Two-dimensional Langevin modeling of fission dynamics of the excited compound nuclei ¹⁸⁸ Pt, ²²⁷ Pa and ²⁵¹ Es

Abstract

A stochastic approach based on one-and two-dimensional Langevin equations is applied to calculate the pre-scission neutron multiplicity, fission probability, anisotropy of fission fragment angular distribution, fission cross section and the evaporation cross section for the compound nuclei 188 Pt, 227 Pa and 251 Es in an intermediate range of excitation energies. The chaos weighted wall and window friction formula are used in the Langevin equations. The elongation parameter, c, is used as the first dimension and projection of the total spin of the compound nucleus onto the symmetry axis, K, considered as the second dimension in Langevin dynamical calculations. A constant dissipation coefficient of K, γK = 0.077(MeV zs) −1/2 , is used in two-dimensional calculations to reproduce the above mentioned experimental data. Comparison of the theoretical results of the pre-scission neutron multiplicity, fission probability, fission cross section and the evaporation cross section with the experimental data shows that the results of two-dimensional calculations are in better agreement with the experimental data. Furthermore, it is shown that the two-dimensional Langevin equations together with a dissipation coefficient of K, γK = 0.077(MeV zs) −1/2 , can satisfactorily reproduce the anisotropy of fission fragment angular distribution for the heavy compound nucleus 251 Es. However, a larger value of γK = 0.250(MeV zs) −1/2 is needed to reproduce the anisotropy of fission fragment angular distribution for the lighter compound nucleus 227 Pa.