Formulation of High-Energy Potential Scattering Problems

Abstract

A method is presented for treating high-energy potential scattering in which the zero-order result is essentially the WKB approximation. The correction terms which appear involve the rate of change of the local wave number and the curvature of the classical trajectory. Unlike the usual WKB procedure which is only asymptotically correct, the formulation remains exact, but not necessarily convenient, even if the corrections are large. The improvement over the WKB approximation is demonstrated explicitly for one-dimensional scattering and for the calculation of phase shifts for scattering from a central potential. It is also shown that this prescription reduces to the Born approximation when the conditions for the validity of that approximation are satisfied. Thus the proposed formulation contains both the WKB and Born approximations as simple limiting cases.