Fission Barriers of Compound Superheavy Nuclei

The dependence of fission barriers on the excitation energy of the compound nucleus impacts the survival probability of superheavy nuclei synthesized in heavy-ion fusion reactions. In this work, we investigate the isentropic fission barriers by means of the self-consistent nuclear density functional theory. The relationship between isothermal and isentropic descriptions is demonstrated. Calculations have been carried out for ${}^{264}\mathrm{Fm}$, ${}^{272}\mathrm{Ds}$, ${}^{278}112$, ${}^{292}114$, and ${}^{312}124$. For nuclei around ${}^{278}112$ produced in “cold-fusion” reactions, we predict a more rapid decrease of fission barriers with excitation energy as compared to the nuclei around ${}^{292}114$ synthesized in “hot-fusion” experiments. This is explained in terms of the difference between the ground-state and saddle-point temperatures. The effect of the particle gas is found to be negligible in the range of temperatures studied.

Figure 1

Calculated isothermal ($F$ at constant $T$) and isentropic ($E$ at constant $S$) axial symmetric fission pathways for ${}^{292}114$ as a function of the total quadrupole moment $Q_{20}$. The isothermal calculations were carried out at $kT=0.5$ and 1.5 MeV. In the isentropic description, $S$ was fixed at the free energy minimum, i.e., $S/k=18.5(69.2)$ at $kT=0.5(1.5)\mathrm{MeV}$.

Figure 2

The temperature along the isentropic symmetric fission pathways of ${}^{278}112$ and ${}^{292}114$. The g.s. and saddle-point configurations are marked by stars. The g.s. temperature was assumed to be $T_{\mathrm{g}.\mathrm{s}.}\sim 750\mathrm{keV}$ and $S=S(T_{\mathrm{g}.\mathrm{s}.})$. The temperature at the saddle point is considerably lower than $T_{\mathrm{g}.\mathrm{s}.}$.

Figure 3

Symmetric isentropic fission pathways of ${}^{264}\mathrm{Fm}$ at the values of $S$ corresponding to $k{T}_{\mathrm{g}.\mathrm{s}.}=0$, 0.5, 1.0, and 1.5 MeV The energy has been normalized to zero at the ground-state minimum. The effect of triaxial degrees of freedom on the first barrier is marked by dashed lines.

Figure 4

The height of the inner fission barrier in ${}^{264}\mathrm{Fm}$, ${}^{272}\mathrm{Ds}$, ${}^{278}112$, ${}^{292}114$, and ${}^{312}124$ as a function of excitation energy $E^{*}$. The effect of triaxiality on the fission barrier has been included. The experimental values of $E^{*}$ corresponding to CN formed in the reactions indicated are marked by arrows.

Figure 5

Proton (thick lines) and neutron (thin lines) spherical density distributions in ${}^{292}114$ calculated at different temperatures (in MeV). The external gas contributions are marked by dotted lines. The number of nucleons in the gas is indicated by numbers. The size of the box in HFB-AX was 20.4 fm.