A stochastic theory of collision phenomena: one-dimensional atom-diatom collision model

A stochastic model of one-dimensional atom—diatom collisions is explicitly solved and studied in this paper. By treating the translational motion as an irrelevant variable, a second order partial differential equation is obtained for which the energy conservation is strictly satisfied. This equation is shown to be solvable in terms of Mathieu functions. It is shown that when certain further approximations are made in the equation, it leads to the equations studied by other authors in the stochastic model of collision phenomena. Various approximate but analytic distribution functions are obtained for the distribution of the observables and some aspects of the model are discussed in terms of the solutions obtained.