Excitation-energy dependence of fission in the mercury region

Background: Recent experiments on $\beta$-delayed fission reported an asymmetric mass yield in the neutron-deficient nucleus ${}^{180}\mathrm{Hg}$. Earlier experiments in the mass region $A=190–200$ close to the $\beta$-stability line, using the $(p,f)$ and $(\alpha ,f)$ reactions, observed a more symmetric distribution of fission fragments. While the $\beta$-delayed fission of ${}^{180}\mathrm{Hg}$ can be associated with relatively low excitation energy, this is not the case for light-ion reactions, which result in warm compound nuclei. The low-energy fission of ${}^{180,198}\mathrm{Hg}$ has been successfully described by theory in terms of strong shell effects in pre-scission configurations associated with dinuclear structures.

Purpose: To elucidate the roles of proton and neutron numbers and excitation energy in determining symmetric- and asymmetric-fission yields, we compute and analyze the isentropic potential energy surfaces of ${}^{174,180,198}\mathrm{Hg}$ and ${}^{196,210}\mathrm{Po}$.

Methods: We use the finite-temperature superfluid nuclear density functional theory for excitation energies up to $E^{*}=30$ MeV and zero angular momentum. For our theoretical framework, we consider the Skyrme energy density functional ${\mathrm{SkM}}^{*}$ and a density-dependent pairing interaction.

Results: For ${}^{174,180}\mathrm{Hg}$, we predict fission pathways consistent with asymmetric fission at low excitation energies, with the symmetric-fission pathway opening very gradually as excitation energy is increased. For ${}^{198}\mathrm{Hg}$ and ${}^{196}\mathrm{Po}$, we expect the nearly symmetric-fission channel to dominate. ${}^{210}\mathrm{Po}$ shows a preference for a slightly asymmetric pathway at low energies, and a preference for a symmetric pathway at high energies.

Conclusions: Our self-consistent theory suggests that excitation energy weakly affects the fission pattern of the nuclei considered. The transition from the asymmetric fission in the proton-rich nuclei to a more symmetric fission in the heavier isotopes is governed by the shell structure of pre-scission configurations.

Figure 1

Ground-state potential-energy surfaces for (a) ${}^{180}\mathrm{Hg}$ and (b) ${}^{198}\mathrm{Hg}$ in the $(Q_{20},Q_{30})$ plane calculated in HFB-${\mathrm{SkM}}^{*}$. The static fission pathway aEF corresponding to asymmetric elongated fragments is marked.

Figure 2

Similar to Fig. 1, but for ${}^{196}\mathrm{Po}$ in HFB-D1S. Two competing fission pathways corresponding to different mass asymmetry are marked.

Figure 3

The total shell correction energy at $T=0$ in ${}^{174,180,198}\mathrm{Hg}$ and ${}^{196}\mathrm{Po}$ along the symmetric (solid line, $Q_{30}=0$) and asymmetric (dashed line) fission pathways.

Figure 4

Potential-energy curves for ${}^{174,180,198}\mathrm{Hg}$ and ${}^{196}\mathrm{Po}$ at different values of excitation energy (in MeV).

Figure 5

Potential-energy surfaces for ${}^{174,180,198}\mathrm{Hg}$ and ${}^{196}\mathrm{Po}$ in the $(Q_{20},Q_{30})$ plane at different values of $E^{*}$ indicated (in MeV). The contour lines are separated by 1 MeV. The lowest static (least-energy) fission pathway is marked with a thick red line. The secondary fission pathways in ${}^{174,180}\mathrm{Hg}$ are marked with a yellow dashed line at the highest excitation energy.

Figure 6

Potential-energy surface for ${}^{210}\mathrm{Po}$ in HFB-${\mathrm{SkM}}^{*}$. Both the dominant, mildly-symmetry-breaking pathway and a secondary, more-severely-symmetry-breaking pathway are marked. The inset offers a closer look at a pre-scission region $(200<Q_{20}<360,0<Q_{30}<20)$ for $E^{*}=0$ MeV and for a higher excitation energy $E^{*}=43$ MeV.