In previous chapters interactions with structureless point charge projectiles have been considered. There are many interactions, however, which involve at least two atomic centers with one or more electrons on each center. In such cases the projectile is not well localized and there is a need to integrate over the non localized electron cloud density of the projectile. Evaluation of cross sections and transition rates for such processes requires a method for dealing with at least four interacting bodies. If multiple electron transitions occur on any of the atomic centers, then some form of even higher order many body theory is required. In general such a many body description is difficult.

In this chapter the probability amplitude for a transition of a target electron caused by a charged projectile carrying an electron is formulated. This probability amplitude may be used for transitions of multiple target electrons if the correlation interaction between the target electrons is neglected. Unless the projectile is simply considered as an effective point projectile with a charge Zeff, the interaction between the target and the projectile electrons may not be ignored. Since this interaction is between electrons on two different atomic centers, the effects of this interaction have been referred to as two center correlation effects (Cf. section 6.2.4).