On the choice of translation factors for approximate molecular wavefunctions

Abstract

A critical analysis is presented for three different methods which introduce translation factors in the molecular approach to atomic collisions. Unlike other contributions in this field, approximate one- and many-electron wavefunctions are explicitly considered from the start. The authors' conclusions are illustrated with the calculation of the charge exchange cross section for He²⁺+H(1s) to He⁺(2s,2p)+H⁺, which exhibits a strong origin dependence in the standard perturbed stationary states (PSS) approach. The authors' main (and new) conclusions are: (i) that the Bates-McCarroll method, and the method of projection on atomic components, are not necessarily convergent, and are exceedingly time consuming for approximate wavefunctions and (ii) that the common translation factor method is the most promising approach at present. However, before it can be used systematically in molecular calculations, more research is needed regarding its sensitivity to the analytical form of the common factor-otherwise some of the defects of the PSS approach reappear (in disguise) using this method.