Coupled channel study of antihydrogen-hydrogen molecular resonance state

We report a theoretical study of antihydrogen-hydrogen molecular resonance states consisting of a positron, an antiproton, an electron and a proton. The four particles strongly correlate and show different character from the hydrogen molecule. Because of the non-separability of the positron and electron motions from the antiproton and proton motions, the adiabatic approximation breaks down at the short antiproton-proton distance. Based on a non-adiabatic method, we directly solve the four-body problem and obtain the resonance energies and widths. In order to examine the roles of positron-antiproton and electron-proton correlations as well as positron-electron and antiprotonproton correlations, we introduce two different types of coordinate systems. One is suited for describing an antihydrogen-hydrogen configuration, and the other is a positronium-protonium configuration. The antihydrogen-hydrogen configuration contributes to the existence of the molecular resonance states, and the positronium-protonium configuration makes the resonance states unstable. Mixing of the two configurations results in an antihydrogen-hydrogen molecular resonance state, and the resonance state has an energy of −0.077 9(3) a.u. from the antihydrogen-hydrogen dissociation threshold with its lifetime 16 (2) fs.