Classical S Matrix: Numerical Application to Inelastic Collisions

A previously developed semiclassical theory of molecular collisions based on exact classical mechanics is applied to the linear atom–diatom collision (vibrational excitation). Classical, semiclassical, and uniform semiclassical results for individual vibrational transition probabilities corresponding to the H2+He system are presented and compared to the exact quantum mechanical results of Secrest and Johnson. The purely classical results (the classical limit of the exact quantum mechanical transition probability) are seen to be accurate only in an average sense; the semiclassical and uniform semiclassical results, which contain interference effects omitted by the classical treatment, are in excellent agreement (within a few percent) with the exact quantum transition probabilities. An integral representation for the S-matrix elements is also developed which, although it involves only classical quantities, appears to have a region of validity beyond that of the semiclassical or uniform semiclassical expressions themselves. The general conclusion seems to be that the dynamics of these inelastic collisions is basically classical, with all quantum mechanical structure being of a rather simple interference nature.