Effects of deformation, pairing and tensor correlation on the evolution of bubble structure within the Skyrme-Hartree-Fock method

We study the effects of deformation, tensor and pairing correlation on the evolution of bubble structure in ⁴⁶Ar, ²²O and Cl isotopes using a deformed Skyrme-Hartree-Fock model with BCS and Lipkin-Nogami number projection approximation. The parameter SLy5 of the Skyrme energy functionals is adopted together with various kinds of density-dependent pairing interaction and various kinds of tensor interaction. In the spherical case, considering pairing correlation (IS + IV) or switch off pairing, there is a clear bubble structure in ⁴⁶Ar with interaction SLy5 + Tw, respectively. For ⁴⁶Ar, we find that deformation weakens the bubble structure strongly, and pairing correlation also weakens the bubble in ⁴⁶Ar and ²²O , respectively. On the other hand, the SLy5 + Tw + IS + IV interaction evolves the bubble structure of neutron-rich Cl isotopes ^43-47Cl in deformed cases because the occupation probability of states 2 s_{1 / 2} decreases from 1 to 0.5.