A study of exchange interactions in alkali molecular ion dimers with application to charge transfer in cold Cs

The formulation of Bardsley et al (Phys. Rev. A 11 1911) for evaluating the asymptotic electron exchange interaction between an alkali ion and its parent atom is extended by the use of a more accurate representation of the asymptotic wavefunction of the isolated atom and also by the inclusion of a further term in the series that accounts for the presence of the ion. The Bardsley analysis is compared with a purely numerical approach in which the Holstein-Herring integrand is constructed from a polarized wavefunction built from numerical solutions of the differential equations of Rayleigh-Schroedinger perturbation theory and the required quadrature is performed numerically. Values of the asymptotic exchange interactions are given for the molecular ions Li(+(2), Na(+(2), K(+(2), Rb(+(2) and Cs(+(2). As an example, exchange interactions for Cs(+(2) evaluated by an ab initio method are compared to those predicted by the Bardsley formula. Potentials for the lowest states of Cs(+(2) are constructed from the ab initio values matched to the asymptotic exchange and long-range polarization interactions, and these potentials are used to predict the 1(2)S(+(g) and 1(2)S(+(u) scattering lengths and low-energy charge transfer cross sections.