The Scattering of Atoms from Diatomic Molecules

Abstract

The quantum mechanics of the collision of an atom with a diatomic molecule is discussed. This is an example of the scattering of particles by a nonspherical potential field. In the region in which the atom and molecule are not interacting, the wave function for the system can be written as the product of a wave function for the free atom and that of the free molecule. By an analysis of this function one can write the asymptotic form of the true wave function in the terms of the scattering coefficients, representing the angular dependence of the transition probabilities. In a previous paper, group theoretical arguments were used to separate the rotational coordinates from the n‐particle Schroedinger equation. A set of coupled differential equations for the internal wave functions was derived. In the present paper, the scattering coefficients are obtained by an analysis of the solutions of the internal wave equations involving the three coordinates specifying the internal configuration. This set of equations is transformed into a set of coupled ordinary differential equations in which the coupling is the result of the transitions in the state of the molecule. The equations are solved by a perturbation method which is valid in the case of low energy collisions in which transitions occur relatively seldom. The angular transition probabilities are obtained explicitly in terms of integrals of the interaction potential and a set of phase shifts.