Classical two-dimensional model for rotational-vibrational atom–diatom inelastic scattering

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Abstract
The classical hard ellipse model for atom–diatom rotationally inelastic (RI) collisions is generalized to include simultaneous vibrational excitation by assuming that this excitation is proportional to the square of the component of momentum transferred along the major axis of the ellipse. Calculations are presented which compare level-to-level RI angular distributions of vibrationally elastic (Δv = 0) and vibrationally inelastic (Δv = 1) scattering. These calculations reproduce the main features observed in recent measurements of level-to-level rovibrationally inelastic scattering for Na2 with Ar. With Δv = 0 and 1, the scattering distributions display rainbow structure whose angular position increases nearly linearly with Δj. In addition, the Δv = 1 scattering shows considerable suppression of small angle scattering (which also has small Δj). We emphasize that this suppression of forward scattering results from a kinematic exclusion of small angle scattering for impulsive inelastic collisions with a slowly rotating molecule irrespective of the origin of inelasticity.