Analytical approximation for vib-rotational cross sections in molecular collisions

An approximate analytical expression is given for vib-rotational cross sections of atom-molecule collisions. This is derived by treating coupling between rotational states in the sudden approximation and applying the distorted-wave and modified-wave approximation in the evaluation of the relevant transition matrix elements. A certain functional form for the potential is also assumed with parameters that must be so chosen as to yield a good fit to the real potential surface in a given application. A crude version of the model, involving several additional approximations, was tested for the He + H₂ system in the energy range 1.2-2.0 eV. Comparison with the more elaborate effective potential calculations by M. Alexander shows fair (better than order-of-magnitude) agreement for each vib-rotational cross section and the energy-dependence is accurately reproduced. The model can be extended to collisions between diatomics.