Abstract
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 are rederived from a new integral representation of a semi-classical S matrix. This derivation treats reactive and non-reactive collisions in a unified 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.
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