Progress in numerical calculations of ion-atom collisions

An ion-atom collision produces a time dependent perturbation of a many fermion system. In this collision, excitation, ionization and charge transfer can occur. The driving mechanism for these processes may be thought of as the potentials seen by individual electrons at any given separation of the projectile and target nuclei. If we think of these potentials as belonging to the target (a nucleus and electrons) and the projectile (another nucleus and electrons) then as detected by an electron the potentials change because: (a) the target and projectile change position, and (b) electrons on the target and projectile change states. Most work in the past fifty years has concentrated on solving the independent particle model (IPM). Cracks are beginning to appear in this model which only allows for type (a) changes in the potential. But in a short review we shall have quite enough to do in understanding the progress made in the last decade on the IPM. This paper is divided into three parts. The first deals with how to reduce the IPM to the single electron model (SEM). The second is on a new method where charge transfer is important. The third confronts some standard models with modern calculations