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

The even-even superheavy nuclei with 104 ≤ Z ≤ 126 and N ≤ 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 ( E 2 ; 2 1 + → 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 ≤ Z ≤ 118. Oblate deformations are favored for Z ≥ 120 isotopes around N = 178 . Remarkably, for a substantial range of transitional superheavy nuclei with N ≳ 184 and N ≳ 240, 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 2 n 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.