e

K auz

P. t- .4 o- o n0> B T 09 T »•0 N M T D H»

T n T Ö N M-H O- O) IM -H O-

ag

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TNTT «r MCM * P-I * * Ca

NNNNNNMN NNNMMtMIM MNNtNMMMMNN N N N M M N NN MMNN NNMNN NN NT.

U

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fr- fr- fr- HH O- O

l? 5 N S ? 15OK «t •* O * in v CD V? O O *-" O-- IT-o» 2« 5< *n02C 05 -e-*

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ü.X nLJ Oi

o o o o o o o o o o o o o o o $.$$$$90000 $ ° $OOOOOOOO OOOOOOO OOOOOOOOOO O O O{KON«-(Noo*< n c M O O C M o m ^ c D O " H W o o o * o f j n es Mr jN^-önoocc N M C K C K N O C M ^vHOtMOOO 1 ONn n in N'OT^'O-o^-n-o -o N T n n -o -o ^ONM^^o^onooo*^ ^ n CM

IC OOCO COOOO OC «CO OOOC OOOOC OC OC-< O O D o o o o T IM "K r. !r:

S *N NT TtMNO B - W e D O ) W «05 — tT K K MNMtM «M««tM NW W K

(t. (b. . «k. (k. (.. fk. fk. i>. e- e» . »v t», fr* fr- fr- fr- fr' fr- fr- fr. fr. fr. fr. fr. fr. fr. o o O oo o o o o o O o Cgggggggg gggggss gggggggggg g g g l I s Il il§l iiiPH O T T O - Q O - n T nTTNnN<0 Nfr - -eQNHHMO-TN *0 M M M C*> T Bn «00-<ON OlftnDT N*<) -CN•4N<ono)TO-o> -o -o -o -H p -o ro -Hntj^N-xon-oo T M o- N B o- ON LI«HBO BNNOT NO NNOHHOHHOMMHH M M M O O O M M M O M O M M M H H M M M O *• 5 T nn nnMn MNMNN NN N-H

OCn

Nn -u N

=-min n ninin <«o<c <« N B O - n n n « T T T T T T B

14Ll

I^" Sli! Ut A

n n n n n n ß n•ö N cö o- ö M N n

L

- 107 -

S S

8 ?

S 5,

n § §

s § sO O «H

fi ? S

O (S OS « rS• * .CD (h O*4 ^ W

- 108 -

TABLE H.«. 103 RH

EVALUATED GROUP CROSS-SECTIONS

GROUP-ENERGYCMEV3

0.100.300.500.700.901.101,301.501.70.1.902,102.503.003.504.004.505.005,506.507.508.509.5010.5011.5012.5013.5014.5015.5016.5017.5018.5019.50

TO CMEV3

0.300.500.700.901.101.301.501.70 .1,902.102.503.003.504.004,505.005.506,507.500. 509.5010.5011.5012.5013.5014.5015.5016.5017.5018,5019.5020.50

X-SECTJONCMB3

44.058126.114230.573516,544627.749633.371678.540745.549826.611803.677915.3721011.49?1031.04?1061.07?1076.74?1143.46?1102.12?1160.97?1146.45?1114.69?1093.78?984,241720.489517,340392,133304.508240,439218,468212.694169.340150.220140.862

ERRORCMB3

13.5598.49616.24422.96818.87424.74724.18734.00224.58167.06142.68434.33633.29733.27135.93038.91151.50251.917113.545126.105127.40890.28757.66549,94425.69316.80014.93618.55420.40836.03032.37930.279

ERRORr/.330.86.77,04.43,03.93.64.63.08.34.73.43 . 23.13.33.44.74.59.911.311.69.28.09.76.6Kr KT-J* U

6.2e.59.621.321,621.5

L

- 109 -

CSJ

CO«-H

rv-*

ID»— «

LO

V

ro«— •

rvi

Sg

3SQi

GO

rx

1C

LO

M

LO «• IO U)

(8U 001 l NOI133S SSO»

L

- 110 -

VII. Derivation of the relative correlation matrices and

covariances

Relative correlation coefficients and covariances between all

uncertainties of the evaluated cross-sections were calculated

according to the general procedure described in Reference 1 ,

section II.2. for those parts of the evaluation based on ex-

perimental data and according to section II.1. of this report for

the parts derived from model calculations. Only correlations between

the cross-sections within each excitation function are given

in the following as no correlations between the excitation19functions are present except for the two reactions F(n,2n) and

P(n,p) at one energy (14 MeV,see Table VII.1.) and this one

point correlation can certainly be neglected for all practical

cases .

In detail the correlation matrices were derived for the 4 reactions

in the following way:19F(n,2n); For the whole energy range the correlation matrix was

derived from the estimated correlation coefficients of

the experimental values (see Table VII.1.)93Nb(n.n')93inNbt

For this case, where the evaluation was done by model

calculations only the covariances were calculated from

the results of the parameter variation according to

equation (ll.2).

31P(n,p) and 1O3Rh(n.n')103mBh:

In these two cases the correlation matrices consist

of two independent submatrices, one for the low

energy part of the excitation function derived

from the experimental data and one for the high

energy parts derived from calculations adjusted

to the 14 MeV data with no correlations between

the two parts. Thus in these cases the submatrices

of the low energy parts were calculated according

to the standard procedure from the experimental

B K values and the matrices for the high energy

parts were calculated from the results of the

cross-section variations according to the procedure

described in section II.1.2.

The relative covariance matrices, that is, the quantities

<a(Ei)xa(Ei')>

are given in Tables VI I. 2. to 5.

- 112 -

Table vii.1.

Relativ« correlation coefficients B _-. assumed for thennKvarious experimental data sets (for definition eee Ref. 1,

section II.2.)

Reaction

19FCn, 2H)1 8F

31P(n,p)31Si

103Rh(n,n')103*Rh

Reference

Brill 61

Rayburn 62

Bormann 65

Nagel 66

Bormann 67A

Bormann 67B

Vonach 68

Chatterjee 69

Menlove 67

Ryves 78

Metzger 48

LUscher SO

Ricamo 51

Grundl 58

Morita 58

Cuzzocrea 59

Grundl 67

Santry 74A

Santry 74B

Paulsen 8OA

Paulsen 8OB

Barnard 78A

Barnard 78B

BnnK

0,50

0. 1O

0.5O

0.9O

0.10

0.40

0.95

0.5O

0.70

O. SO

0.05

O.5O

O. SO

0.70

0.20

0.05

0.85

0.30

0.65

0.71

0.97

0.70

0.70

- 113 -

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X

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IH(M ro <r n <o r». OD CK o <H (M ro« n-ON co CK o *4 ^TH iH IH 1* 1-1 IH 1« *H •* «H CM N X

(9

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- 114 -

S S

i

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- 115 -

c\c f tN^*4mr '3T i '3 f f in (a . '>« '<Y<TL < jNaor i *<CNo>o-NnnBo>ooccc <33»4 « « M x « •« •* « m « 3 « « nv> nn in in « « <o « « « 4 N a o» o> o>'O o o Oo c o

. — .«wro-e-e-o-onLi i . innninJ-c-o-C'O-er^mo-o-o-ooooV4 v* *4 •»

ix.<«n««<oini.ii.ioiniii.i»««!o!e-e-orvS(7»>»ooS

jnnnoS-e-o-o-o-crxeoo-o-o-oo

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nn»*ncD»>oex~«-<oaNKKmorjnin«i^»oo« n xxoir j r j i . io«>v-e>CDgooofDe»»o-»(KO-o-oo

4 o^onOMO-x mi LI V B O - O O

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n r j *r o n n rv « o o rj r i o- o

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O CMTwBMI - )MDCX

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•0

n o

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- 116 - f

'2JfS

in ooo ooo oooooooooooo OSSi1^PSC4 W T T T Ix O

m oooooooooooooooooooggggO O O O O O O O O O O O O O O O O O O g g g

Z

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»«!•>*> V

- 117 -

The authors gratefully acknowledge the assistance of

Dr. W.G. Vonach and J. Kramer in the literature search

and data renormalization procedure. They are also glad to

acknowledge financial support from the Osterr. Bundesministerium

für Wissenschaft.unä Forschung.

Literature

/1/ S. Tagesen, H. Vonach and B. Strohmaier, Physics Data

Nr. 13-1, 1979, ISSNo.344-9401

/2/ M. UhI and B. Strohmaier, Proc. Winter Course on Nuclear

Physics and Reactors, Trieste, 16 Jan - 1O Feb 1978,

IAEA (in press)

/3/ F.D. Becchetti Jr. and G.W. Greenlees, Phys. Rev. 182,

1190 (1969)

/4/ J.R. Huizenga and G. Igo, Nucl. Phys. 29, 462 (1962) and

ANL-6373 (1961)

/5/ W. DiIg et al., Nucl. Phys. A217, 269 (1973)

/6/ C. Kalbach-Cline, Nucl. Phys. A21O, 590 (1973)

/7/ E. Gadioli, E. Gadioli-Erba and P.G. Sona, Nucl. Phys.

A214, 589 (1973) and L. Milazzo-Colli, G.M. Braga-

Marcazzan, Nucl. Phys. A21O, 297 (1973)

/8/ P. Axel, Phys, Rev. 126, 671 (1962)

/9/ A.A. Lapenas, Kh.Ja. Bondars, Ja.K. Vejnbergs, Izmerenie

Spektrov Nejtronov Aktivycionnym Hetodom, zinatne,

Riga, USSR, 1975 and EXFOR VOO02.O2O

/10/ B. Strohmaier and M. UhI, Proc. Int. Conf. on Neutr. Phys.

and Nucl. Data for Reactors and Other Applied Purpose*,

Harwell, 25-29 Sept. 1978, p. 1184

/11/ P.M. Endt and C. van der Leun, Nucl. Phys. A214,1 (1973)

/12/ G.S. Mani, H.A. Melkanoff and I. lori, Rpt. C.E.A. 2379,

1963

/13/ P.G. Perey and B. Buck, Nucl. Phys. 32, 35O (1962)

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/15/ W.L. %Zijp et al., RCN 196 (1973)

/16/ Ü.C.R.L. 5O4OO, Vol. 15 (1978)!

/17/ I.J. van Heerden and W.R. HcMurray, .Z. Physik 26O,i

9(1973)

/18/ H. Göbel, E. Feicht and H. Vonach, Z. Physik 240,

430 (1970)

/19/ G.H. Williams, Thesis Univ. of Texas (1975)

/20/ A.B. Smith, P.T. Guenther and J.F. Whalen, Z. Physik 264,

379 (1973)

/21/ R.E. Coles, AWRE-RPT, No. O66/71 (1971)

/22/ A.I. Abramov, Sov. Journ. Atom. En. 12, 65 (1962)

/23/ N.P. Glazkov, Sov. Journ. Atom. En. 14, 1173 (1963)

/24/ D.C. Kocher, Nucl. Data Sheets B8, 527 (1972)

/25/ D.G. Foster and D.W. Glasgow, Phys. Rev. C3, 576 (1971)

/26/ J.P. Delaroche, Ch. Lagrange and J. Saivy, IAEA Con-

sultants Meeting on the Use of Nuclear Theory in

Neutron Nuclear Data Evaluation, Trieste, 8-15 Dec. 1975,

IAEA-190, Vol. 1, p. 251

/27/ D. Hermsdorf, G. Kiefiig, J. Seeliger, Kernenergie 20,

166 (1977)

/28/ H. Vonach «t al., Z. Physik 237, 155 (1970)

/29/ S. Igarasi «t al., Proc. Conf. Nucl. Cross Sections and

Technology, Washington DC, March 1975, Vol.1,p.320

/30/ E. Barnard, D. Reitmann, Nucl. Phys. A303, 27 (1978)

/31/ J.P. Butler, D.C. Santry, AECL-3043 and UKDL-DFN 94 A

Figur» Caption»

Fig. IV.2.

19Fig. III.t. Experimental data base for the F(n,2n) reaction

in the neutron energy range threshold - 2O MeV.

The figure displays the renormalized cross-section«

and their effective 1a errors (according to Table

III.2., column 8+9) for all measurements reported

in Table III.1.

Fig. III.2. Comparison of the present evaluation with the pre-

vious evaluations of Lapenas

Fig. IV.1. Experimental data base for the reaction P(n,p)

in the neutron energy range threshold - 2O MeV.

The figure displays the renormalized cross-sections

and their effective 1o errors (according to Table

IV.2., column 8+9) for all measurements in Table

IV.1. Also shown are the results of the model

calculations of section IV.2. (Strohmaier 8O).

a) whole energy range

b) E- 1 - 3 MeVnc) E "3-5 MeVnd) E. 5 - 2O MeV

Comparison of the present evaluation with previous

evaluations

a) Comparison with SANDIT and UKDL.

b) Comparison with ENDL-78.

93Fig. V.1. Experimental values of Nb(n,n')

Fig. VI.1.

!93mNbcross-

sections derived from y-production cross-section93measurements in the Nb(n,n'Y) reaction (values

of Table V.2.) and effective 1a errors. Also

shown are the results of the statistical model

calculations of section V.2. (Strohmaier 8O).93Fig. V.2. Nonelastic cross-sections for the Nb+n system derived

from sphere-transmission, (n,n') and (n,n'-y) ex-

periments.

Fig. V.3. Results of the present evaluation

l103mRh1O3Experimental data base for the Rh(n,n')

reaction in the neutron energy range threshold -

20 MeV. The figure displays the renormalized cross-

sections and their effective 10 errors (according

to Table VI.2., column 8+9) for all measurements

reported in Table VI.1. and the cross-sections cal-

culated as described in the next section (Strohmaier 80).

a) full energy range

b) E.n O - 6 MeV

Fig. VI.2. Comparison of the present evaluation with previous

evaluations.