A neutron scattering study of Fe56

fl.E.l:Z.LI

Nuclear Not

to be

Physics reproduced

64 (1965) by

A NEUTRON

130- 146; @ North-Holland

photoprint

or

SCATTERING

W. B. GILBOY A. W.R.E.,

microfilm

without

Publishing

written

STUDY

permission

Co., Amsterdam from

the

publisher

OF Fe56

and J. H. TOWLE

Aldermaston,

Berkshire,

Received 21 September

England

1964

Abstract: Differential cross-sections for elastic and inelastic scattering of neutrons by iron have been measured in the energy range 1 to 4 MeV with a time-of-flight spectrometer. The elastic scattering data have been compared with the predictions of several types of optical potential. In the inelastic data direct interaction effects appeared to be negligible and comparisons with compound nucleus theory have enabled limits to be placed on the spins of several levels in FesB. E

NUCLEAR REACTIONS Fe(n, n), (n, n’), E = 0.98-3.99 MeV; measured a(E; En,, 8). FesB deduced levels. Natural target.

1

1. Introduction Iron is a common structural material for reactors and their associated shields, and this work was undertaken primarily to provide accurate neutron scattering data in the range l-4 MeV. The chief isotope of iron is Fes6 (91.57%) in which both the neutron and proton numbers lie close to the 28 nucleon closed shell and being a spherical even nucleus the low-lying levels are expected to show some vibrational character ‘). The inelastic scattering cross-sections measured here were compared with the predictions of the statistical model ‘) in order to derive further information on the Fes6 level scheme. Many sporadic measurements have been made of the interaction of neutrons with iron “). For example, Cranberg et al. “) (at E, = 2.25, 2.45, 3.0 MeV) and Landon et al. “) (at E, = 2.2 MeV) have measured differential cross-sections for elastic and inelastic scattering using the time-of-flight technique. Inelastic data have also been derived from studies of the de-excitation y-rays following inelastic scattering and the work of Montague and Paul 6, is typical of this method. They used neutron energies up to 3.8 MeV and ring scattering geometry to measure the y-ray production crosssection of iron to an absolute accuracy of 25%, although their relative errors were only about 10%. However, the subsequent derivation of inelastic cross-sections to various levels requires a detailed knowledge of the decay scheme which introduces further uncertainties. In the present work scattered neutrons were observed directly with a time-of-flight spectrometer and their intensities and angular distributions were measured. A careful study of the various corrections was made in efforts to derive accurate absolute cross-sections. The resulting differential cross-sections for elastic and inelastic scat130

NEUTRON

SCATTERING

131

tering were then used to throw light on the nuclear potential and the (n, n’) reaction mechanism respectively. 2. Experimental

Method

The measurements were made on the Aldermaston 6 MV Van de Graaff accelerator using the fast neutron time-of-flight spectrometer which has been fully described in earlier work ‘2*). Briefly, a pulsed neutron beam was scattered by a hollow cylindrical iron sample (2.5 cm outside diam., 1.0 cm inside diam., 5.0 cm high, mass 161.8 g) placed 11.1 cm from the source. Scattered neutrons were detected in the horizontal plane by a collimated detector 171.2 cm away, at scattering angles between 30” and 137”. The absolute differential cross-section scale was fixed with reference to the well known n-p scattering cross-section by observing scattering from the hydrogen in thin polythene samples. The relative detector efficiency was measured by comparison with a calibrated long counter and the detector energy bias was set at about 0.4 MeV. The time measuring electronics were calibrated against standard delay cables. Incident neutron energies of 0.98, 2.01, 3.01 and 3.99 MeV (with spreads 100, 70, 60, 65 keV, respectively) were employed to measure the differential cross-sections for elastic and inelastic scattering. Scattered neutron spectra were also recorded at 125” only (see ref. “)) for neutron energies between 1.40 and 3.01 MeV at 200 keV intervals and the excitation functions for the observed levels were normalized to the absolute scale by comparing the 3.01 MeV results with the integrated differential cross-sections which were measured at the same energy. Finally, the time-of-flight detector was set at 0” and the total cross-section of an iron sample (a solid cylinder, 4.6 cm diam. and 3.50 cm high) was measured by transmission for neutron energies of 2.01, 3.01 and 3.99 MeV with similar energy spreads to those quoted above. 3. Experimental Results and Correction Procedures Typical time-of-flight spectra for neutron energies of 2.01, 3.01 and 3.99 MeV are shown in figs. l-3. The flight times of the inelastic groups were measured using the elastic peak as a convenient datum, and the mean excitation energies calculated for the observed levels are given in table 1. The present results compare well with the more precise (p, p’) data of Mazari et al. 9, and Aspinall lo). In what follows the level energies of Mazari er al. are used in referring to the levels. The 3 MeV spectrum in fig. 2 shows a group apparently corresponding to a level at about 1.75 MeV. No such level is known among the iron isotopes lo) and this peak has been identified as due to double inelastic scattering 11) from the strongly excited 0.845 MeV level. The Monte Carlo multiple scatter correction programme of Parker et al. “) was used to correct the data and this predicted a double scatter peak whose intensity was about 8% of the single scatter group in agreement with experiment. As a further check some scattering runs were done with a smaller iron

W.

132

I

0

0

I

: P

B.

GILBOY

H

i! M3d

J.

H.

I

I

I

13NNVH3

AND

SlNtl03

TOWLE

I

NEUTRON

133

SCATTERING

sample (2.0 cm outside diam., 1.0 cm inside diam., 5.0 cm high and mass 92.5 g). The double scatter peak was reduced to about 6% which again agreed with a Monte Carlo estimate. Multiple inelastic scatter between other combinations of levels also occurs but less

t

1

I

20

0

CHANNEL

2.660

3.119

k RAYS

200

2.?58(2),

40 NUMBER

2.085

60 (2”s

PER

80 CHANNEL)

Fig. 3. Time spectrum for scattering of 3.99 MeV neutrons by iron, f3 = 125”, the flight path is 171.2 cm. The groups at 2.958 MeV and 3.38 MeV are doublets.

Comparison

TABLE 1 of measured level energies (in MeV) with (p, p’) measurements Aspinall et al. lo)

of Mazari ei ~1. s, and

Present work

Mazari

Aspinall

0.841 f .030 2.096f .030 2.678% .025 2.984h.018

0.845 2.085 2.658 2.940 2.958 3.119 3.369 3.388 3.445

0.842 2.079 2.652 2.933 2.955 3.117 3.365 3.384 3.441

3.144f.016 3.369rt.014 3.451 A.010

134

W.

B.

GILBOY

AND

3.

H.

TOWLE

frequently and these events were not resolved from the single scatter groups in the present experiment. The correction programme was used to calculate these contributions which were then subtracted from the observed groups. The intensities of the resulting single scatter groups were corrected for multiple scatter and flux attenuation as described previously “).

------

OBSERVED

-

CORRECTED

DISTRIBUTION FOR

MULTIPLE

SCATTERING

IO00 8 6

100 8 6

0

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0-b

-0.8

-1.0

CO5 8 LAB

Fig. 4. Differential cross-section for elastic scattering of 3.99 MeV neutrons by iron illustrating the importance of the multiple scattering correction. The statistical errors on the observed points are all 5 3 %.

In fast neutron scattering at forward angles elastic scatter is usually much more intense than inelastic scatter. Therefore if the elastic events overlap the inelastic groups even slightly it can have a marked effect on their apparent angular distributions. Spurious forward peaking can arise in this way making it appear that direct interaction effects are present, particularly as the effect worsens with increasing energy. Special attention was paid to this point in this work and several possible effects leading to elastic contamination of the inelastic groups were considered. The Monte Carlo correction programme 12) has recently been improved and extended r3) and it is now possible to predict the energy spectrum of scattered neutrons. This facility was used to investigate the possibility that multiple elastic scattering could degrade neutrons into the inelastic regions of the spectrum. For a nucleus as heavy as iron this was found to be completely negligible. The influence on the time spectra of neutrons scattered from the collimator into the detector was

NEUTRON

examined this effect Finally using the

135

SCATTERING

next with the aid of another Monte Carlo programme which showed that also was very small. the detailed energy spectrum of the source neutrons was carefully measured time-of-flight detector. The neutron source was a tritium gas cell which

DIFFERENTIAL ELASTIC CROSS-SECTIONS En-O.98

I

MtV

1000

E, -2.01

nrv

blO0

IO/, 1.0 0.8

0.6

0.4

0.2

0

-0.2

-0.4 -0.6 -0.8

-1.0

1.0

0.6

0.6

0.4

0.2

En-J.99

E,=J.OI MeV

0

-0.2 -0.4 -0.6 -0.8

HtV

IO00

z

2 3 bwlo 0

,, 1.0

0.8

0.6

0.4

0.2 cos

0

-0.2

e (C.H.)

-0.4 -0.6 -0.8

-1.0

1.0

0.8

0.6

0.4

0.2

0

-0.2

-0.4 -0.6

-0.8 -110

cos e (C.M.)

Fig. 5. Differential elastic scattering cross-sections for iron at 0.98,2.01, 3.01 and 3.99 MeV compared with the theoretical predictions for two types of nuclear potential. The overall errors on the measured points are 5 5 %.

was bombarded with protons through a 2.5 pm nickel window. Runs with no tritium in the cell showed that backgrounds due to the beam striking the cell materials and the beam piping were very small even at the highest energy used (I&, z 5.0 MeV). With the cell filled with tritium it was found that the source neutrons exhibited a

136

W.

>

B.

GILBOY

AND

En-LOlMeV

,ooI

t 3

McV

0.845

-

J.

H.

(0)

LEVEL

li--*

~*_-~-I-

b-50

TOWLE

1.0

0.5

0 co5

-0 5

-1.0

(CM)

8

loo - En-J.01 McV 0.845MeV I

$

l

(bl

LEVEL

*-*1--.--i

l

s > R a

-

b-

2.085 MeV I.

.

IO -

.

1.0

.

cos En= 3.99

40

____--_

20: t

5

-2

-1.0

-0.5

e(m)

Cc) HeV LEVEL

---__&_____-t__-_____-----'-----,

1

IO

.I

l

MrV

0.845

JO

.

0

0.5

1

LEVEL

e-.-.--i

II 1

.

2.085MeV

1

LEVEL

I

_t__~___.___~--;--‘---?-_r____

1

I

----

----

I

______-___________-________--__________

s

'f.

b- IO z

208

JO

..!.'

f.

. 2.658 MeV LEVEL

j .

2.94Ot 2.958tJ.119 MrV LEVELS '-';_"'___T__;_--.----r--

__%_*-A_,

c--m,

20 40 1

20-

IO

_I 3.369t5.388tJ.445MrV

---*--

1.0

I

f

f 11

i __;__T_______---11

0.5

11

.

1

LEVELS

I___;___._______----_

"

0

1

"

1

1’ -0.5

“1

-1.0

co5 8 (c.H)

Fig. 6. Differential inelastic cross-sections of iron (a) The 0.845 MeV level at En = 2.01 MeV indicating typical overall errors. (b) The 0.845 and 2.085 levels at E,, = 3.01 MeV. (c) Various levels at E, = 3.99 MeV. The dashed curves arc Hauser-Feshbach predictions.

137

NEUTRONSCATIXRING

tail extending from the full energy down to a few hundred keV. This was found to be caused by scattering of source neutrons from the materials of the gas cell and the surrounding air. These secondary neutrons totalled about 2% of the source neutrons and gave rise to low-energy tails on the elastic peaks which could cause serious contamination at forward angles of the inelastic groups associated with the primary source neutrons. The intensity of these secondary neutrons was found for the energies corresponding to each inelastic group and the fraction of these which were scattered elastically was then calculated using the elastic differential cross-section appropriate to each energy. The differential elastic cross sections measured in this experiment were used to estimate these corrections. All the scattering data were corrected for flux attenuation, multiple scattering and source-sample angular spreads using the Monte Carlo methods described in refs. ‘*I 13). In particular the shapes of the observed elastic distributions were corrected for these effects, and fig. 4 illustrates the magnitude of the correction for the 3.99 MeV case; the correction to the first minimum in the curve is clearly very important. The fully corrected elastic data are shown in fig. 5 together with various theoretical curves. These differential elastic data are in general agreement with the results of other workers 3, where their results were corrected for multiple scattering. The fully corrected differential inelastic cross-sections derived from the data are shown in fig. 6. As it was difficult to resolve the 0.845 MeV level from the elastic peak for E,,= 3.99MeV only three measurements at backward angles are given in fig. 6(c). These three points suggested an approximately isotropic distribution for the 0.845 MeV group and this assumption (supported also by Hauser-Feshbach predictions) was used to estimate the magnitude of this level and its contribution to the elastic peak at forward angles. Also the incomplete resolution of the 3.119 MeV level from the (2.940+2.958) MeV doublet, (and the 3.445 MeV level from the (3.369+ 3.388) MeV doublet), precludes giving more detailed angular distributions for these levels; instead the angular distributions of these two groups of levels are shown. However, an estimate of the way these cross-sections divide up between the levels is included in the integrated cross-sections given in tables 2 and 3. All the difTABLE 2

Integrated elastic and inelastic cross-sections per atom of natural iron (in b) together with the total cross-sections

(Iv&) 0.98 2.01 3.01

(0.845 ZV 2.02&0.06 2.34&0.07 2.00&0.06

measured

by transmission

level)

(2.085 &V

0.860+0.026 0.729f0.026

level)

0.145f0.005

(by trazmission)

3.20+0.06 3.27+0.07

ferential cross-sections are closely symmetric about 90” (c.m.) and smooth curves fitted to the points were used when integrating these inelastic cross-sections. There

W. B. GILBOYAND J. H. TOWLE

138

are little published data on absolute differential inelastic cross-sections but previous measurements of scattering to the 0.845 MeV level “) are in agreement with the present results. Neutron scattering cross-sections

TABLE 3 per atom of natural iron (in b) at En = 3.99 MeV

% cq (0.845 MeV) UI (2.085 MeV) or (2.658 MeV) or (2.940+2.958 MeV) ul (3.119 MeV) (11 (3.369+3.388 MeV) or (3.445 MeV) or (by transmission)

2.17 10.09 0.427f0.042 0.126&0.007 0.163&0.011 0.153+0.014 0.170~0.017 0.094f0.014 0.123&0.013 3.51 *to.07

The various inelastic groups are referred to the levels of FeSB (9 1.6 % isotopic abundance) but they also include scattering to the levels of the other iron isotopes which lie near these energies.

Excitation functions for the levels at 0.845, 1.409 (Fes4) and 2.085 MeV were measured over the energy range 1.40-3.01 MeV and normalized with respect to the absolute inelastic cross-sections derived from the differential data at 3.01 MeV. These excitation functions were further corrected for relative variations in flux attenuation, multiple scattering and centre-of-mass motion and are given in table 4.

Inelastic scattering cross-sections

TABLE 4 per atom of natural iron as a function of neutron energy u(n, n’) mb

(MS)

0.845 MeV level

1.409 MeV level

2.085 MeV level

1.40 1.61 1.79 1.99 2.20 2.39 2.61 2.81 3.01

580+33 642&36 515&29 717+41 836&46 726i42 799&46 706t43 729;26

57% 5 53& 5 534 5 56&- 6 47* 7 651-10

88&6 108&6 145+5

3.06 3.99

574+38 372&46

55&10&)

126&7

“) Estimated from other data, see text.

NEUTRON

139

SCATTERING

The fully corrected results for the 0.845 MeV and 2.085 MeV levels are shown in fig. 7 where they are compared with various theoretical predictions. The y-ray work of Montague and Paul(j) is in reasonable agreement with these data if the decay scheme quoted by these workers is assumed. POTENTIALS 1400

------PENEY

-

- BUCK

------AVERAGE

-

Vc,

AD HOC -

-1.75 E, MrV

_,.-‘-‘Y\.

I200

i

‘.

/’

‘.

!

-\

I

200

-

I

-0

1 -*.

i

2.085

I.0

MtV

LEVEL

2.0

3.0 E,

4.0

MaV

Fig. 7. Inelastic scatter excitation functions for the 0.845 and 2.085 MeV levels of iron compared with the Hauser-Feshbach predictions for various potentials.

4. Theoretical 4.1. ELASTIC

Comparisons

SCATTERING

The experimental elastic data were compared with optical model calculations in order to find representative nuclear potentials for iron. A spherical potential of the Bjorklund-Fernbach type 14) containing real and imaginary terms and a real spinorbit term was used and this is represented below

where p(r)=

[l+expr+)]-l,

&)=exp[-

[+)2].

Ro=roAa.

Several parameters in expression (1) which are not sensitively determined by elastic data were held constant at the following values: Vs, = - 10 MeV, r,, = 1.25 fm,

W.

140

B. GILBOY AND J. H. TOWLE

a = 0.65 fm, b = 1.00 fm; these values are taken from extensive

comparisons

with

other neutron data r5). The computer code ABACUS 2 was used to calculate the shape elastic cross-section asn(8) and also (TAthe absorption cross-section for these potentials. The symmetry of the observed inelastic angular distributions and theoretical estimates by Sheldon r6) indicate that direct interaction effects are unimportant at the energies studied and bA is taken to be the cross-section for compound nucleus formation. The compound nucleus decays almost entirely via compound elastic scattering bCE and inelastic scattering pi. Therefore ocE was found from CT~-or (exp), where CT~ (exp) is the difference between the measured total and elastic cross-sections. The resulting cCE was added to gsE (0) before comparing with the experimental elastic distribution. This method of calculating the compound elastic contribution correctly allows for any uncertainties due to limited resolution between elastic and inelastic events and it also ensures a good fit to the observed cT value as a good fit to the elastic data is approached. TABLE 5 Nuclear

potentials

(hz)

(M2V) 0.98

obtained

“)

42.91

b)

42.75

from

fitting

elastic

scattering

VCI WV)

data GA

(b)

1.91 2.04

1.61 1.61

1.22 1.22

2.01

“)

47.44

3.66

2.01

1.46

3.01

“)

48.56

10.26

1.70

1.65

3.99

“) b,

41.70 47.86

9.70 10.56

1.98 1.91

1.52 1.56

“) Assuming isotropic b, Using a,,(B) from

ocs(8). HF calculations.

Initially o,-- was assumed to be distributed isotropically (c.m.) and V,, and V,, were varied to optimize the fit to the elastic data. These calculations were repeated for the 0.98 MeV and the 3.99 MeV data using relative ocE(B) distributions derived from some preliminary Hauser-Feshbach (HF) calculations 2, but the optimum parameters were not very different from those obtained with the isotropic assumption although the quality of the fitting was slightly improved. These ad hoc parameters are given in table 5 together with their associated cross-sections. The calculated elastic angular distributions are shown in fig. 5 where the 0.98 and 3.99 MeV curves are those derived using the a,,(HF). Quite reasonable fits to the data at 3.01 and 3.99 MeV were achieved by the above procedure, but the 2.01 and 0.98 MeV data were not fitted well probably due to the resonant nature of the cross-section at these energies. The elastic data were next compared with the energy independent non-local model

NEUTRON

of Perey and Buck i7). Equivalent

141

SCATTERING

local potentials

were derived

from

eq. (35) of

their paper + and these can be closely represented over the energy range O-15 MeV by potentials of the form described above with the following parameter values: I’,,

= -(46.98-0.285

V,, = - (9.27-0.053

E,,) MeV, E,,) MeV,

R, = 4.93 fm,

a = 0.65 fm,

R, = 4.80 fm,

b = 1.08 fm.

The same spin-orbit term as was used in the ad hoc case was also included. These Perey-Buck curves are shown in fig. 5 and the agreement with the data is not as good as for the ad hoc fits, although the fits again improve with increasing neutron energy. The elastic data were further compared with a potential recently proposed by Moldauer I*) which was obtained by fitting absorption, scattering and polarization data for spherical nuclei (A = 40-150) in the neutron energy range O-l MeV. This potential was of similar form to expression (1) but with different radii for the real and imaginary parts. For iron his parameters were V,-a = -46 MeV, V,-, = - 14 MeV, Vs, = -7 MeV, R, (real) = 5.04 fm, R, (imaginary) = 5.54 fm, a = 0.62 fm, b = 0.5 fm. Apart from the 2.01 MeV case, the fits were not very good. The fit to the 0.98 MeV data was particularly poor as the predicted curve lay well above the experimental points in similar fashion to the Perey-Buck curve shown in fig. 5. Thus it seems that Moldauer’s average potential does not describe iron very well. The ad hoc potentials in table 5 appear to show up a strong energy-dependence for the absorptive potential but it should be noted that even these large parameter changes did not produce satisfactory fits to the lower-energy elastic data. Maddison “) has done a more thorough search of parameter space for these 0.98 MeV data and he gets a better fit using V,, = -45.9 MeV, V,, = -5.0 MeV, r,, = 1.3 fm, a = 0.33 fm and b = 0.58 fm. Therefore the low values of V,, in table 5 may partly be a consequence of assuming too large a value for the diffuseness parameter. It is concluded that with the present energy spreads the elastic cross-section for iron is too resonant below 20) about 2.5 MeV for a reliable derivation to be made of the energy dependence of the optical model parameters. The good empirical fits to the 3.01 and 3.99 MeV data show no large energy dependence energy range. 4.2. INELASTIC

over that limited

SCATTERING

The symmetry about 90” (c.m.) of the present inelastic angular distributions suggests that the compound nucleus statistical model of Hauser and Feshbach “) is applicable to the Fe56(n, n’) process up to 4 MeV at least. Sheldon 16) calculates that 3 MeV neutrons on Fe 56 should give rise to a compound nucleus with a mean level spacing of 0.33 keV. Therefore several hundred compound nuclear levels are excited within the present energy spreads which gives a representative level population and justifies the statistical assumption. Hauser-Feshbach theory treats the decay t Equivalent potentials computed by D. Wilmore, AERE, Harwell.

142

of the compound

W. B. GILBOY AND

nucleus

as a non-coherent

J.

H.

.LOWLE

competition

between

all possible

decay

modes and it has been increasingly used 7***21-23) to derive spin and parity assignments for levels excited by neutron scattering. Statistical model calculations of inelastic neutron cross-sections require the transmission coefficients for all open channels in addition to the spins and parities of the final states. The elastic scattering comparisons in the previous section have yielded nuclear potentials from which the transmission coefficients in the entrance channel were calculated. It was also assumed that the exit channel transmission coefficients could be calculated from the same potential, taking into account any dependence on neutron energy which may exist “I). The present elastic scattering comparisons do not unambiguously show up an energy dependence of the imaginary potential and the ad hoc potential which gave the best fit to the 3.99 MeV elastic data was used in the following HF calculations on Fe56. TABLE 6

Isotopic

FesB(n, n’)

cross-sections

at

E,,=

3.99

MeV

Level (MeV)

(I%)

0.845 2.085

406146 138& 8

2.658

163&12

2.940+2.958

159+15

3.119

178*19

3.369+3.388 3.445

87f15 134% 14

In order to compare calculated cross-sections with experiment it was necessary The measured values for natural iron to derive Fe56 isotopic (n, n’) cross-sections. were corrected for Fe54 levels wherever these lay under the Fe56 groups. The strengths of the Fe54 contributions (apart from the strongly excited 1.409 MeV level) were estimated by assuming them all to be equal to the average excitation of the Fe5’j levels excluding the strong 0.845 MeV level. The 1.409 MeV level was not resolved from the 0.845 MeV level at En = 3.99 MeV and its excitation was estimated by extrapolating the present value at E,,= 3.01 MeV and the 3.5 MeV value in ref. 6). The Fe56 isotopic cross-sections derived in this way from the 3.99 MeV measurements are given in table 6. In addition it was desirable to estimate the way in which the cross-sections divide up between the unresolved (2.940-t-2.958) MeV and (3.369+3.388) MeV doublets. ‘*lo) the 2.940 MeV and 3.388 MeV levels were found to be In (p, p’) experiments the weaker components. The present authors have often used the Fe56(n, n’) spectrum for time calibration purposes and it has been noticed that the centroid of the (2.940+ 2.958) MeV doublet agreed better with a smooth time calibration line if it was as-

NEUTRON

SCATTERING

143

sumed that the 2.940 MeV level was only relatively weakly excited. Recent (n, n’) work at Los Alamos 34) has partly resolved the higher energy doublet at En = 4.1 MeV and the 3.388 MeV member forms about 30% of the total strength. These indications were taken into consideration when searching for J” assignments to fit the data. The Hauser-Feshbach option of ABACUS 2 was used to compute inelastic scattering at En = 3.99 MeV to levels in Fe 56. The calculated values for many combinations of spin and parity were compared with the measured cross-sections in an attempt to determine the J” assignments. To avoid uncertainties in the absolute values of both measured and calculated cross-sections (see refs. ‘98, “)) the predicted total inelastic cross-section was normalized to the experimental value. Then the relative excitations of the observed groups of levels were compared with the theoretical values and a quantity ZA’ was computed where A = [o(exp)-a(calc)]/Aa(exp) for each group and Ao(exp) is the standard deviation of the measured cross-section. These ZA’ values were printed on the computer output and they enabled the J” sets to be quickly evaluated. TABLE

Summary Level MeV 0 0.845 2.085 2.658 2.940 2.958 3.119 3.369 3.388 3.445 3.601 3.840 Columns Columns

of previous

7

spin

assignments

Jn (1)

(2)

(4)

(5)

(6)

o+ 2f 4f 2+

Of

o+ 2+ 4+ 2+

o+ 2+

o+ 2+

2+

2+

4*, 5+, 6-

2+ 5+ 2+

2+ 2+

3-

3+, 3-

3+(3-,

3f

5+(3+, 3-)

3+(5+)

2+ 3f(4f,

(3) o+ 2f 4+(3+)

2+ 2+ 3-) 2+ 2-)

3f

(l)-(4) involve p-y, y-y studies of MrP and CP decay z5-zs), respectively. (5) and (6) are neutron and electron scattering data ‘% 30), respectively.

Since it was impracticable to investigate J” values for all the nine excited states of Fes6 which were observed, the number of possibilities was drastically reduced by taking into account other data wherever possible. Table 7 lists most of the previous assignments which were derived from a variety of experiments 25-3o). On this basis, together with experience gained in some preliminary comparisons in this present work the f?rst four states were chosen to be: ground state (Of), 0.845 MeV (2+), 2.085 (4+), 2.658 (2+). The 2.940 MeV level is probably only weakly excited which suggest a high spin (2 5) and 6+ was chosen to fit in with a vibrational level

144

W.

B.

GILBOY

AND

J.

H.

TOWLE

scheme. The (3.369 + 3.388) MeV doublet is relatively weakly excited which tends to discount previous 2+ assignments for both levels and a choice of (3+, 5+) respectively agrees better with the total (n, n’) excitation and the ratios of the two components. The excitation of the 3.601 MeV and 3.840 MeV levels was obtained by subtracting the total observed scattering cross-section from the total cross-section and, as it was small, assignments of 3.601 MeV (4+) and 3.840 MeV (5+) were appropriate, (although a Of level would be excited to approximately the same extent as a 4+ or 5+ state). The remaining three levels at 2.958, 3.119 and 3.445 MeV are all quite strongly excited and assignments of 2+, 2-, 3+ or 3- were necessary to predict the right magnitudes of the cross-sections; all these 64 combinations were compared with experiment. These comparisons were found to be rather insensitive and there was not great statistical significance between the best and worst fits. However the better fits to the data did favour 2+ assignments to the 3.445 MeV level and, to a lesser degree, the 3.119 MeV level. Although a spin of 3 was slightly favoured in the case of the 2.958 MeV level the results were quite consistent with previous 2+ assignments. On the basis of these comparisons a suggested level scheme for Fe56 is as follows: ground state (Of), 0.845 MeV (2+), 2.085 (4+), 2.658 (2+), 2.940 (6+), 2.958 (2+), 3.119 (2+), 3.369 (3+), 3.388 (5+), 3.445 (2+), 3.601 (4+), 3.840 (5+). Fig. 6(c) shows some calculated angular distributions for this level scheme. Within the present experimental errors the shapes of the angular distributions were not strongly dependent on level spin and did not help to further resolve spin ambiguities. Fnally, excitation functions for the first two levels were calculated using the above level scheme, and fig. 7 shows the results. Using both an average ad hoc potential derived from the elastic scattering comparisons (Vc, = -48 MeV and Vc, = - 5 MeV) and also the Perey-Buck non-local potential the fit to the 0.845 MeV experimental data was poor as the two theoretical curves rise far too quickly. These calculations assume that the absorptive part of the optical potential is energy-independent. A similar behaviour has been observed previously for lead ‘l, 31) where it was ascribed in part to an increase in the imaginary potential with increasing neutron energy. Optical model fits to a wide range of elastic scattering data 32) have also indicated such a variation and there is theoretical support 33) for this assertion. In order to obtain a fit to the present excitation function it was necessary to use a variation (assumed linear) with channel energy of the form Vc, = - 1.75 En MeV which seems to be an excessively rapid variation. However this may be due to our assumption that the discrepancy was wholly due to energy dependence of V,, when it may partly be caused by imperfections in HF theory which can cause the excitation function to rise too rapidly near threshold ““),

5. Discussion Taking the present data together with recent (n, n’) measurements at Los Alamos34) and the low-energy work of Langsdorf et al. 35) and Cox 36), the elastic and inelastic

NEUTRON

scattering

of neutrons

by iron

SCATTERING

145

is now well documented

up to 5 MeV. The good

absolute accuracy of these data can be used to fix the scale for the Montague and Paul (n, n’y) results which give a reliable interpolation over the range 0.8 - 3.8 MeV. Interpolation of elastic scattering data between the energies studied can be made using the optical model potentials derived here. The non-local model also gave a reasonable representation of the elastic scattering above 2 MeV. In contrast, HauserFeshbach theory using transmission coefficients derived from energy independent potentials does not satisfactorily predict the excitation of the 0.845 MeV level which accounts for the bulk of the inelastic scattering in the energy region studied. However, the excitation curve can be fitted with standard Hauser-Feshbach calculations, although somewhat artificially, by using an energy-dependent imaginary potential and taking the J” assignments suggested above. There is no strong disagreement between the present assignments for the Fes6 levels and most of the previous information in table 7, though it should be remembered that the present (n, n’) data are rather insensitive for distinguishing between 2+ and 3- states, both of which would be strongly excited here. The 2.940 MeV level is apparently only weakly excited and probably has a spin J 2 5. The high spin (> 3) possibilities suggested for the 3.119 MeV level are strongly rejected and 2+ or 3are most likely; electron scattering evidence 3 “) supports the latter choice. A previous 2+ assignment 26) for the weakly excited 3.388 MeV level is probably wrong and best agreement was obtained here with J” = 5’. None of the earlier assignment for the 3.445 MeV level were eliminated but the present evidence points to a 2+ choice. Our present knowledge of the level scheme of Fes6 is still not sufficiently precise for us to make a detailed comparison with nuclear models. Inelastic scattering measurements with both electrons 30) and cc-particles 37) have established some collective behaviour for the levels at 0.845, 2.085, 2.685 and 3.119 MeV but at present there are no similar indications for the other levels studied here. Therefore it appears likely that the level structure consists of a mixture of vibrational and intrinsic particle excitations and a better understanding of the Fes6 nucleus must await more refined experimental and theoretical studies, We wish to thank Mr. A. D. Purnell for his valuable assistance during this work. We are also indebted to Mr. R. Batchelor for his encouragement and advice during the preparation of the manuscript.

References 1) K. Alder et al., Revs. Mod. Phys. 28 (1956) 432 2) W. Hauser and H. Feshbach, Phys. Rev. 87 (1952) 366 3) M. D. Goldberg, V. M. May and J. R. Stehn, Brookhaven 400, second edition (1962) 4) L. Cranberg and J. S. Levin, Phys. Rev. 103 (1956) 343; L. Cranberg and N. K. Glendenning, UCRL-9295 (1960) 5) H. H. Landon, A. J. Elwyn, G. N. Glasoe and S. Oleksa,

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