Optical potential approach to the calculation of vib-rotational relaxation rates

An optical-potential method is developed for the calculation of cross sections for vib-rotational transitions in atom-molecule collisions. In this framework the multi-channel scattering equations are replaced by a pair of coupled equations for each vib-rotational transition. The effect of the large manifold of open rotational channels is introduced through an optical potential in each of the coupled equations. Both a phenomenological (trial function) procedure and a theoretical approximate method for obtaining the optical potentials are given. The method remains computationally feasible even in systems with very many open channels. To test the method, the cross section for the 10→00 transition in He + H₂, He + D₂, He + T₂ was calculated over a wide range of energies and compared with results in the literature. An interesting scaling property is observed to hold with respect to the energy dependence of the above cross sections.