The rapid calculation of rotationally and vibrationally inelastic molecular collision cross sections

Abstract

Several new approximate methods for the calculation of rotationally and vibrationally inelastic molecular collision cross sections are presented. Sample calculations have been performed in all cases and comparison made with exactly calculated cross sections. For rotationally inelastic scattering we present the Centrifugally Decoupled Exponential Distorted Wave (CDEDW) approximation. This approximation uses the same centrifugal decoupling technique as is used in the coupled states or p-helicity decoupling approximations, to reduce the number of channels which are coupled together in the differential equations of scattering theory. The simplified set of equations which results is then solved using the exponential distorted wave approximation. The method is applied to rotationally inelastic scattering in the Ar + N2 system and is shown to give highly reliable results. For processes involving simultaneous vibrational and rotational inelasticity we have developed a fast, nearly entirely analytic, method which treats the rotational inelasticity using the infinite order sudden approximation and the vibrational inelasticity using an adiabatic distorted wave approximation. Results are presented for vibrationally inelastic cross sections in the He + H2 system. For this very light system, the sudden approximation for the rotational inelasticity breaks down. We argue, however, that for heavier systems, for which exact computations are presently impossible, the approximation will be valid.