Threshold Effect in Elastic Scattering According to the Optical Model

Abstract

An expression is derived for change in the differential elastic scattering cross section caused by the presence of a reaction threshold, in a situation in which it is useful to average over many compound resonances. The derivation is based on the assumptions underlying the optical model and on the usual statistical assumptions made in the evaluation of energy-averaged cross sections. In essence the derivation gives the angular distribution of that part of the fluctuation cross section which is caused by the reaction, and relates this in a simple way to the reaction cross section.It is shown, although not in a rigorous manner, that for closelyspaced resonances an energy average of the usual Wigner cusp expression, as given by Baz and Newton for example, yields the previously calculated threshold effect on the differential elastic scattering cross sections. Also an expression is given for the threshold effect on the differential elastic scattering cross section in a situation in which the phase shift of each partial wave consists of a part that varies slowly with energy and a part that fluctuates about zero as the energy of the bombarding particle is changed.For simplicity all calculations are restricted to the case of spinzero target nucleus and spin-zero and spin-one-half bombarding particle. Furthermore, the derivations assume that only one incident partial wave is dominant in the reaction cross section near threshold. The calculations are applied to recent measurements of Wells, Tucker, and Meyerhof of the differential elastic and inelastic neutron scattering cross sections of cerium in the neighborhood of the threshold for excitation of the 1.60-MeV, ${2}^{+}$, first excited state of ${\mathrm{Ce}}^{140}$. It is shown that the computed threshold effect appears to account completely for a marked decrease which had been found in the differential elastic scattering cross section of Ce above 1.60-MeV.