Towards prediction of the rates of antihydrogen positive ion production in antihydrogen-excited positronium reaction

We present the 4-body calculation of the antihydrogen-positronium scattering aiming at the prediction of cross sections for the production of antihydrogen positive ions. The latter are expected to be a useful source of ultra-cold atoms for the test of matter-antimatter gravity. We convert the Schrodinger equation to a set of coupled integro-di fferential equations that involve intermediate states and are solved using the compact finite di fference method. We will present the investigation of the rearrangement reaction between the ground-state antihydrogen atom and the excited positronium.