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 antiproton–proton 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.
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 antiproton–proton 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.
The "molecule" positronium hydride (PsH), consisting of one atom each of positronium and hydrogen, has one well-known particle-stable state of total energy $E=\ensuremath{-}1.575$ Ry. In addition, for each
L it must have an infinite Rydberg series of excited states whose principal configuration is (${e}^{+}{\mathrm{H}}^{\ensuremath{-}}$), converging to a limit at $E=\ensuremath{-}1.0555$ Ry, the energy of ${\mathrm{H}}^{\ensuremath{-}}$. All of these excited states are energetically able to dissociate into ground-state Ps + H, and the higher-lying states can also decay with emission of excited Ps and ground-state H. These Rydberg states should appear as resonances in Ps + H scattering. In this paper I compute the lowest
S-wave resonance parameters, using an optical-potential formalism based on the (${e}^{+}{\mathrm{H}}^{\ensuremath{-}}$) configuration. The results are in rough agreement with those previously obtained using Kohn variational or complex-rotation techniques with highly correlated trial functions. The physical description of the PsH excited states is thus clarified.