A four-body calculation of s-wave resonant scattering between positronium and antihydrogen atom

We present a four-body calculation of s-wave scattering between a positronium (Ps) and an antihydrogen atom (H-bar) in the vicinity of the first Ps excitation threshold energy. We convert the Schroedinger equation to a set of coupled integro-differential equations that let us determine the multi-channel scattering wave functions. The internal region of these functions is expanded in terms of the square integrable four-body functions that can be regarded as a kind of 'intermediate states' of the scattering and are obtained by the diagonalization of the full four-body Hamiltonian. The convergence of the scattering cross sections is examined with respect to the number of the intermediate states included in the coupled-channel calculation. It is demonstrated that the intermediate states are essential to describe the resonant scattering of Ps + H-bar. Around the resonance energy, the positron of Ps transfers to H-bar, and the electron is associated with the antihydrogen positive ion. We have updated our previous calculation and have obtained the converged cross sections in the collision energy interval from 3.54 eV to 5.71 eV. The energy regions where the cross section undergoes rapid variation are found to correspond to the resonance energies of the lowest four resonance states predicted by the complex coordinate rotation method. (author)