Elastic Scattering

Abstract

Since it provides rich information on atoms and molecules interacting at relatively low energies and is responsible for many thermodynamic and transport phenomena, elastic scattering is not only of practical interest in its own right, but also has provided exploratory ground for theorists aiming to develop theories for more complicated scattering phenomena. The theories now have been well worked out in many directions [4.1–19], but we shall take up the subject here to develop some basic theoretical tools to be applied later to some problems of practical interest. We shall first consider the simple WKB approximation to elastic scattering and then discuss corrections of the WKB result by using uniform semiclassical wave functions, which simplify discussions of multiturning-point problems. Since one of the aims of this monograph is to develop approximation formulas useful for experimentalists, we shall also consider some procedures for calculating phase shifts, given a potential function. The differential equations of interest here are either a one-dimensional Schrödinger equation in the Cartesian coordinate representation or the radial Schrödinger equation in the spherical coordinate representation. We consider the WKB approximation for the Schrödinger equation in the prolate-spheroidal-coordinate system in Chap. 11, where scattering by an ellipsoid particle is discussed.