Opacity Analysis of Inelastic Molecular Collisions. VI. The Sudden Approximation for Rotational Excitation

Abstract

The limited coupling domain (where only first‐order‐allowed transitions are important) for rotational excitation is considered using the quantum mechanical sudden approximation. The derivation of the approximation is discussed using a variational procedure and a simplified form, valid for large angular momentum, is introduced. A further simplification is achieved using the limited coupling form of the $S$ matrix, which interpolates between the weak coupling (distorted‐wave) limit and the dominant coupling regime. Explicit results are obtained for differential and total cross sections of specified first‐order‐allowed rotational transitions of diatomic molecules. The inelastic cross sections are expressed in terms of a coupling parameter and a common cross section, and the angular distribution, evaluated using a semiclassical summation, is peaked at a forward angle ${\theta }_0$ , with ${\mathrm{E\theta }}_0$ increasing with increasing collision energy.