A stochastic approach based on four- and five-dimensional (5D) Langevin equations has been used to simulate the fission dynamics of the excited compound nucleus ${}^{233}\mathrm{Th}$ at low excitation energies. In the dynamical calculations, not only has the two-center shell model parametrization of nuclear shape been taken into account but also the projection of total spin of the compound nucleus to the symmetry axis, $K$. In the 5D dynamical model was used four collective shape coordinates $\left\{z_0/R_0,{\delta }_1,{\delta }_2,\eta \right\}$ plus the projection of total spin of the compound nucleus to the symmetry axis, $K$, and in the four-dimensional (4D) dynamical model used three collective shape coordinates $\left\{z_0/R_0,{\delta }_1={\delta }_2=\delta ,\eta \right\}$ plus the projection of total spin of the compound nucleus to the symmetry axis. The potential energy at low excitation energy was calculated by the finite range liquid drop model when considering shell and pairing effects. The Werner-Wheeler approximation was used to calculate the inertia tensor and the wall-and-window model with a reduction coefficient, $k_s$, was applied to calculate the fraction tensor. The fission probability, the mean total kinetic energy of fission fragments, the fission fragment mass yield, and the fission time distribution have been calculated for the excited compound nucleus ${}^{233}\mathrm{Th}$. Furthermore, the fission fragment mass yields have been calculated for ${}^{222}\mathrm{Th}$, where the symmetric fission component is dominant as well as for ${}^{226}\mathrm{Th}$, where the asymmetric component rapidly grows. In the calculations, the reduction coefficient was considered as a free parameter and its magnitude inferred for the excited compound nucleus ${}^{233}\mathrm{Th}$ by fitting measured data on the fission probability. It was shown that the results of calculations for the fission probability is in good agreement with the experimental data by using the magnitude of the reduction coefficient equal to $k_s=0.29$ for the excited compound nucleus ${}^{233}\mathrm{Th}$. Furthermore, in the 5D Langevin model the influence of different parameters, i.e., the reduction coefficient of nuclear dissipation, $k_s$, the deformation parameters, ${\delta }_i$, the dissipation coefficient of K, ${\gamma }_K$, the shell damping parameter, $E_d$, and the fission time were investigated on the simulation of fission dynamic of the excited compound nucleus ${}^{233}\mathrm{Th}$. According to the comparison of the results of the 4D and 5D Langevin models, it was shown that the 5D model is able to reproduce the experimental results more appropriately than the 4D model.

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• Fission
• Models & methods for nuclear reactions
• Nuclear reactions
• A ≥ 220
• Langevin algorithm