Towards prediction of the rates of antihydrogen positive ion production in collision of antihydrogen with excited positronium

We present a 4-body calculation of scattering between an antihydrogen atom (H) and a positronium (Ps) aiming at the prediction of cross sections for the production of antihydrogen positive ions H⁺. The antihydrogen positive ions are expected to be a useful source of ultra-cold anti-atoms for the test of matter-antimatter gravity. We convert the Schrödinger equation to a set of coupled integro-differential equations that involve intermediate states which facilitate the internal region description of the scattering wavefunction. They are solved using a compact finite difference method. Our framework is extended to scattering between an excited Ps and H. Cross sections of the reactions, Ps (1s/2s/3s) H to e^-+H⁺ in s-wave collisions, are calculated. It is found that the reactions originating from Ps (1s/2s) + H produce H⁺ with a constant cross section within 0.05 eV above the threshold while the reaction cross section from Ps (3s) decreases as the collision energy increases in the same energy interval. Just above the threshold, the cross section of H⁺ production from Ps (3s) + H in s-wave collision is 7.8 times larger than that from Ps (1s) + H in s-wave and 2.3 times larger than that from Ps (2s) + H> in s-wave. The near-threshold de-excitation reaction from Ps (3s) + H occurs more rapidly than the H⁺ production.