Variational calculation of positron-atom scattering using configuration-interaction-type wave functions

Abstract

The Kohn variational method is used with a configuration-interaction (CI)-type wave function to determine the phase shifts and ${Z}_{\mathrm{eff}}$ for positron-copper scattering. The method is first tested for positron-hydrogen scattering and it is found to give phase shifts and ${Z}_{\mathrm{eff}}$ within 1--2% of the best previous calculations. Although the phase shift for Cu converged more slowly with ${L}_{\mathrm{max}}$ (the maximum angular momentum of the electron and positron orbitals included in the short-range basis), it was still possible to get reliable estimates of the phase shifts by including orbitals with $\mathcal{l}<~18$ and the use of an extrapolation technique. Calculation of ${Z}_{\mathrm{eff}}$ was more problematic since the convergence of ${Z}_{\mathrm{eff}}$ with respect to ${L}_{\mathrm{max}}$ was very slow. Despite the uncertainties, it was clear that the p-wave phase shift was showing signs of forming a shape resonance at about 0.5 eV incident energy. This resulted in a p-wave contribution to ${Z}_{\mathrm{eff}}$ that was larger than that of the s wave for $k>~{0.1a}_{0}^{\ensuremath{-}1}.$ Speculative calculations based upon a model potential suggest that a p-wave shape resonance centered at thermal energies, e.g., about 0.025 eV, could result in a thermally averaged ${Z}_{\mathrm{eff}}$ exceeding 10 000.