Eikonal theory of electron- and positron-atom collisions

We review recent developments in the application of eikonal methods to the field of electron and positron collisions with atoms. The foundations of the eikonal approximation are first analyzed within the framework of potential scattering, with particular attention to those aspects of the theory which can be generalized to atomic collision processes. We next discuss various many-body applications of the eikonal method, namely: the Glauber approximation, the eikonal-Born series method, optical model theories, the eikonal distorted wave method and the multistate eikonal approximation. We also analyze eikonal exchange amplitudes. Applications of these methods are then considered, first for the case of elastic scattering and then for various inelastic processes.