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 p+H2+→pp+H and dissociation p+H2+→p+p+H at kinetic energies up to 200 eV. The electronic motion is accurately solved quantum mechanically, while the motion of the heavy particles p and p is described by classical mechanics. The p-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 pp formation in contrast to the importance of electron emission for the atomic-hydrogen target. For this reason, pp formation occurs efficiently even well beyond the ionization threshold if the target is a molecule