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

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