Microscopic study on asymmetric fission dynamics of ${}^{180}\mathrm{Hg}$ within covariant density functional theory

The asymmetric fission dynamics of ${}^{180}\mathrm{Hg}$ has been analyzed in the framework of the time-dependent generator coordinate method (TDGCM) based on covariant density functional theory (CDFT) with the relativistic PC-PK1 functional. Three-dimensional $({\beta }_2,{\beta }_3,q_N)$ constrained CDFT calculations have been performed to determine the scission configurations. Remarkably, an asymmetric fission valley is observed in the potential energy surface in the ${\beta }_2\text{−}{\beta }_3$ plane and the heavy/light fragments at scission are ${}^{101}\mathrm{Rh}/{}^{79}\mathrm{Br}$, in good agreement with the data. Furthermore, we find that the heavy fragments of lowest-energy scission configurations, compared to those of other scission points, have rather small quadrupole deformations (${\beta }_2\sim 0.4$) and certain octupole deformations (${\beta }_3\sim 0.3–0.4$), which are driven by the extended neutron octupole shell gap with $N=56$. Based on the scission configurations, the estimated total kinetic energy distribution is consistent with the trend of experimental data. Finally, the dynamical TDGCM calculation reproduces the asymmetric yield distribution of the low-energy fission of ${}^{180}\mathrm{Hg}$, especially for the peak positions.

Figure 1

Potential energy surfaces of ${}^{180}\mathrm{Hg}$ in the ${\beta }_2\text{−}{\beta }_3$ plane [panels (a), (b)] and in the ${\beta }_2\text{−}{q}_N$ plane for fixed ${\beta }_3=0.00$ [panel (c)] and ${\beta }_3=2.08$ [inset of panel (b)] calculated by the constrained CDFT with PC-PK1 functional. The purple solid and red dotted curves in panels (a), (b) denote the static fission path and scission line, respectively. The filled circle in the inset of panel (b) denotes the scission point. The symmetric elongated and compact fission modes are shown by the solid and dashed curves, respectively, in panel (c).

Figure 2

The potential energies (a) and mass (b) and neutron (c) numbers of heavy fragments, and quadrupole (d) and octupole (e) deformations of fragments along the scission line labeled by the corresponding ${\beta }_3$ value. Density distributions for some selected scission configurations are also shown in panel (a).

Figure 3

Potential energy surfaces of ${}^{100}\mathrm{Ru}$ calculated by CDFT with PC-PK1 functional. The star indicates the corresponding quadrupole and octupole deformations of the heavy fragment at the minimum of the scission point. The purple dashed curve denotes the configurations obtained by only constraining ${\beta }_3$ and leaving ${\beta }_2$ as free.

Figure 4

Neutron single-particle energies as a function of the quadrupole (lower scale) and octupole (upper scale) deformation parameters in ${}^{100}\mathrm{Ru}$. The dotted curve denotes the Fermi level. The left panel is for ${\beta }_3=0$, and the right panel is plotted following the purple dashed curve in Fig. 3.

Figure 5

The calculated Coulomb repulsive energy of the nascent fission fragments for ${}^{180}\mathrm{Hg}$ as a function of fragment mass, in comparison to the experimental data of the total kinetic energy [3].

Figure 6

Mass distribution of the fission fragments of ${}^{180}\mathrm{Hg}$ calculated by $\text{TDGCM}+\text{GOA}$ based on CDFT, in comparison with the data [1, 3] and the theoretical results in the framework of Brownian shape motion on five-dimensional potential energy surfaces, denoted as BSM(M) [15].