Multiple transition points in a semiclassical treatment of electronic transitions in atom(ion)-diatom collisions

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Abstract
A semiclassical treatment of multiple transition points for electronic transitions in atom(ion)‐diatom collisions is presented. The treatment, based on a theory by W. H. Miller and T. F. George [J. Chem. Phys. 56, 5637 (1972)], involves the semiclassical evaluation of a path integral connecting the initial and final states of a given collision. The evaluation considers first the classical limit of an electronic propagator, which is a function of the time development of the nuclear degrees of freedom, and then the classical limit of a nuclear path integral containing the electronic propagator. The treatment of multiple transition points in the electronic propagator is presented in analogy with the problem of motion over multiple barriers. For transition points close in time a uniform approximation must be introduced in the evaluation of the electronic propagator. This is distinguished from another uniform approximation which might be necessary in the evaluation of the nuclear path integral. The resulting forms of classical S matrix elements derived from these approximations are given, and their application to H+ + D2 collisions is discussed.