Simulation of the fission process of the excited compound nuclei Rn210 and Fr215 produced in fusion reactions within the framework of the modified statistical model

Abstract

In the framework of the modified statistical model there have been simulated fission process of the excited compound nuclei $^{210}\mathrm{Rn}$ and $^{215}\mathrm{Fr}$ produced in $^{16}\mathrm{O}+^{194}\mathrm{Pt}$ and $^{19}\mathrm{F}+^{196}\mathrm{Pt}$ reactions and calculated the evaporation residue cross section, the fission cross section, the fission probability, the average prescission neutron multiplicity, the mean fission time, and the anisotropy of fission fragments angular distribution as a function of excitation energy. The classical collective motion of the excited compound nuclei about the ground state, the temperature dependence of the location, the height of fission transition points, and the projection of the total spin of the compound nucleus onto the symmetry axis $K$ have been considered in the statistical calculations. A constant nuclear dissipation was applied in the statistical calculations. In the statistical calculations, the temperature coefficient of the effective potential $k$ and the scaling factor of the fission-barrier height ${r}_{s}$ were considered as a free parameter and their magnitudes inferred by fitting measured data on the evaporation residue cross section and the fission cross section for the excited compound nuclei $^{210}\mathrm{Rn}$ and $^{215}\mathrm{Fr}$. It was shown that the results of calculations are in good agreement with the experimental data by using appropriate values for these parameters equal to $k=0.0160\ifmmode\pm\else\textpm\fi{}0.0050\phantom{\rule{0.28em}{0ex}}\mathrm{Me}{\mathrm{V}}^{\ensuremath{-}2}$ and ${r}_{s}=1.0030\ifmmode\pm\else\textpm\fi{}0.0020$ for $^{210}\mathrm{Rn}$ and $k=0.0065\ifmmode\pm\else\textpm\fi{}0.0040\phantom{\rule{0.16em}{0ex}}\mathrm{Me}{\mathrm{V}}^{\ensuremath{-}2}$ and ${r}_{s}=1.0040\ifmmode\pm\else\textpm\fi{}0.0015$ for $^{215}\mathrm{Fr}$. Furthermore, by using appropriate values of parameters $k$ and ${r}_{s}$ have been calculated the average prescission neutron multiplicity, the fission probability, the mean fission time, and the anisotropy of fission fragments angular distribution for the nuclei $^{210}\mathrm{Rn}$ and $^{215}\mathrm{Fr}$. Comparison of the theoretical data with the experimental data were shown that the modified statistical model is well able to reproduce different experimental data. Although, at high excitation energies the results of calculations for the anisotropy of fission fragments angular distribution and fission probability are slightly lower than the experimental data.