Electron and positronium scattering by rare-gas atoms: free electron gas approximations and orthogonality

Measured total cross sections for scattering of Positronium (Ps) by various atomic and molecular targets are very similar to electron scattering cross sections above the Ps ionization threshold [1].  Below the ionization threshold measurements for rare-gas atoms exhibit small cross sections. Previously we used a Free Electron Gas (FEG) model for the exchange and correlation potentials supplemented by an Orthogonalizing Pseudopotential (OPP) to study Ps scattering with rare-gas atoms [2]. For the heavy rare-gases we obtained good agreement with experiment, although we did not find evidence of a Ramsauer-Townsend minimum. For the lighter rare gases like He and Ne agreement with experiment was worse. Free electron gas approximations do not take into account the effects of orthogonality between target and continuum orbitals. In this work we investigate the effect of enforcing orthogonality in electron and Ps scattering by rare-gas atoms. To enforce orthogonality we use a Lagrange multiplier method and make a comparison to results using the OPP and to experimental results. ¹S. J. Brawley et al., Science 330, 789 (2010).  ²R. S. Wilde and I. I. Fabrikant, Phys. Rev. A 98, 042703 (2018).