Protonium formation in collinear collisions between antiprotons and hydrogen molecular ions: Quantum-classical hybrid method versus adiabatic approximation

A quantum-classical hybrid (or semiclassical) method is applied to protonium formation p̄+H₂⁺→p̄p+H and dissociation p̄+H₂⁺→p̄+p+H at kinetic energies up to 2000.3em0exeV. The electronic motion is accurately solved quantum mechanically, while the motion of the heavy particles p̄ and p is described by classical mechanics. The p̄-p-p collinear configuration is assumed as a preliminary to three-dimensional calculations, and to assess the validity of the adiabatic approximation. Vibrational excitation to the dissociative continuum is crucial in p̄p formation in contrast to the importance of electron emission for the atomic-hydrogen target. For this reason, p̄p formation occurs efficiently even well beyond the ionization threshold if the target is a molecule.