Semiclassical algebraic approach to translational-vibrational energy transfer in molecular collisions

Translational-vibrational energy transfer in molecular collisions is studied by means of a semiclassical approach. The trajectory for the relative motion is obtained from the classical equations of motion for an effective interaction potential. The problem is then reduced to solving the Schroedinger equation for a harmonic oscillator with a time-dependent perturbation. Further simplification is achieved by expanding the interaction potential in a Taylor series around the quantum mechanical expectation value of the vibrational coordinate. The advantage of using Lie algebraic methods is illustrated. Energy conservation and detailed balance within this approximate scheme are discussed. Results are shown for a simple atom-diatom collision model. (author) 1 tab., 2 figs., 14 refs