Dissipation of the tilting degree of freedom in heavy-ion-induced fission from four-dimensional Langevin dynamics

Abstract.

A stochastic approach based on four-dimensional Langevin fission dynamics is applied to the calculation of a wide set of experimental observables of excited compound nuclei from ¹⁹⁹Pb to ²⁴⁸Cf formed in reactions induced by heavy ions. In the model under investigation, the tilting degree of freedom (K coordinate) representing the projection of the total angular momentum onto the symmetry axis of the nucleus is taken into account in addition to three collective shape coordinates introduced on the basis of $\{c,h,\alpha\}$ parametrization. The evolution of the K coordinate is described by means of the Langevin equation in the overdamped regime. The friction tensor for the shape collective coordinates is calculated under the assumption of the modified version of the one-body dissipation mechanism, where the reduction coefficient k_s of the contribution from the “wall” formula is introduced. The calculations are performed both for the constant values of the coefficient $k_{s}$ and for the coordinate-dependent reduction coefficient $k_{s}(\mathbf{q})$ which is found on the basis of the “chaos-weighted wall formula”. Different possibilities of the deformation-dependent dissipation coefficient $(\gamma_{K})$ for the K coordinate are investigated. The presented results demonstrate that an impact of the $k_{s}$ and $\gamma_{K}$ parameters on the calculated observable fission characteristics can be selectively probed. It was found that it is possible to describe the experimental data consistently with the deformation-dependent $\gamma_{K}(\mathbf{q})$ coefficient for shapes featuring a neck, which predicts quite small values of $\gamma_{K}=0.0077$ (MeV zs)^-1/2 and constant $\gamma_{K}=0.1$-0.4 (MeV zs)^-1/2 for compact shapes featuring no neck.