The nuclear fission process as Brownian motion: Modifying the Kramers fission rates

In 1940 Kramers demonstrated theoretically the influence of dissipation on the rate of the thermal escape of a Brownian particle from metastable state. He pointed out the nuclear fission process as a possible application of his results. In his derivation only the canonical ensemble and harmonical shapes of the potential were considered. We generalize the Kramers results for the case of the microcanonical ensemble which is more relevant for the fission process and derive the corrections to the original Kramers formulas accounting for the anharmonic character of the collective potential near its quasistationary and barrier points. The finite "distance" between the barrier and scission points is accounted for as well. We perform quantitative study of the agreement between the generalized and corrected Kramers fission rates and the exact dynamical quasistationary rates in the case of typical fission potentials.