Validity of the sopkovich approximation

Abstract

Distorted-wave Born approximation calculations for high energy peripheral collisions are frequently circumvented by a simple prescription, emerging from the high energy WKB approximation, in which the plane-wave Born approximation amplitudes are multiplied by the factor exp( i[ δ l + δ l′ ]), where δ l and δ l′ are phase shifts characteristic of elastic scattering in the incident and final channels, respectively. The validity of this recipe for medium-energy nuclear reactions is tested through numerical calculations with a simple nonrelativistic potential model. For sufficiently weak potentials, the recipe appears quantitatively reliable but, in realistic situations of moderate or strong absorption, although it frequently well approximates the exact angular distribution, this prescription can give quantitatively unreliable values for the important partial-wave amplitudes as well as it can miss important features of the cross section. The implications of the numerical results for several related approximations are also discussed.