Exotic symmetries as stabilizing factors for superheavy nuclei: Symmetry-oriented generalized concept of nuclear magic numbers

Abstract

We introduce the concept of the nuclear octupole fourfold (i.e., applying simultaneously to all the four octupole deformations ${\ensuremath{\alpha}}_{30}$, ${\ensuremath{\alpha}}_{31}$, ${\ensuremath{\alpha}}_{32}$, and ${\ensuremath{\alpha}}_{33}$) neutron ``magic number'' $N=196$ and discuss the physical consequences of its presence. Our theoretical predictions are obtained using the realistic phenomenological mean-field approach with the deformed Woods-Saxon potential, the latter employing the new parametrization optimized in our preceding articles. Correlations among 4 parameters in the set of 12 parameters of the Woods-Saxon potential are detected and removed employing Monte Carlo approach leading to stabilization of the predictive power of the modeling. Our main focus is examining the impact of the four-fold octupole magic number $N=196$ on the stability properties of superheavy nuclei with $114\ensuremath{\le}Z\ensuremath{\le}130$ and $166\ensuremath{\le}N\ensuremath{\le}206$. Calculations suggest that majority of the examined nuclei are either spherical or octupole deformed, octupole-tetrahedral geometry playing the dominating role lowering the ground-state energy by up to 8 MeV. The origin and manifestations of this domination are illustrated and discussed. It turns out that, in several cases, alternative point-group symmetries may lead to noticeable lowering of the nuclear energy; this concerns the ${C}_{2v}$ geometry associated with ${\ensuremath{\alpha}}_{31}$, the ${D}_{3h}$ geometry related to ${\ensuremath{\alpha}}_{33}$, and ${D}_{2d}$ corresponding to the combination of ${\ensuremath{\alpha}}_{32}$ and ${\ensuremath{\alpha}}_{20}$ quadrupole component.