Some Applications of the R-Matrix Theory to Reactive and Elastic Molecular Scattering

Abstract

Wigner's R‐matrix theory of collisions is applied to three topics in molecular scattering. We present sufficient conditions for a derivation of an activated‐complex theory of chemical reaction rates, and of a statistical theory of reactive collisions. In the statistical theory we find that the natural choice of the probability of decay of the collision complex into a given channel of the reaction product is a quantity proportional to the rate of production in that channel. Different assumptions have been made in the literature on the removal of the dynamics from the probability of decay, and a brief comparison is presented. A connection is noted between the activated‐complex and the statistical theory. Last, we discuss resonances in the total cross section for elastic scattering at low relative kinetic energy. Some illustrative calculations are made with the Breit—Wigner one‐level formula and the WKB approximation for the eigenstates of the collision complex.