Progress in the application of classical S-matrix theory to inelastic collision processes

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Abstract
Methods are described which effectively solve two of the technical difficulties associated with applying classical S‐matrix theory to inelastic/reactive scattering. Specifically, it is shown that rather standard numerical methods can be used to solve the ’’root search’’ problem (i.e., the nonlinear boundary value problem necessary to impose semiclassical quantum conditions at the beginning and the end of the classical trajectories) and also how complex classical trajectories, which are necessary to describe classically forbidden (i.e., tunneling) processes, can be computed in a numerically stable way. Application is made to vibrational relaxation of H2 by collision with He (within the helicity conserving approximation). The only remaining problem with regard to applying classical S‐matrix theory to complex collision processes has to do with the availability of multidimensional uniform asymptotic formulas for interpolating the ’’primitive’’ semiclassical expressions between their various regions of validity.