A note on the asymptotic behaviour of asymmetric charge transfer theories

Abstract

The author reduces the problem of finding the leading velocity dependence of the peaked impulse approximation (PIA), the impulse approximation (IA) and the strong-potential Born (SPB) approximation to that of examining the asymptotic behaviour of the double scattering amplitude in the second Born (B2) approximation. Although no strict mathematical proof is given, he presents evidence (both theoretical and numerical) that this procedure is indeed justified. In contrast to the nu -11 dependence of the B2 approximation, the post (prior) form of the PIA gives rise to a leading nu -11-2l' ( nu -11-2l) velocity dependence irrespective of the final (initial) orbital quantum number l (l'). The origin of this discrepancy is discussed and new insight on the use of the peaking approximation is gained. He infers that the asymptotic behaviour (to leading order only) of the IA and SPB approximation agrees with that of the B2 approximation.