Volume
35B, number
6
SMALL-ANGLE
PHYSICS
SCATTERING
LETTERS
OF
5 July 1971
NEUTRONS
BY
DEFORMED
NUCLEI
G. PALLA Central
Research
Institute
Received
for Physics,
Budapest,
Hungary
10 ikay 1971
It has recently been suggested that longrange interactions may be responsible for the “anomalous” small-angle elastic scattering on 232Th and 238 U. It is shown that the existence of an anomaly must be considered as a misinterpretation of the effect of nuclear deformation on the values of the differential cross-section.
Small-an le elastic scattering of neutrons by 238~ and 23 !! Th nuclei has long been studied, and an unexpected excess in the differential crosssection relative to the optical model values has been found at scattering angles below about 15’ [l-3]. It has been suggested that this increased small-angle scattering might be produced by long-range interactions namely those between the nuclear Coulomb field on the one hand and the magnetic moment and an induced electric dipole moment of the neutron on the other. However, even when the optical potential accounts for the long-range interactions and the extra strong spin-orbit interaction, and interference terms are considered in the differential cross-section, the optical model still does not explain the enhanced scattering [3-71. According to other suggestions the smallangle “anomaly” may be associated with specific features of the nuclei in question, namely with the o-instability [B] and the fissionability [3]. In an attempt to interpret the enhanced scattering in terms of the a-decay or fission process, it was shown experimentally that contributions from the (n, cm’) or (n, nf) ractions fail to explain the “anomaly” [9]. The spherical optical model has turned out to be completely inappropriate for interpretation of nucleon scattering by deformed nuclei. In view of the large deformation of the 238U and 232Th nuclei a more realistic model in which their nonspherical shape is considered would be desirable. In the present work the coupled differential equation formalism elaborated by Tamura [lo] has been applied to the analysis of the neutron elastic scattering on 238~ and 232Th at 14.7 and 15 MeV neutron energy, respectively. The ex-
perimental scattering and total cross-section data were taken from references [ll, 121 for 238~ and [2,12,13] for 232Th. The cross -section calculations were per formed by the JUPITOR code [13] on an ICT 1905 computer. It was assumed that the coupling of other than O’, 2+ and 4+ states of the lowest rotational band is negligible; thus they were included in the imaginary part of the potential. The Wilmore-Hodgson optical potential was used with modified absorption strength, because the above inelastic channels were taken into account directly. The parameters of this potential are given in table 1; /32 values were taken from experimental data on Coulomb scattering [14]. It should be noted that elastic scattering data on uranium and thorium contain a considerable contribution from inelastic scattering because of the finite energy resolution and the low lying nuclear levels, and thus a sum of elastic and some of the inelastic scattering cross-sections must be fitted to such experimental data:
u(e)=u(“+n,n) + 22 a); 1=2
4
) 12,)
?
9
where the second term gives the contributions from the first 2+ and 4+ states being calculated simultaneously.
Parameters
Table 1 of the optical model potentials
238u
43
8.5
8.3
1.25
0.66
0.48
0.24
232Th
43
8.3
8.3
1.25
0.66
0.48
0.25
477
Volume
35B, number
PHYSICS
6
Fig. 1. Differential
cross-sections
Fig. 2. Differential
cross-sections
for 14.7 MeV neutrons values. The experimental
5 July 1971
LETTERS
scattered from uranium calculated data are from ref. [ll].
for 15 MeV neutrons scattered from thorium The experimental data are from ref. [Z, 131.
calculated
with different
with different
@2
p2 values.
Good fits to the experimental data were obtained for both nuclei. The results are shown in figs, 1 and 2 and in table 2. In order to demonstrate the effect of the deformation on the smallangle differential cross-section the results of the calculation with different p2 values and spherical optical potential are also shown.
It is concluded that the small-angle scattering on 238~ and 232Th observed about 14 MeV energy can be correctly interpreted on the basis of an optical model including the nuclear deformation. So the earlier views on the existence of “anomaly” are to be considered as misinterpretations of the phenomenon of enhanced scattering.
Table 2 Comparison of the experimental and calculated total cross-section values
The author is indebted to Dr. Gy. Bencze for his valueable remarks.
Nucleus
478
0:::
(barn)
238U
5.810.2
232Th
6.OkO.15
References [l] Y. A. Aleksandrov, G. V. Anikin and A. S. Soldatov Zh. Eksp. i Teor. Fiz. 40 (1961) 1878; Soviet Phys. JETP 13 (1961) 1319.
Volume
35B, number
6
PHYSICS
LETTERS
[2] Y. V. Dukarevich and A. H. Dyumin, Zh. Eksp. i Teor. Fiz. 44 (1963) 130; Soviet Phys. JETP 17 (1963) 89.
5 July 1971
[8] P. Hrask6 and 2s. Kovessy, Acta Phys. Hung. 20 (1966) 227. [9] A. Adam, P. Hrask6 and G. Prilla, Phys. Letters 22 (1966) 475. [lo] 1. Tamura, Rev. Mod. Phys. 37 (1965) 679. [ll] A.Adam, F. Desk, P. Hrask6, L. JCki, A.Kiss, 2s. Kovessy and G. Palla, Acta Phys , Hung. 25 0968) 261. [12] k. J. Howerton. UCLR-5226, UCRL-6351. [13] T. Tamura, Computer Program JUPITOR-1 for Coupled Channel Caluclations ORNL-4152/19706. [14] G. H. Fuller and L. W. Cohen, Nuclear Data Tables A5 (1969) 433.
[3] A. J. Elwyn, J. E. Monahan, R. 0. Lane, A. Langsdorf Jr. and F. P. Mooring, Phys. Rev. 142 (1966) 758. [4] R. F. Redmond, Phys. Rev. 40 (1965) B1267. [5] D. B. Fossan and M. Walt, Phys. Rev. Letters 12 (1965) 672. [6] G. V. Anikin and I. I. Kotuhov, Jadern. Fiz. 12 (1970) 1121. [7] H. S. Lebedeva and V. M. Morozov, Zs. Atomnaja Energia 28 (1970) 4.
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