Semiclassical collision theory within the Feynman path-integral formalism: The perturbed stationary state formulation

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Abstract
Classical equations are derived for the relative motion of two molecules as the internal degrees of freedom make a given quantum transition by extending the semiclassical theory of Peckhuks into the adiabatic representation. Using a stationary phase approximation to Feynman’s path integral representation of quantum mechanics as a starting point, classical trajectories are obtained which fulfill angular momentum and energy conservation. The features of the adiabatic treatment are analyzed through the numerical integration of the collinear harmonic oscillator-atom collision. The calculations show that the use of a perturbed basis appreciably reduces the computational time required by the iterative procedure of integration. However no solution can be obtained as in the diabatic approach for some classically forbidden transitions.