Introduction

The accurate solution of the Schrödinger equation (SE) for electron-impact collisions leading to discrete elastic and inelastic scattering progressed rapidly with the increase in computing power from the 1970s. A review of the principal methods, including second Born, distorted wave, R-matrix, intermediate-energy R-matrix, pseudo-state close coupling and optical model is given in [1]. However, electron impact collisions leading to ionization on even the simplest atom, hydrogen, were by comparison poorly described; significant progress dates only from the early 1990s when Bray and Stelbovics [2] developed a technique called convergent close coupling (CCC). In this approach they used an in-principle complete set of functions to approximate the hydrogenic target states, both bound and continuous, and used the coupled channels formalism to expand the scattering wave function in these discretized states, reducing the solution of the SE to a set of coupled linear equations in a single co-ordinate. The method was tested in a non-trivial model [3] and shown to provide convergent cross sections not only for discrete elastic and inelastic processes but also for the total ionization cross section. Shortly thereafter the method was applied to the full collision problem from atomic hydrogen and one of the major achievements of the method was that it yielded essentially complete agreement with the (then) recent experiment for total ionization cross section [4]. In the following years, the method was applied to other atoms with considerable success; the range of applications of CCC are covered in the review of Bray et al. [5].