Analysis of nuclear fission properties with the Langevin approach in Fourier shape parametrization

The Langevin approach is extendedly applied to study the dynamical process of nuclear fission within the Fourier shape parametrization, where the potential energy is calculated with the macroscopic-microscopic model based on the Lublin-Strasbourg drop model and the Yukawa-folded potential. The fragment mass distribution and the total kinetic energy as a function of heavy fragment mass in 14 MeV $n+^{235}\mathrm{U}$ fission are calculated and compared with the evaluated data from ENDF/B-VIII.0 and the experimental data. It is found that the Wall model for the friction tensor is available to describe both of the mass distribution and the total kinetic energy (TKE) distribution in the nuclear fission within the present model. In addition, the mass distributions and the TKE distributions in 14 MeV $n+^{233,236,238}\mathrm{U}$ and $^{239}\mathrm{Pu}$ fission are well described. Furthermore, the behavior of the correlation of the distance between the centers of mass of two fragments with the heavy fragment mass at the scission point is found to be consistent with that of the TKE distribution where the shortest ${R}_{12}$ locates around ${A}_{h}=135$ which is due to the influence of the shell effects.