Potential Scattering in the Eikonal Approximation

Abstract

A systematic study is made of the limits of validity of the eikonal approximation in nonrelativistic potential scattering theory. We suggest that for a large class of potentials, and for all momentum transfers, each term of the eikonal multiple-scattering series gives the asymptotic value (for large incident wave numbers) of the corresponding term in the Born series. This property, together with the requirement of unitarity, implies that in weak-coupling situations the eikonal approximation is consistently worse than the second Born approximation. For intermediate couplings we find that the eikonal method is remarkably good at all angles for potentials of the Yukawa type. For the case of strong coupling ($|{V}_{0}|>E$) we find that for all potentials studied there is good agreement between exact and eikonal results at small angles. Analytical and numerical results are given for a variety of interaction potentials.