Precision of approximate kramers formulas for the fission rate: Canonical and microcanonical ensembles

The precision of the Kramers formulas, which are frequently used to calculate the rate of fission of excited nuclei, is studied quantitatively bymeans of a numerical simulation. The deformation dependence of the level-density parameter is taken here into account in contrast to what was done in previous studies on this subject. It turns out that, as the excitation energy becomes lower, the error in the integral Kramers formula decreases monotonically, reaching 2% (precision of dynamical simulation) for a potential-barrier height three to four times greater than the temperature. The approximate Kramers formula obtained from the aforementioned integral formula is in substantially poorer agreement with the results of the dynamical simulation. In the same region of the controlling parameter, its typical error may change sign and reaches 5 to 15%.