Exploring relativistic symmetry in shell evolution in the N=32 and N=34 isotones within a relativistic point-coupling model and the similarity renormalization group

The relativistic symmetry in the shell evolution in N = 32 and 34 isotones from Si to Ni is explored based on the relativistic point-coupling model combined with the similarity renormalization group (SRG). Taking the proton pseudospin doublets n1 p and n2 d and the spin doublets r1d, r1 f , and n2p as examples, the correlations of relativistic symmetry with subshell evolution, proton number, and quantum numbers of states are investigated. The origin and breaking mechanisms of pseudospin symmetry (PSS) and spin symmetry (SS) have been explored by the analytical decomposition of the Dirac Hamiltonian with SRG. The nonrelativistic term primarily determines the PSS quality, while the dynamical term and spin-orbit interaction significantly influence PSS. For SS, the spin-orbit interaction prevails. Despite substantial energy splittings within subshells, the pseudo(spin) doublets display similarities in their lower (upper) wave function components. Notably, PSS restoration is associated with bubblelike structures and subshell emergence/disappearance. A more diffuse potential in exotic nuclei facilitates improved PSS restoration, as demonstrated by the mean field potential E and its derivative E'(r) analysis.