Rotationally inelastic collisions of $H2+$ ions with He buffer gas: Computing cross sections and rates

We present quantum calculations for the inelastic collisions between $H2+$ molecules, in rotationally excited internal states, and He atoms. This work is motivated by the possibility of experiments in which the molecular ions are stored and translationally cooled in an ion trap and a He buffer gas is added for deactivation of the internal rotational population, in particular at low (cryogenic) translational temperatures. We carry out an accurate representation of the forces at play from an ab initio description of the relevant potential energy surface, with the molecular ion in its ground vibrational state, and obtain the cross sections for state-changing rotationally inelastic collisions by solving the coupled channel quantum scattering equations. The presence of hyperfine and fine structure effects in both ortho- and para-$H2+$ molecules is investigated and compared to the results where such a contribution is disregarded. An analysis of possible propensity rules that may predict the relative probabilities of inelastic events involving rotational state-changing is also carried out, together with the corresponding elastic cross sections from several initial rotational states. Temperature-dependent rotationally inelastic rates are then computed and discussed in terms of relative state-changing collisional efficiency under trap conditions. The results provide the essential input data for modeling different aspects of the experimental setups which can finally produce internally cold molecular ions interacting with a buffer gas.