Classical and quantum centrifugal decoupling approximations for HCl–Ar

Abstract

The centrifugal decoupling approximation previously employed in quantum mechanics is extended to classical mechanics. Both classical and quantum centrifugal decoupling (CCD and CD, respectively) calculations are performed for HCl–Ar. Total cross sections are obtained from the CCD and CD calculations. The CCD and CD total cross sections are shown to be in good agreement with the corresponding exact classical trajectory (EC) and close coupled (CC) cross sections, respectively. The conservation of the projection (Omega) of the rotational angular momentum along the body-fixed z-axis is studied as a possible explanation for the success of the CCD and CD approximations in predicting total cross sections. By examining the CC body-fixed S-matrix elements and studying the behavior of Omega during the course of an exact classical trajectory, it is found that Omega is conserved only under very limited conditions. Detailed examination of the calculations shows that the CD approximation may be good even when Omega varies rapidly.