Effects of the multiplicity of impacts on vibration–translation energy transfer in collinear collisions

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Abstract
An idealized model of nonreactive collinear C–B+A collisions has been developed for the calculation of the number of impacts and amount of vibration–translation energy exchange at each impact as functions of the mass distribution and the initial collision energy. The maximum number of impacts that a single collision can have is n*=90 °/φ, where φ= tan−1 [mB(mA + mB + mC)/mAmC]1/2; for nonintegral values of 90 °/φ, n* = [90 °/φ], where the square brackets denote the algebraically largest integer which just exceeds the nonintegral value 90 °/φ. The model is applied to the collinear collisions H–F+F, F–H+F, Cl–H+Cl, Br–H+Br, I–H+Cl, and several other hypothetical systems with particular emphasis on the dependence of energy exchange on the number of impacts. Comparison with exact trajectory calculations at high collision energies shows a diminished inelasticity as the result of repeated encounters between A and B in a single collision.