Near-threshold behavior of positronium-antiproton scattering

Abstract

Using the convergent close-coupling theory we study the threshold behavior of cross sections for positronium (Ps) of energy $E$ scattering on antiprotons. In the case of $\mathrm{Ps}(1s$) elastic scattering, simple power laws are observed for all partial waves studied. The partial-wave summed cross section is nearly constant, and dominates the antihydrogen formation cross section at all considered energies, even though the latter is exothermic and behaves as $1/{E}^{1/2}$. For $\mathrm{Ps}(2s$), oscillations spanning orders of magnitude on top of the $1/E$ behavior are found in the elastic and quasielastic cross sections. The antihydrogen formation is influenced by dipole-supported resonances below the threshold of inelastic processes. Resonance energies form a geometric progression relative to the threshold. The exothermic antihydrogen formation cross sections behave as $1/E$ at low energies, but are oscillation free. We demonstrate that all these rich features are reproduced by the threshold theory developed by Gailitis [J. Phys. B: At. Mol. Phys. 15, 3423 (1982)].