Eikonal Approximation in Partial Wave Version

The eikonal approximation (EA) and eikonal-related approximations have been systematically discussed for atomic collision problems by several authors. i ) In fact this method is equivalent to an infinite order perturbation with the perturbation series summed up in a particular way so that the straight path integral of interaction potential appears as a phase of the exponential function. Such a term can be used to describe some kind of distortion of the incident or scattered projectile motion due to the interaction potential between the projectile and the target. Because of the additivity of the phase integral of interactions, the phase-distortion is possessed of intuitive clarity for describing the multiple scattering from many electron targets. It is recognized that the dynamical picture prQvided by the eikonal approximation is a multiple scattering one in the essential spirit from the methodological point 6f view, although it includes some ambiguity in the procedure of a linearization over the related Hamiltonian or the Green function. 2 ) In practical applications the eikonal and eikonal-related approximations have been known to work well for atomic as well as nuclear scattering in intermediate and high energy regions. l