In the framework of the transition state theory (TST), the rate of thermally activated escapes from a locally stable state in phase space is determined by the unidirectional flux through a conveniently chosen dividing surface. It is known that the occurrence of trajectories that recross this surface renders the true rate smaller than the TST rate by the so-called transmission factor. By means of a statistical theory we show how the mean number of recrossings can be related to the transmission factor. Formulas are derived for the average number of recrossings at the top of a parabolic barrier and through an energy surface in phase space. The former case is relevant for the spatial diffusion regime and the latter for the energy diffusion regime. The resulting transmission factors are in good agreement with the exact ones.

• Received 26 October 1994

DOI:https://doi.org/10.1103/PhysRevE.51.1868