Integral Kramers formula for the fission rate versus dynamical modeling: The case of deformation-dependent temperature

Abstract

We have derived approximate analytical formulas describing the quasistationary fission rate of excited nuclei (the Kramers rates). These rates are compared with those resulting from dynamical modeling using the Smoluchowski equation (the dynamical rates). Contrary to the original Kramers approach, we have accounted for the microcanonical nature of the fission process. The influence of the potential at the scission point on the fission rates is also studied. Comparison with the dynamical rates enables us to define the accuracy of the Kramers rates in the wide range of the ratio of the fission barrier height B f to the temperature at the quasistationary state T c up to 16. These high values are not reachable within the traditional Langevin approach.

Testing the energy diffusion approximation for the escape of a Brownian particle from a potential pocket

“…We are not aware of any crossing of the scientific activity of the authors of Refs. [17,18] on one hand and of Ref. [9] on the other hand.…”