Molecular Collisions. X. Restricted-Distorted-Wave–Born and First-Order Sudden Approximations for Rotational Excitation of Diatomic Molecules

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Abstract
Although a number of approximation methods have been widely used in the field of molecular rotational excitation and scattering, their interrelationships and ranges of applicability have not always been clearly established. The present work is a comparison of several of these approximations. Considered are the time-independent treatments such as the distorted wave approximation (DWA), the restricted distorted wave (RDW) and the RDW–Born approximations, and the time-dependent ones such as the sudden approximation (SA), full trajectory and straight-line limit, and the first-order perturbation approximations. Equivalence is demonstrated between the RDW–Born and first-order SA, and convenient analytical forms are presented for the resulting transition probabilities.