Generating phase shifts from pseudo state energy shifts

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 pseudo-state to tune a semi-empirical optical potential. The L = 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 Zeff at the center of the resonance is about 1500.