Differential and integrated cross sections for the formation of antihydrogen by the impact of intermediate-energy (20–500 keV) antiprotons on positronium are calculated using the first Born approximation. The calculations are carried out for the formation of antihydrogen in ground and various excited electronic states (n=1–3) when positronium, the target atom, is in the ground state, and for the formation of antihydrogen in the ground state when the positronium is in various excited electronic states (n=1–2). The 1/n^3 behavior for the capture cross sections is used to calculate the total (that is, all states added together) integrated cross sections. The cross sections for the formation of antihydrogen presented here are obtained from those for the formation of positronium by the impact of positrons on hydrogen atoms by using charge invariance and the principle of detailed balance.
Nahar SN, Wadehra JM. Formation of ground and excited states of antihydrogen. Phys. Rev. A. 1988;37(11):4118-4124. doi: 10.1103/PhysRevA.37.4118