Positronium scattering by molecules: free electron gas plus orthogonalizing pseudopotential model

Experimental total cross sections for scattering of Positronium (Ps) by various atomic and molecular targets are 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$^2$. In general, we obtained good agreement with experiment, but did not find evidence of a Ramsauer-Townsend minimum. We extend the OPP to non-spherical targets and apply the FEG plus OPP model to calculate elastic scattering cross sections for Ps scattering by the molecular targets H$_2$, N$_2$ and CO$_2$. In previous calculations, using only the FEG potentials for N$_2$, we found scattering resonances below the ionization threshold$^3$. The OPP can take account of the repulsive effect of the Pauli Exclusion Principle which can influence the shape and position of these resonances. $^1$S. J. Brawley {\it et al.}, Science {\bf 330}, 789 (2010). $^2$R. S. Wilde and I. I. Fabrikant, Phys. Rev. A {\bf 98}, 042703 (2018). $^3$R. S. Wilde and I. I. Fabrikant, Phys. Rev. A {\bf 97}, 052708 (2018).