Semiclassical Theory of Electronic Transitions in Low Energy Atomic and Molecular Collisions Involving Several Nuclear Degrees of Freedom

A semiclassical theory is developed for describing electronic transitions in low energy atomic and molecular collisions, such as A+BC, that involve quantized nuclear degrees of freedom (i.e., rotation and vibration) as well as translation. The principal physical idea is that in this low energy regime the dynamics is essentially classical motion of the nuclei on electronically adiabatic potential energy surfaces, with transitions between surfaces being events which are localized in space and time. The quantum principle of superposition is incorporated in the formulation in that classical dynamics is used to construct the classical limit of amplitudes (i.e., S matrix elements) for transitions from a specific initial electronic-rotational-vibrational state of A+BC to a specific final electronic-rotational-vibrational state of A+BC or AB+C, etc. Approximate and ``exact'' versions of the theory are developed, and in the ``exact'' version it is seen clearly that electronic transitions are inherently a ``classically forbidden'' process in that the classical action along the trajectories appropriate for such transitions has an imaginary contribution.