$\bar{H}$ and $\bar{H}^{+}$ production cross sections for the GBAR experiment

The production and cooling of the + ion is the key point of the GBAR experiment (Gravitational Behaviour of Antihydrogen at Rest), which aims at performing the free fall of antihydrogen atoms to measure , the acceleration of antimatter on Earth. + ions will be obtained from collisions between a positronium cloud and antiprotons delivered by the AD/ELENA facility at CERN, with intermediate formation of antihydrogen atoms. In order to optimise the experimental production of + ions, we computed the total cross sections of the two corresponding reactions, within the same theoretical framework of the Continuum Distorted Wave – Final State (CDW-FS) model. The different contributions of the excited states have been systematically investigated for different states of Ps. The results exhibit an increase of the production toward low kinetic energies, in agreement with experimental data and previous calculations, whereas the largest + production is obtained with low energy ground-state antihydrogen atoms. These theoretical predictions suggest that the overall production of + could be optimal for 2 keV antiproton impact energy, using positronium atoms prepared in the 2p state.