Neutron Total Cross Sections, 2.5-15 MeV. II. Effects of Nuclear Deformation

Abstract

A spherical nonlocal optical-model analysis was performed on a homogeneous set of moderate-precision neutron total cross sections for 78 elements and 14 separated isotopes. The presence of fluctuations in the cross sections prevents the effective application of the optical model for nuclei with $A<45$ unless the data are averaged over many experimental resolution widths. The dependence of the magnitude of the fluctuations on the ground-state spin of the target nucleus was observed. The analysis of the data for 46 spherical or soft nuclei within the regions $46<~A<~150$ and $188<~A<~206$, 2 transitional nuclei within the region $185<~A<~187$, and 19 hard-deformed nuclei within the regions $152<~A<~184$ and $228<~A<~239$ clearly indicates the effects of nuclear deformation. The spherical nonlocal optical potential of Perey and Buck describes (within 3%) the interaction of fast neutrons ($3.0<~{E}_{n}<~15.0$ MeV) with 46 spherical or soft nuclei. The analysis yields considerably less accurate (17%) results for the 19 hard-deformed nuclei. The surface thickness is approximately the same for all spherical nuclei (with the possible exception of light nuclei below $A=46$), to the extent that the nonlocal optical potential has the same form as the nuclear-matter distribution. The systematic nature of the deviations of the data from the theoretical predictions leads to a conjecture which spans the mass range $45<~A<~239$.