Generalization of Kramers's formula: Fission over a multidimensional potential barrier

We generalize Kramers's rate expression for diffusion over a potential barrier to the case of a diffusion problem for $n$ degrees of freedom. These can be thought of as the shape degrees of freedom of a fissioning nucleus. We present our formula for the fission width and discuss its dependence on the parameters—the mass tensor, the friction tensor, and the shape of the potential landscape.