Potential scattering in the eikonal approximation. II

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Abstract
A systematic study is made of several properties of the eikonal approximation and related methods. We first discuss various corrections to the eikonal approximation, in particular the eikonal-Born series method and the eikonal expansion of Wallace. We then show that the eikonal approximation satisfies unitarity in a very special way. Finally, we analyze in detail the very-strong-coupling situation. We show that in this case, and if the incident wave number is sufficiently large, the eikonal approximation yields excellent results for small-angle scattering.