Deformed magic numbers at $N=$178 and $Z=$120, 124 in the 112 $\leq N \leq $ 190 superheavy region from Skyrme mean-field calculations

Abstract

Background: Various motivations for exploration of superheavy region revolve around the question on whether 126 is a spherical proton magic number, as is the case for neutrons. In exploring this region, identification of nuclei with relatively longer half-life as compared to its neighbours is crucial for experimental studies. Such information is provided from theoretical predictions, which are however, heavily dependent on the theoretical model used and observable quantities under investigation. Purpose: Limiting ourselves to the Skyrme Hartree-Fock-plus-Bardeen-Cooper-Schrieffer approach, we aimed to analyse the appearance of a nuclear region with relatively high stability associated with emergence of spherical and deformed magic numbers in the region of $170 \le N \le 190$ ($112 \le Z \le 130$) based on various observables. Methods: Three Skyrme parametrizations namely the SkM* frequently employed for fission calculations, and the SLy5 and SLy4 commonly used for superheavy region, are considered to provide comparisons within the Skyrme mean-field approach. We evaluated the variation of electric quadrupole deformation ($β_{20}$), binding energy per nucleon ($BE/A$), two-nucleon separation energy differential ($δS2_{q}$), alpha-decay energy ($Q_α$) and alpha-decay half-lives ($T_{1/2}$). Conclusion: Our analyses suggest that neutron number $N = 178$ is candidate for deformed magic number around proton number $114 \le Z \le 118$. For protons, $Z = 120$ and $124$ appears to be a candidate for deformed magic number at around $N = 172 \sim 178$. Both sets of deformed magic numbers appear at oblate ground-state deformation.