Temperature dependence of nuclear fission time in heavy-ion fusion-fission reactions

TL;DR

This paper introduces a new theoretical model based on the Ornstein-Uhlenbeck first-passage time method to accurately describe nuclear fission times at high excitation energies, improving upon Kramers' theory.

Contribution

The authors develop a novel theory for nuclear fission time at high temperatures, replacing Kramers' formula with an Ornstein-Uhlenbeck-based approach suitable for $T>1$ MeV.

Findings

The new model fits experimental data with a constant nuclear friction parameter.

Kramers' theory requires unphysical friction values at high energies.

Analytical formulas are provided for implementation in simulation codes.

Abstract

Accounting for viscous damping within Fokker-Planck equations led to various improvements in the understanding and analysis of nuclear fission of heavy nuclei. Analytical expressions for the fission time are typically provided by Kramers' theory, which improves on the Bohr-Wheeler estimate by including the time-scale related to many-particle dissipative processes along the deformation coordinate. However, Kramers' formula breaks down for sufficiently high excitation energies where Kramers' assumption of a large barrier no longer holds. In the regime $T>1$ MeV, Kramers' theory should be replaced by a new theory based on the Ornstein-Uhlenbeck first-passage time method that is proposed here. The theory is applied to fission time data from fusion-fission experiments on $^{16}$O+$^{208}$Pb $\rightarrow$ $^{224}$Th. The proposed model provides an internally consistent one-parameter fitting of fission data with a constant nuclear friction as the fitting parameter, whereas Kramers' fitting requires a value of friction which falls out of the allowed range. The theory provides also an analytical formula that in future work can be easily implemented in numerical codes such as CASCADE or JOANNE4.