The adiabatic distorted wave infinite order sudden (ADWIOS) approximation for the calculation of inelastic molecular collision cross sections

Abstract

A new approximate method is presented for the rapid calculation of vibrationally–rotationally inelastic molecular collision cross sections. The method treats the coupling between the rotational states, belonging to the same vibrational level, using the sudden approximation. The vibrational states are treated using an adiabatic basis. With this basis it is found that a first order distorted wave approximation gives good agreement with fully converged close coupling calculations. Some previously developed techniques are extended to permit reliable analytic expressions to be formulated for the angle fixed S matrix elements which appear in the theory. The great computational efficiency of the method is based on these analytic formulas which eliminate the need for the numerical solution of differential equations and for the numerical evaluation of difficult integrals. The angle fixed S matrices which result are then treated within the framework of the recently developed sudden approximation to yield inelastic cross sections. The method is applied to the calculation of vibrationally–rotationally inelastic cross sections for the He+H2 system and comparisons are made with close coupling calculations which are fully converged in both rotational and vibrational basis. Analysis of the results shows that for the He+H2 system the sudden approximation fails significantly within the n=1 vibrational manifold at total energies below 1.1425 eV but the validity of the approximation clearly improves with increasing energy. The He+He2 system was used in the present work as it was the only suitable one for which exact calculations were available in the literature for comparison purposes. For heavier systems the sudden approximation will be valid at much lower energies.