Semiclassical calculations of vibrational energy transfer: Comparison of the harmonic and the Morse oscillator in collinear and perpendicular collisions with a structureless atom

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Collinear and perpendicular collisions of an atom with a diatom are considered using both the harmonic and the Morse molecular binding potentials. A uniform semiclassical approximation is used to calculate individual vibrational transition probabilities and averaged energy transfers. Differences in individual probabilities and in averaged energy transfers in collinear as well as in perpendicular collisions depend strongly on the reduced mass ratio m. For a large m, the discrepancy between the harmonic and the Morse oscillator is large, while with decreasing m the agreement becomes progressively better. In the collinear geometry more energy is transferred to the harmonic oscillator than to the Morse oscillator, while the reverse holds in the perpendicular geometry. These effects are explained qualitatively by studying the time dependence of the oscillator energy during a classical trajectory.