Opacity Analysis of Inelastic Molecular Collisions. IV. Statistical Aspects of Rotational Excitation Theory

Abstract

Cross sections for specified rotational transitions of diatomic molecules are expressed in terms of opacity functions in the dominant‐coupling regime and in the limited‐coupling domain (where only first‐order‐allowed transitions occur). The statistical approximation is used to evaluate the opacity functions in the dominant coupling (the “inner”) region. The “outer” zone of limited coupling includes the large angular momenta where the Born (or distorted wave) approximation is satisfactory, as well as the region of somewhat lower $J$ requiring numerical treatment (at least the solution of a limited set of coupled equations). The use of the statistical approximation for direct transitions is discussed in terms of a limited energy average of the $S$ matrix. The vanishing of the average of the diagonal $S$ matrix elements is sufficient for a simple statistical estimate of the total cross section; however, a much more stringent requirement must be met (vanishing of the averaged $S$ matrix itself) for statistical prediction of specific inelastic transition probabilities.