Comments on eikonal and sudden approximations

Abstract

An approximation scheme is presented which leads systematically from the exact Moller (or scattering) operator to the eikonal approximation and then to the sudden approximation. In terms of the Moller (or scattering) operator, the eikonal approximation is local in position space and is parametrised by the average incoming free momentum. Carrying the procedure a step further decouples the internal and translational motions to produce the sudden approximation. Distorted as well as straight-line approximations are considered. To do so distorted scattering conditions are presented which define distorted M Moller, transition and scattering operators. Some properties of these operators are discussed. Relations with the usual Moller, transition and scattering operators are presented. Finally, an eikonal approximation to the Moller super-operator is presented which does not depend explicitly upon the form of the dynamics that is used. Quantally, the eikonal Moller super-operator is equivalent to the eikonal Moller operator and, in the limit of small h, reduces to the classical eikonal Moller super-operator. This classical Moller super-operator gives a particle picture for the eikonal approximation in contrast to the traditional wave picture.