Molecular Collisions. XIV. First-Order Approximation of the Generalized Phase Shift Treatment of Rotational Excitation: Atom–Rigid Rotor

Abstract

The generalized phase shift approach to the rotational excitation problem, introduced in Paper XII of this series, is applied to the atom–rigid rotor case in the lowest (first‐order) approximation. The treatment involves the computation of generalized action integrals over curved trajectories. Numerical results are presented to illustrate the dependence of the transition probabilities on the usual physical parameters, as well as a new parameter, $\zeta$ , which is proportional to the ratio of the moment of inertia of the van der Waals' atom–diatom system to that of the diatomic rotor (and thus to the ratio of the collision time to the diatom rotation time). In the limit $\text{ζ\hspace{0.17em}→\hspace{0.17em}0}$ , the development reduces to the sudden approximation. In the large impact parameter limit (straight‐line trajectories), the deviation from the sudden approximation is described by “resonance functions” identical to those obtained implicitly by Van Kranendonk. The numerical results are presented in a manner which illustrates the deviation from each of these two limits.