An integral representation of isolated binary collisions in vibrational relaxation

Abstract

Path integral techniques are used to show that the quantum mechanics of a harmonic oscillator driven by Campbell’s noise provides an exact integral representation for a model of condensed phase vibrational relaxation in which the rate of transitions from one excited state to another is governed by independent, pairwise collisions between the excited state species and the molecules of the surrounding medium. In the limit of infrequent collisions and delta correlated noise, this exact representation of the rate can be reduced to the product of the frequency of collisions and a quantity that is related to the likelihood of a vibrational transition in a given collision. In this form, the vibrational relaxation rate has the same structure as the rate expression that can be regarded as the defining relation of the isolated binary collision model.