Generating Phase Shifts from Pseudostate Energy Shifts

Abstract

A simple way to generate low energy phase shifts for elastic scattering using bound-state calculations is postulated, validated, and applied to the problem of ${e}^{+}$-Mg scattering. The essence of the method is to use the energy shift between a small reference calculation and the largest possible calculation of the lowest energy pseudostate to tune a semiempirical optical potential. The $\ensuremath{\ell}=1$ partial wave for ${e}^{+}$-Mg scattering is predicted to have a shape resonance at an energy of about 0.13 eV. The value of ${Z}_{\mathrm{eff}}$ at the center of the resonance is about 1500.