Near-threshold Ps(n=2)-p scattering

We study the threshold behavior of elastic and inelastic collisions of the excited positronium (Ps) atom with the proton using the theory developed by Gailitis [J. Phys. B {\bf 15}, 3423 (1982)]. We show that partial cross sections for elastic and quasielastic processes exhibit pronounced oscillations above the threshold and diverge as $1/E$ where $E$ is the collision energy. This behavior is limited from below by the energy equal to the relativistic splitting between degenerate Ps states. {\it Ab initio} close coupling calculations are in excellent agreement with the results of the threshold theory. The oscillations almost completely disappear in the total (summed over partial waves) cross sections. However, dipole-supported resonances appear in inelastic processes, in particular in the important process Ps($nl)+p\to$ H$(n'l')+e^+$ below higher-energy thresholds. Above thresholds these cross sections don't exhibit oscillations but have the $1/E$ divergence in an exothermic case. These results are important for current attempts to produce antihydrogen in a similar charge-conjugated reaction Ps($nl)+\bar{p}\to \bar{\rm H}(n'l')+e^-$.