Rotational–Translational Energy Transfer. II. Comparison of Action-Angle Solution in the Near-Static Approximation with Exact Results

Abstract

In Part I, the differential equations for molecular rotational–vibrational–translational energy transfer were re-expressed in terms of action-angle variables. In the present paper, approximate integral solutions and exact results for rotational–translational transfer are compared for a wide range of collisional and molecular parameters at small fractional changes in translational energy. The results are in good agreement over the range investigated except at low moments of inertia. Thereby, conditions where the present approximation is best correspond to some which are least accessible by approximate or numerical quantum mechanical methods. The present approximation employs for zeroth order a classical analog of the static approximation in quantum mechanics, rather than the adiabatic approximation, and the results have implications for the ranges of molecular parameters where each should be preferable in the quantum case.