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

Abstract

An approximate method is presented for the rapid calculation of rotationally—vibrationally inelastic molecular collision cross sections. The method, called the distorted wave infinite order sudden (DWIOS) approximation, treats the coupling between rotational states associated with a given vibrational level using the infinite order sudden approximation. Transitions between the different vibrational manifolds are treated using a generalised form of the distorted wave approximation. The method is a further development of one recently proposed by Gerber. Its most important new feature is that it yields a symmetric T matrix. In applying the method further approximations are made so as to reduce the formulae for the T matrix elements to an almost entirely analytic form, and an analytic expression for a new type of distorted wave integral is developed and presented in the paper. This expression is a generalisation of the well known Mies formula. The DWIOS method is applied to the calculation of rotationally—vibrationally inelastic HcH 2 cross sections, and comparisons are made with exact and other approximate calculations. Despite the fact that this system is one to which the sudden approximation is poorly suited, good agreement — often within 20% — is obtained over a wide energy range. Over a more limited energy range the method yields better agreement with the “exact” close-coupling results than does the coupled states approximation.