Applying Kramers formula for the nuclear fission problem: How accurate is it?

We compare results of dynamical modeling of the fission process with predictions of the Kramers formulas. For the case of large dissipation these are two: the integral rate R_I and its approximation R_O . As the ratio of the fission barrier height B_f to the temperature T, ε, reaches 4, any analytical rate is expected to agree with the dynamical quasistationary value R_D within 2%. We perform modeling using several potentials and find that the difference between the R_O and the R_D sometimes exceeds 20% even for ε > 4. Such discrepancy is not acceptable nowadays because it is comparable to the quantum, non-markovian and multidimensional effects. The features of the potentials which cause this disagreement are identified and studied. It is demonstrated that this is the R_I, not the R_O, which meets the expectation above irrespectively of the potential profile.