Stochastic theory of molecular collisions

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Abstract
This paper investigates treating inelastic collisions as a stochastic process for the diffusion of probability between quantum states. It is shown that when the interaction is strong, the time‐dependent Schrödinger equation may be approximated by a Pauli master equation. Under certain circumstances this can be further approximated by a Fokker–Planck partial differential equation. These equations can be used to model various collision phenomena. Inelastic and dissociative collision processes are discussed, and it is indicated how the theory may be extended to systems with several degrees of freedom. The theory extends smoothly between (a) the perturbation and (b) statistical limits, although it should be better near limit (b). Nevertheless, comparisons even near limit (a) with a similar exact quantum mechanical collinear vibrational problem show that the diffusion model gives qualitative agreement and predicts certain trends correctly. For example, the usual sudden and adiabatic regimes are readily achieved, total probability is conserved, and multiquanta transitions are easily handled. It is hoped that the conceptual simplicity of the model will be useful in analyzing and perhaps correlating the behavior of large theoretical and experimental collision problems.