Resonance scattering of positronium by N$_2$

Since the discovery [1] of the similarity between electron and positronium (Ps) scattering by atoms and molecules, much theoretical effort has been directed to explain this intriguing observation. A particularly interesting phenomenon is the presence of a resonance in Ps scattering by nitrogen molecules [2] which looks similar to the $\Pi_g$ resonance in electron scattering by the same target if cross sections for both processes are plotted as functions of the projectile velocity. For correct treatment of Ps-molecule scattering incorporation of the exchange interaction and short-range correlations is of a paramount importance. In the present work we have used a free-electron-gas model to describe these interactions in collisions of Ps with the N$_2$ molecule. The results agree reasonably well with the experiment, but the position of the resonance is somewhat shifted towards lower energies, probably due to the fixed-nuclei approximation employed in the calculations. $^1$ S. J. Brawley {\it et al.}, Science {\bf 330}, 789 (2010). $^2$ M. Shipman {\it et al.}, Phys. Rev. A {\bf 95}, 032704 (2017).