We overview our recent calculations of scattering cross sections of positronium–antihydrogen collisions. We discuss the cross sections calculated in the vicinity of the four-body resonances of H ¯ Ps and above the energy threshold for the formation of the antihydrogen positive ions (H ¯ +). In the former energy region where a Rydberg series of resonances dominated by the H ¯ +-e - interaction appears, we show a good agreement between the resonant profiles in the cross sections and the resonance energies calculated by the complex coordinate rotation method. H ¯ + production cross sections near the threshold energy are reported for the positronium being initially in the (n, l) states with n≤ 3 , together with all competing elastic/inelastic cross sections. Comparison of our results with the latest continuum distorted wave final state calculation is presented. A qualitative discrepancy concerning the dependence of cross sections on the angular momentum of Ps is indicated.
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