The two-centre convergent close-coupling (CCC) approach is used to calculate antihydrogen formation cross sections via positronium scattering on antiprotons. These cross sections have been expressed in terms of simple algebraic functions in accordance with their predicted threshold behaviours. The two-centre CCC method has also been upgraded to incorporate positron scattering on charged targets. This allowed for the cross sections to be determined for various transitions of positron scattering on a positive helium ion
