Fission half-lives of superheavy nuclei in a microscopic approach

A systematic study of 160 heavy and superheavy nuclei is performed in the Hartree-Fock-Bogoliubov (HFB) approach with the finite-range and density-dependent Gogny force with the D1S parameter set. We show calculations in several approximations: with axially symmetric and reflection-symmetric wave functions, with axially symmetric and non-reflection-symmetric wave functions, and finally with some representative triaxial wave functions. Relevant properties of the ground state and along the fission path are thoroughly analyzed. Fission barriers, $Q_{\alpha }$ factors, and lifetimes with respect to fission and $\alpha$ decay as well as other observables are discussed. Larger configuration spaces and more general HFB wave functions as compared to previous studies provide a very good agreement with the experimental data.

Figure 1

Isotopes considered in this work.

Figure 2

Single-particle energies of the nucleus ${}^{270}$Hs as a function of the deformation parameter ${\beta }_2$ (top $x$ axis) and the quadrupole moment $Q_2$ (bottom $x$ axis). Continuous and dashed lines represent positive- and negative-parity states, respectively, and the bullets indicate the Fermi level.

Figure 3

Ground-state deformation parameters: (a) ${\beta }_2$, (b) ${\beta }_3$, (c) ${\beta }_4$, and (d) ${\beta }_6$ for superheavy nuclei. Notice that the deformation scale is panel dependent.

Figure 4

Ground-state pairing energies for superheavy nuclei: (a) protons and (b) neutrons.

Figure 5

$Q_{\alpha }$ values: theoretical values marked by dots are compared with experimental data [10, 94]. The different lines correspond to the indicated isotope.

Figure 6

(a) Two-neutron separation energies as a function of the neutron number. (b) Two-proton separation energies as a function of the proton number. The lines represent isotonic chains; the one at the lower left corner corresponds to $N=150$, and the one closer to the upper right corner corresponds to $A=190$. Experimental data are taken from Ref. [94].

Figure 7

Behavior of several magnitudes for the nuclei ${}^{274}$Hs, ${}^{278}$Ds, and ${}^{282}$Cn along different fission paths. Neutron and proton pairing energies $E_P^N$ (a) and $E_P^P$ (b) are in MeV, (c) inertia parameter $B$ is in ${10}^{-6}{\text{b}}^{-2}{\text{MeV}}^{-1}$, (d) HFB potential energy is in MeV, (e) triaxial deformation parameter $\gamma$ is in degrees, (f) octupole moment $Q_3$ is in ${\text{b}}^{3/2}$, (g) hexadecapole moment $Q_4$ is in ${\text{b}}^2$, and (h) the subintegral function of the action integral $dS/d{Q}_2$ is in ${\text{b}}^{-1}$.

Figure 8

The PES as a function of quadrupole and octupole moments for (a) ${}^{274}$Hs and (b) ${}^{282}$Cn. The energy origin has been set at the energy minimum.

Figure 9

Fission barriers for the nuclei Fm, No, and Rf along the AS-RS (continuous lines) and the AS-NRS path (long-dashed lines). The short-dashed lines in the lighter isotopes for $Q_2>50$ b correspond to the elongated fission paths. For clarity reasons in the ordinate axis the ground-state energy of each isotope has been set to zero and shifted by 10 MeV in each isotope.

Figure 10

Fission barriers for the Sg, Hs, and Ds isotopes along the AS-RS (continuous lines) and the AS-NRS path (dashed lines). The green short-dashed lines around the ground state for $A>184$ correspond to NRS solutions. For clarity reasons the ground-state energy of each isotope has been set to zero and shifted by 10 MeV in each isotope in the ordinate axis.

Figure 11

Same as Fig. 10, but for the Cn and $Z=114$ and 116 isotopes.

Figure 12

Same as Fig. 10, but for the $Z=118,120,$ and 122 isotopes.

Figure 13

Same as Fig. 10, but for the $Z=124$ and 126 isotopes.

Figure 14

The spontaneous fission and the $\alpha$-emission half-lives in SHEs. Experimental data are taken from Refs. [9, 10, 107].

Figure 15

The dominant decay modes of SHEs. The logarithm of the shortest half-lives (in seconds) is also indicated.