Dispersive versus constant-geometry models of the neutron- 208Pb mean field

Abstract

Phenomenological optical-model analyses of differential elastic scattering cross sections of neutrons by 208Pb indicate that the radius of the real part of the potential decreases with increasing energy in the domain 4 < E < 40 MeV. On the other hand, the experimental total cross section is compatible with a real potential whose radial shape is energy independent. In order to clarify this situation, we compare a “constant geometry” model whose real part has an energy-independent radial shape with a “dispersive model” whose real part has an energy-dependent radial shape calculated from the dispersion relation which connects the real and imaginary parts of the field. The following three main features are considered, (i) The junction of the optical-model potential with the shell-model potential at negative energy, (ii) The agreement between the calculated total and differential cross sections and their experimental values, (iii) The extent to which the real part of the optical-model potential can be accurately determined by analyzing the total cross section only. It is concluded that the presently available experimental data support the existence of an energy dependence of the radial shape of the real potential, in keeping with the dispersion relation. A new parametrization of a “dispersive” mean field is also presented. It does not involve more parameters than the previously published one but takes better account of the physical properties of the spectral functions; it is shown to improve the agreement between predicted and experimental scattering data.