Theory of reaction product velocity distributions

Abstract

A general method has been developed for calculating reaction product velocity distributions for bimolecular inelastic reactions. The method is based on the treatment of the reaction as a collision process and is an extension to inelastic collisions of the usual collision integral in the Boltzmann equation. The result is applicable to arbitrary velocity distributions of the initial reactants and to arbitrary differential cross sections for the reaction. The method is illustrated by calculating the product velocity distributions for hard sphere reactions and for isotropic constant mean-free-time reactions, with Maxwellian velocity distributions for the initial reactants. These results are compared with the unimolecular decomposition approximation. The application of the method to the interaction of crossed beams and to the interaction of a beam with a Maxwellian gas is also discussed.