Homonuclear ion-atom collisions: Application toLi+−Li

Abstract

We present a theoretical framework for homonuclear, ground-state ion-atom collisions wherein the indistinguishability of direct elastic and resonant charge exchange (RCE) scattering channels is discussed. The discussion in terms of the total cross section(${\ensuremath{\sigma}}_{\text{tot}}$) is motivated and derived. The standard cross-section expressions for direct elastic(${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\sigma}}}_{\text{el}}$) and RCE (${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\sigma}}}_{\text{ce}}$) channels are obtained as high-energy approximations to ${\ensuremath{\sigma}}_{\text{tot}}$. We show that the total cross section resolves the inconsistency, at low energies, between the diffusion cross section (${\ensuremath{\sigma}}_{D}$) and the high-energy approximation to the total cross section (${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\sigma}}}_{\text{tot}}$). The validity of the equivalence relation between the ${\ensuremath{\sigma}}_{D}$ and $2\ifmmode\times\else\texttimes\fi{}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\sigma}}}_{\text{ce}}$ is also discussed. The differences which result in cross sections which are frequently used in the description of ion-atom collision is illustrated with specific calculations for an ${\mathrm{Li}}^{+}\ensuremath{-}\mathrm{Li}$ system. The use of ${\ensuremath{\sigma}}_{\text{tot}}$ is advocated as a correct and consistent way to represent cross sections.