Mean First-Passage Times and the Dissociation of Diatomic Molecules

Abstract

The collisional activation of diatomic molecules to dissociation can be considered as a random walk with an absorbing barrier in the energy space of the molecules. In such a model, the rate of activation to dissociation is related to the mean first‐passage time of the molecules across the absorbing barrier. We have computed here the mean first‐passage time for an ensemble of oscillators in an initial Boltzmann distribution with transitions limited to nearest‐neighbor states (| Δv |=1) and for an ensemble of oscillators initially in the ground state (v=0) which undergo transitions between nonnearest‐neighbor states (| Δv |≥1). It is shown that the magnitude of the mean first‐passage time is very sensitive to the height (in energy space) of the absorbing barrier and to the ``jump distance,'' | Δv |>1, for nonnearest‐neighbor transitions. The implications of these results on the mechanism of the activation and dissociation of diatoms are discussed briefly.