Positron collisions from simple atoms and positronium-hydrogen collisions

I plan to present calculations of three-body, effective three-body and four-body collisions at low energies that involve a positron. We applied the hyperspherical hidden crossing method with a correction term to Ps formation in low energy e$^+$-H [1,2], e$^+$-Li [2,3,4] and e$^+$-Na collisions [2]. We considered the alkali atoms Li and Na as effective one-electron atoms, so that e$^+$-Li collisions and e$^+$-Na collisions can be considered as effective three-body collisions. The calculations provide an explanation of the extremely small S-wave Ps formation cross section for e$^+$-H, e$^+$-Li and e$^+$-Na collisions in terms of destructive interference. The S-wave cross section for Ps formation in e$^+$-Li and in e$^+$-Na collisions increases with decreasing momentum of the incoming Ps, which is consistent with the Wigner threshold law [5]. We have also studied at low-energies a fundamental four-body Coulomb process, that of elastic Ps-H scattering [6]. Using the Kohn variational method (and variants of this method) we have computed accurate $^{1,3}$S- and $^{1,3}$P-wave phase shifts. We also have some preliminary $^{1,3}$D-wave phase shifts.\\[4pt] [1] S.~J.~Ward, J.~H.~Macek and S.~Yu.~Ovchinnikov, Phys.~Rev.~A {\bf 59}, 4418 (1999).\\[0pt] [2] S.~J.~Ward and J.~Shertzer, New.~J.~Phys. {\bf 14}, 025003 (2012).\\[0pt] [3] S.~J.~Ward and J.~Shertzer, Phys.~Rev. A {\bf 68}, 032720 (2003).\\[0pt] [4] S.~J.~Ward, J.~Shertzer, S.~Yu.~Ovchinnikov, and J.~H.~Macek, Phys.~Rev.~A {\bf 75}, 012713 (2007).\\[0pt] [5] P. Wigner, Phys.~Rev. {\bf 73}, 1002 (1948).\\[0pt] [6] Denton Woods, S.~J.~Ward and P.~Van Reeth, Bull.~Am.~Phys.~Soc. {\bf 58}, no.~6, p.~175 (2013).