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

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 $\alpha$-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 $\gamma$-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 $\alpha$-decay energies $Q_\alpha$ 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.