The fission cross section of 228Th near threshold

Nuclear Physics @ North-Holland

THE

A419 (1984) 497-508 Publishing Company

FISSION

CROSS

SECTION

G.D. Nuclear Physics Division, UKAEA,

JAMES

OF =Th and

D.B.

NEAR

THRESHOLD

SYME

Atomic Energy Research Establishment, Harwell, England and J. GRAINGER

Physics Department, Queen Mary College, University of London, England Received

13 October

1983

Abstract: The fission cross section and fragment angular distribution for the reaction Z28Th(n, f) have been measured over the neutron energy range 350 keV to 1200 keV at values of the neutron energy resolution in the range 20 keV to 37 keV. An absolute determination of the fission cross section at 1635 keV gave the value 370 * 32 mb to which the data are normalised. Forty crosssection data points are available but only twenty-two of these allow a trustworthy anisotropy to be quoted. The data confirm the structure noted by Vorotnikov et al. near 450 keV and at 1.1 MeV but also reveal a pronounced resonance at 760 keV. The fragment anisotropy values are predominantly forward peaked and indicate a spin projection K =f for all resonance groups. The way in which the results reflect on our understanding of the fission potential barrier is noted.

E

NUCLEAR observed

REACTION sub-threshold

228Th(n, f), E = 350-1200 keV; fission cross-section resonances;

measured Us, dvr(E)/dfl; deduced spin projection K.

1. Introduction Over the past fifteen years detailed measurements on structure in sub-threshold fission cross sections combined with theoretical advances have greatly enhanced our knowledge and understanding of the fission potential barrier. Research which unravels the intricacies of the double-humped fission potential barrier has been comprehensively reviewed by Bjornholm and Lynn ‘). Measurements 2,3) on the thorium isotopes 230Th and 232Th have played an important role in this work by revealing the “thorium anomaly”, a discrepancy between experimental and theoretical estimates of the height of the inner barrier and the second minimum of a double-humped barrier. Developments based on the work of MGller and Nix “) indicate how this anomaly may be resolved in terms of a triple hump in the fission potential barrier 576). E ven so, a totally acceptable fit to the best available fission cross-section and fragment angular distribution data on 230Th has yet to be produced. It seems likely that improved cross-section and fragment angular distribution measurements for a lighter actinide, 228Th, would provide further valuable tests for 497

498

G.D. James et

the theories of the fission potential such measurements.

al. / Fission cross section

barrier.

The aim of this paper

is to report

There are no previous measurements of fragment angular distribution reaction 228Th(n, f), but the cross section has been measured by Vorotnikov

on

for the et al. ‘).

These results, measured with a neutron energy resolution of 100 keV, show considerable cross-section structure near threshold, notably resonances at about 450 keV and 1.1 MeV and a shelf at about 800 keV. The data presented here cover the neutron energy range 350 keV to 1200 keV and were made at values of neutron energy resolution mostly in the range 20 keV to 37 keV. Although 40 cross-section data points are available, only 22 of these allow a trustworthy anisotropy to be quoted. The cross-section data confirm the resonances reported by Vorotnikov et al. at about 450 keV and 1.1 MeV but also indicate a pronounced resonance at 760 keV with an observed width of 55 keV. Almost all the fragment anisotropy data are forward peaked and indicate a spin projection K = 0.5 for the three resonance regions observed. The 20 pg sample of 228Th used in this experiment and the 16 mCi of gaseous daughter product 220Ra presented a radiological hazard. The experimental arrangement and the precautions taken to counter this hazard are described in sect. 2. The fission fragments were detected in a cylindrical arrangement of Makrofol KG which enabled their spatial distribution to be determined after etching and sparking under carefully controlled conditions. A complete description of the processing methods used to derive the fragment angular distribution has already been published “). Only a brief resume of these methods is given in sect. 2. The fission cross-section data are normalised to an absolute value deduced from an absolute determination of the neutron flux and fission-fragment count rate at the normalisation energy, 1.635 MeV. This determination fission cross-section

and the corrections involved are described in sect. 3. The 22XTh and fragment angular distribution results obtained are presented

in sect. 4. Finally, in sect. 5, the way in which the results obtained reflect on our understanding of the fission potential barrier and the pointers they give to further work are noted.

2. Experimental

arrangement

and procedure

In this experiment, the neutrons are produced from the ‘Li(p, n) reaction using a 2 mm diam. proton beam from a 6 MeV Van de Graaff generator and a LiF target. The arrangement of fissionable foil and Makrofol detector is illustrated in fig. 1. The proton beam direction passes through the centre of the fissionable deposit which is spread uniformly over a circular area of 20 mm diam. The deposit is of 20 Pg 228Th. The detector consists of a cylindrical surface of 10 pm thick Makrofol KG, 100 mm long and 200 mm diam. together with a disc of Makrofol 200 mm diam. The axis of the Makrofol cylinder is set along the proton beam direction. The disc is made of two semicircular pieces of Makrofol cut from a roll 100 mm wide.

499

G.D. James et al. / Fission cross section

Makrofol surface

Axis of detector geometry

Neutron dire&on ICQmm

228 Th fcil CUmm dvzml Fig. 1. Geometry

of cylindrical

Makrofol

detector,

fission target

and ‘Li neutron

source.

The Makrofol is kept in position by attachment to a cylindrical backing of polythene 1.5 mm thick using small pieces of adhesive tape. The fission foil and Makrofol detector are housed in a cylindrical steel vacuum chamber 253 mm diam. and 750 mm long which is pumped to a pressure of about 0.03 Torr (fig. 2). The fission foil is attached to an end face which is 0.7 mm thick over an inner diameter of 100 mm. The thickness is chosen to reduce scattering corrections while ensuring accurate positioning of the foil. The Makrofol detector on its polythene support fits tightly into a shallow cylindrical cap made of 0.5 mm Cu sheet and carried on a long trolley which runs on rails in the chamber. The polythene

backing

and copper

holes which help to ensure

c

former

are punctured

that the Makrofol

Mmn

by a number

stays in position

of 20 mm diam. as the chamber

is

3

Fig. 2. The cylindrical detector chamber. The Makrofol detector is retained in a shallow copper cylindrical cap carried on a trolley (not shown) which runs on rails in the chamber and is spring-loaded into position by the chamber face furthest from the foil through which the detector is loaded into the chamber.

G. D. James et al. / Fission cross section

500

evacuated. mounted

The Makrofol

cylinder

on the end of the trolley

is held against and pushing

the foil-bearing against

which the trolley and detector

are loaded into the chamber.

the detector

from a position

foil to be loaded

At this position

the radiation_field

one metre

plate by a spring,

the far end face through This arrangement

allows

away from the fission foil.

from the 20 pg **‘Th foil is 6 mR/h.

The loading

face of the chamber is sealed into a glove box, through which the chamber is loaded, to contain the hazard presented by 16 mCi of the gaseous daughter product ‘*“Rn. The glove-box pressure is reduced to 13 Torr below atmospheric pressure by means of a Secomak pump, the exhaust of which is delayed, in a polythene bag with a double skin, for at least 0.5 h before venting to the atmosphere through a glass fibre filter. The exhaust of the fission chamber vacuum pump is similarly delayed. The method used to process the Makrofol sheets by etching and sparking under carefully controlled conditions and the corrections applied for hole overlap, background counts and fragment detection efficiency have been fully described elsewhere “). For some detector foils exposed to 228Th, there is a significant increase in background when the foils are etched to below 9 pm. This probably results from damage due to a-bombardment and precludes, for these foils, the derivation of results at lower thicknesses. At 9 pm the background for plastic foils exposed to the **‘Th source is 21 counts for 900 cm*. Fig. 3 shows the efficiency of detection for foils reduced to 9.5 km and 9 km. Only the values at the positions indicated by the open circles, drawn at the average value of the fragment entry angle (Yfor each bin, are used in data reduction. For a foil thickness of 9 km the minimum value of detector efficiency is 0.93. Experimental runs are normalised to equal numbers of incident neutrons by means of a long counter situated on the beam axis behind the vacuum chamber and 1870 mm from the LiF target. In one series of measurements a 235U-bearing

Fig, 3. Fragment detection efficiency as a function of fragment angle for two etched thicknesses of Makrofol. Only the values shown by circles, and corresponding to the mean angle of fragment emergence a for each angular bin, are used in data reduction. Thus the minimum efficiency used for 9 pm foil is 0.93.

501

G. D. James et al. / Fission cross section

ionisation

chamber

was used to confirm

this normalisation

to within

2%. Also, an

absolute flux scale was established from the known properties of the long counter “). This scale was corroborated from a measurement of the proton beam current and the properties of the 7Li(p, n) reaction and also by a measurement of the yield of fragment mass 140 in the neutron-induced fission in a disc of 23xU. The neutron energy resolution is determined by the value of the energy loss of protons in the LiF at the energy of the experiment, and, because of the kinematic spread in neutron energies over the fission target, by the distance between the LiF target and the fissionable deposit (28 mm). The proton energy loss is found by measuring the rise in neutron yield in the proton beam direction at the threshold of the 7Li(p, n) reaction. This measurement also allows the proton energy indicated by the Van de Graaff instrumentation to be referenced to the known threshold energy, 1.881 MeV [ref. I”)]. The peak of the distribution occurs at an energy roughly neutron

equal to the proton energy loss in the target below the maximum possible energy. For a LiF to fissionable target distance of 28 mm, the decrease in

neutron energy from the centre to the perimeter of the 20 mm diam. 228Th foil varies almost linearly with neutron energy from 21 keV at 500 keV to 30 keV at 1 MeV. At 750 keV this energy decrease is 25 keV. A range of proton target thicknesses from 14 keV to 44 keV was used during the experiment. Of the 40 runs, 35 have proton target thicknesses in the range 20 keV to 37 keV. Half the runs are grouped around two target thicknesses, 25 keV (12 runs) and 36 keV (8 runs). The resolution functions resulting from convoluting three of these proton target thicknesses with a 25 keV energy fig. 4.

drop

across

the fissionable

The angular resolution function has been calculated The results obtained for a LiF-target to fissionable-foil illustrated

in fig. 5. Table

1 lists the nominal

target

are illustrated

as described separation

in

previously ‘). of 28 mm are

bin range and angle, the average

value

of the reaction angle 0 recorded in a bin and the average value of the angle LYat which fragments emerge from the foil for each bin. For small angle bins, the nominal angles differ considerably from the average value of reaction angle recorded. This shift has a marked effect on the anisotropy derived from the data. Except for the 4.5” bin, the average bin angle.

value of the angle of emergence

3. Absolute

(Yis within 0.5” of the nominal

fission cross section at 1.635 MeV

A value for the absolute fission cross section was determined at the normalisation energy 1.635 MeV. It is derived from the fission count rate from a known mass of 228Th when irradiated in a known neutron flux. The mass of 22RTh was found, by low geometry cY-spectrometry, to be 20.7 *0.4 pg at the time of foil fabrication. The mass on subsequent dates was found from the 228Th half-life 1.9131 *to.0009 y. The fission count rate is derived from the observed number of holes in the Makrofol

G.D. James et al. / Fission cross section

so2

0.3 r

Shift from maximum ntiton

energyIkeV)

Fig. 4. Resolution functions for three values of the proton target thickness used in the experiment. These are 14 keV for curve 1, 25 keV for curve 2 and 36 keV for curve 3. These curves are calculated by convoluting a rectangular function corresponding to the thickness of the proton target with a function which describes the kinematic change in neutron energy with angle over the fissionable deposit. They give not only the resolution width but also the neutron energy shift down from the maximum neutron energy in the direction of the proton beam.

detector as discussed in the previous section. The neutron flux at the 228Th foil is determined from the strength of the ‘Li(p, n) neutron source. This is derived from the number of counts observed in the long counter which had been standardised “) in terms of an equivalent

point source.

Corrections TABLE

Average

reaction

Bin range

to the fragment

1

angle 0 and angle of emergence bin for the case I= 28 mm Nominal

bin angle

a for each angular

(deg.)

(deg.)

(0) (deg.1

(ff) (deg.)

O-Y

4.5 13.5 22.5 31.5 38.0 42.0 50.5 58.5 67.5 74.0 78.5

17.75 20.39 25.74 33.09 38.89 42.62 51.39 59.03 67.65 73.82 78.23

6.73 14.00 22.62 31.45 37.85 41.84 50.60 58.63 67.61 74.00 78.54

9-18 18-27 27-36 36-40 40-44 47-54 54-63 63-72 72-76 76-8 1

count

rate and

503

G.D. James et al. / Fission cross section

0.25

90

120

Reaction angle 9 (degl Fig. 5. Distribution

neutron

of the reaction

flux were made

angle

0 for each of the angular

for the presence

bins used in the experiment

of a low-intensity

low-energy

neutron

component “) in the ‘Li(p, n) reaction and also for the effect of neutron scattering from parts of the experimental equipment. For the fragment counts, corrections are also made for the angular dependence of neutrons from the ‘Li(p, n) reaction, for flux non-uniformity due to the plane geometry of the foil, and, on the assumption of fragment isotropy, for the nominal angle (81’ to 90”) for which data are not recorded. In addition, for the long counter, a correction is made for neutron scattering

from the 1870 mm of air separating

Five determinations a weighted mean observed fission an error derived The measurement follows:

error

it from the neutron

source.

of the absolute

22RTh fission cross section at 1.635 MeV gave value of 370.0 mb. The weights are derived from the number of counts. The five determinations are in close agreement and give from the weighted deviations from the weighted mean of 0.6%. is subject to three other sources of error which contribute as

in the solid angle subtended

by the ***Th foil at the neutron

source,

7.1%; error in the long counter calibration and the correction factor for neutron scattering and the low-energy neutron group, 4.5%; error in the 228Th mass determination, 2%. These give a combined error of 8.7% and a value for the 228Th fission cross section at 1.635 MeV of 370*32 mb. Two of the five determinations described above allowed an independent estimate of the neutron flux from the induced activity in a 1.482 g 20 mm diam. 238U disc placed outside the vacuum chamber immediately in front of the **‘Th foil. For these runs additional scattering corrections are made for the presence of the uranium disc. The neutron flux is determined from the growth and decay of the activity of the 1.596 MeV y-ray from 14”La measured by a calibrated Li(Ge) detector.

504

Although neutron

G.D. James et al. / Fission cross section the observed flux deduced

the difficulties

14”La activity

was determined

from this measurement

encountered

which was much stronger

in calibrating

to high precision

was limited

the Li(Ge)

than the line under

in accuracy

detector

investigation.

by means Within

(l%), to *17%

the by

of a source

this error,

the

neutron flux agrees with that derived from the long counter. The neutron flux was also estimated from a measurement of the proton current and the properties of the ‘Li(p, n) reaction I’). Due to current leakage, associated with the way in which the LiF target is cooled, the proton current could only be measured to an accuracy of zt20%. that derived from the long counter.

Within

this error,

4. Fission cross section and fragment

the neutron

flux agrees with

angular distribution

The results obtained for the 22XTh fission cross section and 20”/80” fragment anisotropy are listed in table 2 at forty values of neutron energy in the range 350 keV to 1200 keV. The table also gives the LiF target thickness used at each neutron energy, a relative correction factor, and the chi-squared per degree of freedom obtained when fitting the angular distributions. The fission cross-section data are normalised to the value 370 mb at 1.635 MeV determined in sect. 3. At each energy, the fission cross section is the product of a normalisation constant, a relative correction factor and the number of fission counts relative to the number of neutron counts. The experimental runs fall into three groups each with its own normalisation constant. These constants were determined with standard deviations of 4.7%, 4.2% and 2.3%. The relative correction factor is the ratio of the correction factor at each energy, for neutron scattering and the low-energy neutron group as noted in sect. 3, divided by its value at 1635 keV. The error in the correction factor at 1635 keV is contained in the error on the absolute fission cross section. At other energies the relative correction factor entails an additional error of 1.7% due to the limitations of the data mesh from which the factor is calculated. Except at the normalisation energy, the errors quoted in table 2 are derived from a combination of the error in the normalisation constant, a 1.7% error in the relative correction factor, and the Poisson error in the number of fission and neutron counts. The total error in the cross section at each energy is derived by combining the errors given in table 2 with the 8.7% error in the normalisation cross section. Fragment anisotropy values are quoted for only twenty-two values of neutron energy. These are the only measurements for which the chi-squared per degree of freedom for the fragment angular distributions lie within the 99% probability value for chi-squared. Clearly the data are subject to larger errors than those ascribed by the standard statistical procedures used to derive the errors quoted. Above a neutron energy of 925 keV, where all the cross-section values exceed 250 mb, the statistical behaviour of the data is more acceptable. In this energy range, 10 results out of 13 (77%) are accepted at the 99% level. Of the 40 results, 35 were regarded as indicating forward

505

G. D. James et ai. / Fission cross section TABLE

2

‘*aTh fission cross section and 20”/80” Neutron energy WV)

Proton target thickness CkeV)

Relative correction factor

Cross section (mb)

fragment anisotropy XL

Error bnb)

Error

0.85 3.25

0.15 1.33

1.61 2.60

2.15

0.8

2.46

1.79

0.31

2.19

1.52 1.12

0.07 0.12

2.02 1.41

1.48 3.11

0.16 0.64

1.52 1.42

2.26 1.39 0.98

0.28 0.24 0.03

2.45 2.32 1.68

1.47

0.11

2.23

1.84 2.17 1.76

0.05 0.08 0.15

0.45 0.6 1.33

2.01

0.09

0.41

2.03 1.83 1.87 2.15 2.07

0.09 0.13 0.08 0.12 0.12

0.52 1.93 0.59 1.02 1.30

1.5

0.07

0.78

-

350 375 393 400 425 442 450 470 500 530 540 560 590 625 650 660 700 725 740 750 775 780 800 820 825 860 900 925 950 975 Y96 1000 1025 1050 1075 1100 1125 1150 1175 1200 1635

19 22 29 26 25 16 37 25 31 26 37 28 27 24 24 36 36 25 36 23 27 36 25 36 27 36 33 20 22 25 16 15 25 14 25 21 28 22 22 25

0.846 0.839 0.833 0.831 0.838 0.816 0.844 0.890 0.920 0.946 0.951 0.962 0.977 0.966 0.974 0.974 0.970 0.968 0.981 0.981 0.980 0.982 0.989 0.997 0.998 1.010 1.014 1.027 1.031 1.028 1.016 1.014 1.021 1.028 1.035 1.021 1.020 1.049 1.049 1.044 1.000

50.5 30.9 36.0 29.9 16.7 32.9 48.8 44.8 37.0 25.9 23.2 25.8 27.3 23.8 8.9 25.9 57.1 131.6 188.7 228 194 199 91.9 164.0 142.0 177 230.3 344 315 339 338 352 332 342 332 331 258 263 253 302 370

5.5 3.0 3.7 4.1 2.0 2.8 3.7 3.2 1.9 1.9 1.5 1.4 1.9 2.5 1.1 1.6 3.0 8.5 9.7 12 14 10 6.7 9.0 9.7 11 8.4 13 19 23 19 23 21 22 19 15 16 12 16 18 32

(per degree of freedom)

Anisotropy

506

peaking spin-J

G.D. James et al. / Fission cross section

of the fragment components

ate symmetric

top wave functions

and were analysed was imposed ponents.

anisotropy

and were analysed

of a spin projection

K = 4 distribution

I*). The remaining

using two components

by the unacceptable

using four

as defined by the appropri-

five results are sideways peaked

of J, K values,

fits generated

by least-squares

when

I, 4 and $, 1. This limitation using more

than two com-

The cross-section and fragment anisotropy results of table 2 are illustrated in fig. 6. The errors shown are those quoted in table 2 and, except at 1635 keV, they do not include the 8.7% error in the normalisation cross section. The general form of the cross section structures near 760 keV has not of 55 keV when at this resolution

published by Vorotnikov et al. is confirmed, notably the resonant 450 keV and 1.1 MeV. However, the pronounced resonance at been previously revealed. This resonance has an observed width measured with an energy resolution of about 30 keV. Measured the resonance is smooth and shows little sign of detailed structure.

In this respect and in width it is similar to the resonance at 715 keV in the fission cross section ‘) of ““Th. By contrast the resonance at 500 keV covers a greater neutron energy range and seems to show some detailed structure.

5. Discussion The results obtained in this experiment give an absolute value for the **‘Th fission cross section at 1.635 MeV, a measurement of the fission cross-section structure observed near threshold, and a measurement of the fission-fragment angular distribution near threshold. The absolute value of the fission cross section of 228Th at 1.635 MeV, 370 * 32 mb, is about three times greater than the value 126 mb recorded by Vorotnikov et al. ‘). However, it is only about a third of the value of 1300 mb expected from the systematic behaviour of the plateau values of fission cross section which show an almost linear dependence 13) on Z4”/A. This discrepancy may arise because

at 1.635 MeV

the “‘Th

fission

cross

section

may not have

reached

its

plateau value and may still be influenced by strong fluctuations. The fission cross-section structure observed near threshold confirms the results published by Vorotnikov et al. ‘) except for the pronounced resonance at 760 keV. This resonance is strongly reminiscent of the resonance at 715 keV in the fission cross section of 230Th and is most probably another example of a vibrational resonance. The angular distribution data are generally forward peaked and indicate K =i for most of the resonances observed. The observed anisotropy is not quite as strong as for *“OTh and this may indicate a considerable admixture of states with K >i. Lynn “) has investigated this possibility by studying the deviation, due to coupling of single-particle and vibrational motions, of the properties of low-lying states associated with secondary and tertiary wells from the expectations of a more simple transmission model. These deviations are found to be considerable. Lynn shows that, particularly for 228Th, this coupling can give rise to gross resonance

507

G. D. James et al. / Fission cross section

01

I

500

I

I

IOCQ

1500

Neutron Fig. 6. The fission cross section and 20”/80” fragment 350 keV to 1200 keV measured with neutron energy

anisotropy resolution

energy

(keV1

for the reaction *“Th(n, f) from in the range 20 keV to 37 keV.

structure in the fission cross section with very different parameters from those expected in a pure transmission model of the fission barrier, notably a strong admixture of states with higher values of K. The results obtained in the present experiment are qualitatively in agreement with these theoretical developments.

G.D. James et al. / Fission cross section

508

By improving

the neutron

energy resolution

of measurements

on 228Th the present

experiment threshold.

has revealed a richness of structure in the fission cross section near The experiment has also provided a good indication of the fragment

anisotropy

in the vicinity of this structure.

The results are of interest

in corroborating

the predictions of certain theoretical developments. They indicate strongly the need for measurements with better energy resolution, perhaps as high as 5 keV below 1 MeV and, if the cross section at 1635 keV is indeed influenced by strong fluctuations, with good resolution up to about 3 MeV. On a highly radioactive material like 228Th such measurements will not be easy. Improvements could be achieved, without increasing the mass of 228Th used, by using a high voltage generator like the Dynamitron which can provide several hundred micro-amps of proton beam current. This work could not have been carried out without the help of many people to whom the authors are grateful. At all times, Dr J.E. Lynn has given us full support and encouragement. The fissionable material was provided by Mrs K.M. Glover, Dr B. Whittaker made the 22XTh foil, loaded it into the fission chamber and carried out the mass determination. Much of the equipment was assembled with the help of Mr M.A. Wilkins.and Mr A.D. Gadd. Calibration constants, needed to convert the long counter data to an equivalent point source, were kindly supplied by Dr J.M. Adams. Mr I.R. Collingwood and his staff gave valuable guidance on radiological protection and provided monitoring support. The high voltage generator was run by operators who were always most helpful.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) IO) 11) 12) 13) 14)

S. Bjornholm and J.E. Lynn, Rev. Mod. Phys. 52 (1980) 72.5 G.D. James, J.E. Lynn and L. Earwaker, Nucl. Phys. A189 (1972) 225 J. Blons, C. Mazur and D. Paya, Phys. Rev. Lett. 35 (I 975) 1749 P. Moller and R. Nix, Physics and chemistry of fission, vol. 1 (IAEA, Vienna, 1974) p. 103 J.W. Boldernan. D. Gogny. A.R. de L. Musgrove and R.L. Walsh, Phys. Rev. C22 (1980) 627 J. Blons, C. Mazur, D. Paya, M. Ribrag and H. Weigmann, Int. Winter Meeting on nuclear physics, Bormio, 1980 P.E. Vorotnikov, Z.S. Gladkikh, A.V. Davydov, SM. Dubrovina, G.A. Otroshchenko, E.S. Pal’shin, V.A. Shigin and V.M. Shubko, Yad. Fiz. 16 (1972) 196; Sov. J. Nucl. Phys. 16 (1973) 505 G.D. James, D.B. Syme and J. Grainger, Nucl. Instr. 205 (1983) 151 J.M. Adams, A.T.G. Ferguson and’C.D. McKenzie, report AERE-R6429 (1970) M.L. Roush, L.A. West and J.B. Marion, Nucl. Phys. Al47 (1970) 235 H. Liskien and A. Paulsen, At. Nucl. Data Tables 15 (1975) 57 E.P. Wigner, Group theory and quantum mechanics, transl.: J.J. Griffin (Academic Press, New York, 1959); see also refs. ‘,‘) R.L. Henkel, Fast neutron physics, ed. J.B. Marion and J.L. Fowler (Interscience, New York, 1963) p. 2001 J.E. Lynn, J. of Phys. G9 (1983) 665