Pseudospin-orbit splitting and its consequences for the central depression in nuclear density

The occurrence of the bubble-like structure has been studied, in the light of pseudospin degeneracy, within the relativistic Hartree-Fock-Bogoliubov (RHFB) theory. It is concluded that the charge/neutron bubble-like structure is predicted to occur in the mirror system of {Si-34, Ca-34} commonly by the selected Lagrangians, due to the persistence of Z(N) = 14 subshell gaps above which the pi(nu)2s(1/2) states are not occupied. However, for the popular candidate Ar-46, the RHFB Lagrangian PKA1 does not support the occurrence of the bubble-like structure in the charge (proton) density profiles, due to the almost degenerate pseudospin doublet {pi 2s(1/2), pi 1d(3/2)} and coherent pairing effects. The formation of a semibubble in heavy nuclei is less possible as a result of small pseudospin-orbit (PSO) splitting, while it tends to appear at Z = 120 superheavy systems which coincides with large PSO splitting of the doublet {pi 3p(3/2), pi 2f(5/2)} and couples with significant shell effects. Pairing correlations, which can work against bubble formation, significantly affect the PSO splitting. Furthermore, we found that the influence on semibubble formation due to different types of pairing interactions is negligible. The quenching of the spin-orbit splitting in the p orbit has been also stressed, and it may be considered the hallmark for semibubble nuclei.