Opacity analysis of inelastic molecular collisions. VI. The sudden approximation for rotational excitation

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 θ₀, with Eθ₀ increasing with increasing collision energy.