Abstract
The precision of approximate Kramers formulas for the nuclear-fission rate in the presence of shell corrections in a quasistationary state is studied. The rates in question obtained analytically are compared with their numerical counterparts resulting from a dynamical simulation based on the Smoluchowski equation. It is shown that the integral Kramers formula is applicable even in the presence of shell corrections. As the excitation energy of the nucleus being considered decreases, the inaccuracy of this formula decreases monotonically, reaching 2% (inaccuracy of the dynamical simulation) in which case the dimensionless controlling parameter (entropy barrier) becomes greater than four. At small and intermediate values of this parameter, the accuracy of the integral Kramers formula is higher than the accuracy of the approximate Kramers formula obtained from it.
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