The Coupled-Channels Integral-Equations Method in the Theory of Low-Energy Electron-Molecule Scattering

Abstract

The part of this workshop that is devoted to electron-molecule collisions is concerned with two somewhat complimentary classes of approaches to this problem: L2-variational methods, such as the R-matrix and T-matrix methods, and eigenfunction-expansion methods, such as the close-coupling or coupled-channel method. The former approaches are discussed in accompanying articles by Schneider and by Fliflet. In this paper, we shall be concerned with the coupled-channels method for low-energy electron-molecule scattering.1–4 Various aspects of the physics of electron-molecule collisions have been discussed in detail elsewhere. Thus the present review will emphasize techniques for solving the problem. We first describe how to formulate and carry out such a calculation (Secs. II and III) and then suggest where likely pitfalls lie and ways to avoid them (Sec. IV). Since most of the applications to date of the coupled-channel method have employed approximate local potentials, the development in this paper will deal primarily with the solution of differential equations via an integral-equations algorithm. The case of integrodifferential equations (which arise when electron exchange effects are rigorously taken into account) will be discussed briefly in Sec. V.