Uniform expansion of the transition rate in Kramers' problem

Kramers' model of diffusion over potential barriers, e.g., chemical reactions, based on the noise activated escape of a particle from a potential well, is considered. Kramers derived escape rates valid for intermediate and large damping, and in a separate analysis, for small damping. In the small damping limit, Kramers' intermediate result reduces to the transition state rate which does not agree with the small damping result. A new escape rate is derived that is uniformly valid for all values of the damping coefficient. The new rate reduces to Kramers' results in the appropriate limits and, in particular, connects Kramers' intermediate and small damping results.