Semi-classical S matrix theory of reactive and non-reactive atom-molecule collisions

Expressions for the transition probabilities in collinear collisions of an atom with a diatomic molecule in the uniform. primitive, and classical semi-classical approximations of W.H. Miller arc rederived from a new integral representation of a semi-classical S matrix. This derivation treats reactive and non-reactive collisions in a unit-led manner and gives additional insight into the nature of the semi-classical approximation. The derivation and resulting expressions are given in terms of a general internal diatom coordinate which can be chosen for computational convenience. The new integral expression is compared with ones given previously.