${\bar {\mathrm {H}}^{+}}$ production from collisions between positronium and keV antiprotons for GBAR

In the framework of the GBAR (Gravitational Behaviour of Antihydrogen at Rest) experiment, cross sections for antihydrogen ion ( $\bar {\mathrm {H}}^{+}$ ) production in collisions between antiprotons ( $\bar {\mathrm {p}}$ ) and excited positronium atoms (Ps), with intermediate production of antihydrogen ( $\bar {\mathrm {H}}$ ), have been computed using a perturbative theory, namely Continuum Distorted Wave - Final State (CDW-FS). The results suggest to use antiprotons at 1, 2 or 6 keV with, respectively, Ps(3p,3d), Ps(2p) or no Ps excitation. A simulation using these cross sections is under development to investigate the reaction chamber geometry and the parameters of the different beams (positrons, antiprotons and laser). This simulation, focusing on Ps(3d), predicts at least one $\bar {\mathrm {H}}^{+}$ ion per pulse of 3·10$^{6}$ $\bar {\mathrm {p}}$ at 1 and 6 keV, and highlights both the interest of positronium excitation and the need for short pulses of particles.