$\bar {\sf {H}}^{+}$ ion production from collisions between antiprotons and excited positronium: cross sections calculations in the framework of the GBAR experiment

Abstract : In the framework of the gravitational behaviour of antihydrogen at rest (GBAR) experiment, cross sections for the successive formation of $\bar {\sf {H}}$ and $\bar {\sf {H}}^{+}$ from collisions between positronium (Ps) and antiprotons ( $\bar p$ ) have been computed in the range 0-30 keV $\bar p$ energy, using the continuum distorted wavefinal state theoretical model in its three-body and four-body formulations. The effect of the electronic correlations in $\bar {\sf {H}}^{+}$ on the total cross sections of $\bar {\sf {H}}^{+}$ production has been studied using three different wave functions for $\bar {\sf {H}}$ (the matter equivalent of $\bar {\sf {H}}^{+}$). Ps excited states up to n$_p$ = 3, as well as $\bar {\sf {H}}$ excited states up to n$_h$ = 4, have been investigated. The results suggest that the production of $\bar {\sf {H}}^{+}$ can be efficiently enhanced by using either a fraction of Ps(2p) and a 2 keV ($\bar p$) beam or a fraction Ps(3d) and antiprotons with kinetic energy below 1 keV