Exploring the Neutron Magic Number in Superheavy Nuclei: Insights into N = 258

In the framework of axial symmetric relativistic Hartree–Bogoliubov (RHB) theory and the Skyrme Hartree–Fock–Bogoliubov (HFB) theory, the evolution of shell structure, density distribution, and ground state deformation in superheavy nuclei proximate to N=258 are investigated within the relativistic functionals DD-PC1 and DD-ME2, as well as the non-relativistic functional UNEDF0. The results from DD-ME2 and UNEDF0 indicate that N=258 is a neutron magic number, whereas DD-PC1 does not anticipate the existence of a bound N=258 magic nucleus. Further discussion suggests that the emergence of the magic number N=258 is related to the depression of the central density.