Theoretical studies of positronium formation in positron collisions with lithium and hydrogen atoms

The Kohn variational method has been used to study elastic scattering and positronium (Ps) formation in positron collisions with atomic hydrogen and lithium, in the energy region where only these two channels are open. In common with other alkali metals, lithium is interesting in that its valence electron is sufficiently weakly bound that positronium formation is exothermic, and hence an open channel for incident positrons of zero energy. For such a process, Wigner's threshold theory predicts an s-wave cross section which has an inverse dependence on the wavenumber, k, of the projectile as k→0. Using a model potential and very elaborate trial functions, a detailed investigation of s- and p-wave positron-lithium scattering has been made in the energy range 0-1.84eV, and preliminary results have also been obtained for d-wave scattering. The s-wave Ps formation cross section, as calculated variationally, appears to be in accordance with the Wigner theory, although this partial wave contributes negligibly to the Ps channel across most of the energy range considered. The p and d partial waves make a much more substantial contribution to the rearrangement process. New cross sections for positron-hydrogen scattering have been calculated for the energy region close to the positronium formation threshold, and results have been compared with the predictions of R-matrix threshold theory.