Nonrelativistic description of nucleon-nucleus scattering

Abstract

Within the three-dimensional semiclassical approximation, an analytic expression is obtained for the amplitude of proton-nucleus scattering at intermediate energies of incident protons. The method for deriving this amplitude is based on the use of the high-energy approximation with distorted waves. In view of the short-range character of proton-nucleon interaction, the process of proton-nucleus scattering is represented as a series of single scattering events occurring on each individual nucleon. With the aid of the proposed mathematical formalism, a recursion relation is derived that makes it possible to express the nuclear form factor obtained within the distorted-wave method in terms of the sum of an infinite Born series. Parameters that characterize the distributions of protons and neutrons in the spherical nuclei ⁴⁰Ca, ⁴⁸Ca, ⁹⁰Zr, and ²⁰⁸Pb and which include the width of the surface layer of nucleons and the root-meansquare radii of the proton-, neutron-, and nucleon-density distributions are determined from an analysis of the measured cross sections for the elastic scattering of 1-GeV protons, a modified Fermi function being employed for the nucleon-density distribution.