Systematic study of superheavy nuclei within a microscopic collective Hamiltonian: Impact of quantum shape fluctuations

Abstract

The even-even superheavy nuclei with $104 \leqslant Z \leqslant 126$ and $N\leqslant 258$ have been investigated using a microscopic five-dimensional collective Hamiltonian (5DCH) based on constrained triaxial relativistic Hartree-Bogoliubov calculations with the PC-PK1 density functional. The 5DCH approach effectively captures the characteristic of isospin dependence of nuclear binding energies, two-nucleon separation energies, and $α$-decay energies across isotopic chains and demonstrates consistent accuracy as $Z$ increases, underscoring the model's predictive power. The collective potentials, average quadrupole deformations, and characteristic collective observables: $E(2^+_1)$, $R_{42}$, and $B(E2; 2^+_1\to 0^+_1)$ reveal a shape transition from well-prolate deformation around $N=150$ and $N=210$ to medium-deformed $γ$-soft shape around $N=176$ and $N=246$, and finally to a spherical shape near $N=184$ and $N=258$ for the isotopic chains with $104\leqslant Z\leqslant 118$. Oblate deformations are favored for $Z\geqslant 120$ isotopes around $N=178$. Remarkably, for a substantial range of transitional superheavy nuclei with $N\gtrsim184$ and $N\gtrsim240$, no $0^+$ states bounded by the fission saddles are predicted within their very shallow potential wells due to quantum shape fluctuations (QSFs). Additionally, sharp variations predicted for two-neutron separation energies $S_{2n}$ and $α$-decay energies $Q_α$ at $N=184$ and $258$ in mean-field calculations are significantly reduced and shifted to $N=182$ and $256$ in the 5DCH calculations, which is caused by the rapid evolution of the dynamical correlation energies related to QSFs around the nuclear spherical shells.

Figures (34)

• Figure 1: Binding energy difference between the AME2020 data Wang2021CPC and (a) the TRHB calculations, and (b) the TRHB+5DCH for superheavy even-even nuclei with data available ($102 \leqslant Z \leqslant 118$). $\sigma_1$ represents the root-mean-square deviation from the available 56 measured (solid symbols) and empirical (open symbols) masses, whereas $\sigma_2$ pertains solely to the 10 measured masses.
• Figure 2: (Color online) Collective potentials in the $(\beta, \gamma)$ plane for the even-even Ds ($Z=110$) isotopic chain calculated by the constrained TRHB with PC-PK1 functional. All energies are normalized with respect to the binding energy of the lowest minimum within the fission barrier. The energy difference between adjacent contour lines is 0.5 MeV. The red stars indicate the average deformations of the ground states $0^+_1$.
• Figure 3: Three-dimensional plots of collective potential $V_{\rm coll}$ for $^{282}$Ds (a) and $^{298}$Ds (b) calculated using the constrained TRHB method with the PC-PK1 functional. Candidate $0^+$ states for each local minimum are marked by red solid dots, positioned at the average deformations of the corresponding state. The adjacent fission saddle is indicated by a red triangle. Probability density distributions in the ($\beta, \gamma$) plane for the candidate $0^+$ states are shown on the right of the panels, with red representing the peak density.
• Figure 4: (Color online) (a) Energy difference between the fission saddle and the candidate $0^+$ state in the deepest minimum for each superheavy nucleus. The zero-point vibrational energies of the $0^+$ candidates and the heights of adjacent fission saddles are also shown in panels (b) and (c), respectively. All energies are in the units of MeV.
• Figure 5: (Color online) Quadrupole deformations $\beta$ (panel a) and $\gamma$ (panel b) of the mean-field minima calculated from TRHB, and average quadrupole deformations $\langle\beta\rangle$ (panel b) and $\langle\gamma\rangle$ (panel c) of ground states $0^+_1$ from 5DCH for the even-even SHN with $104 \leq Z \leq 126$ from proton drip-line to $N=258$.