Fission characteristics of the excited compound nucleus ${}^{210}\mathrm{Rn}$ in the framework of the four-dimensional dynamical model

The evaporation residue cross section, the anisotropy of the fission fragments angular distribution, the fission probability, the mass-energy distribution of the fission fragments, and the average prescission neutron multiplicity have been calculated for the compound nucleus ${}^{210}\mathrm{Rn}$ by using four-dimensional Langevin equations with dissipation generated through the chaos-weighted wall and window friction formula. Three collective shape coordinates plus the projection of the total spin of the compound nucleus to the symmetry axis $K$ were considered in the four-dimensional dynamical model. In the dynamical calculations dissipation coefficient of $K,{\gamma }_k$ was considered as a free parameter, and its magnitude was inferred by fitting measured data on the evaporation residue cross section and the anisotropy of the fission fragments angular distribution for the compound nucleus ${}^{210}\mathrm{Rn}$. It was shown that the results of the calculations are in good agreement with the experimental data by using values of the dissipation coefficient of $K$, equal to ${\gamma }_k=\left(0.185-0.200\right){\left(\mathrm{MeV}\mathrm{zs}\right)}^{-1/\phantom{12}2}$. It also was shown that the influence of the dissipation coefficient of $K$ on the results of the calculations of the fission probability, the mass-energy distribution of the fission fragments, and the average prescission neutron multiplicity for the compound nucleus ${}^{210}\mathrm{Rn}$ is small.

Figure 1

The Helmholtz free energy for the compound nucleus ${}^{210}\mathrm{Rn}$ as a function of the collective coordinates $q_1$ and $K$ at $T=0.0,T=2.0\mathrm{MeV}$, and $I=50\hslash$. The numbers on the contour lines represent the free energy values in MeV. The dashed curve shows the dependence of saddle-point deformations on $K$.

Figure 2

The results of the evaporation residue cross section as a function of excitation energy for ${}^{210}\mathrm{Rn}$ calculated with the 4D-dynamical model and by using different values of ${\gamma }_K$. The experimental data (filled circles) are taken from Ref. [49].

Figure 3

The same as in Fig. 2 but for anisotropy of the fission fragment angular distribution as a function of excitation energy for ${}^{210}\mathrm{Rn}$. The filled circles are the experimental data [50].

Figure 4

The anisotropy of the fission fragment angular distributions for the compound nucleus ${}^{210}\mathrm{Rn}$ as a function of scattering angle at different values of bombarding energies. The filled circles are the experimental data [50]. The dashed and dotted curves correspond to fitted values calculated with the 4D-dynamical model and by using different values of ${\gamma }_K$.

Figure 5

The same as in Fig. 4 but for the fission probability as a function of excitation energy for ${}^{210}\mathrm{Rn}$. The filled circles are the experimental data [50].

Figure 6

The same as in Fig. 4 but for the average prescission neutron multiplicity as a function of excitation energy for ${}^{210}\mathrm{Rn}$. The filled circles are the experimental data [51].

Figure 7

A contour diagram of the mass-energy distribution of the fission fragments for the compound nucleus ${}^{210}\mathrm{Rn}$ calculated with the 4D Langevin equations and by using ${\gamma }_k=0.185{\left(\mathrm{MeV}\mathrm{zs}\right)}^{-1/\phantom{12}2}$ at $E^{*}=80\mathrm{MeV}$. The numbers on the contour lines are the yield of the fission fragments in percentages. The total yield is normalized for 200%.

Figure 8

The fission rate calculated for ${}^{210}\mathrm{Rn}$ at fixed spin $I=30\hslash$ and at $E^{*}=80\mathrm{MeV}$. The open squares and open circles are the calculated results calculated with the 4D Langevin equations and by using different values of the dissipation coefficient of $K$.