Benchmark calculation of hydrogen (antihydrogen) formation at rest in positronium-proton (-antiproton) scattering

Abstract

We use the equivalence of positron scattering on atomic hydrogen, and positronium-proton scattering, to provide benchmark results for (anti)hydrogen formation in positronium (Ps) scattering on (anti)protons in a low-energy region. Using the two-center e +-H convergent close-coupling approach convergence to a few percent accuracy is demonstrated, in the only required zeroth partial wave, by substantial variation in the treatment of the two centers. A simple relation for the cross section at low Ps energies (k2) is given, with the 1/k behavior demonstrated to strictly hold only at threshold.