Semiempirical polarization potential for low-energy positron-atom and positron-atomic-ion interactions. I. Theory: Hydrogen and the noble gases

A simple model for the effects of polarization is introduced for the study of positron-atom interactions. The model is also used to study positronium-atom interactions by treatment of such systems as the interactions of positrons with polarizable anions. The model depends upon the average dipole polarizability of the atom (or ion) and one disposable parameter, an effective radius. The effective radius is determined by fitting calculated scattering lengths for H and He and the calculated positronium affinity of H to their well-established values, and by interpolating on the ionization potentials for other atoms. The model produces quite satisfactory phase shifts and cross sections for positrons scattering elastically off H, He, Ne, Ar, Kr, and Xe. The model appears to be equal or superior in predictive power to the much more elaborate polarized-orbital model recently formulated by McEachran et al. The model predicts that none of the rare-gas atoms studied will bind a positron. As a measure of how far from binding they are, negative values of the positron affinity are devised by appealing to effective-range theory and a heuristic argument involving the dependence of the calculated scattering length on the disposable parameter in the model.