The relativistic mean field (RMF) model has achieved great success in describing various nuclear phenomena. However, several serious defects are common. For instance, the pseudo-spin symmetry of high-l orbits is distinctly violated in general, leading to spurious shell closures and . This leads to problems in describing structure properties, including shell structures, nuclear masses, etc. Guided by the pseudo-spin symmetry restoration [Geng et al., Phys. Rev. C, 100: 051301 (2019)], a new RMF Lagrangian DD-LZ1 is developed by considering the density-dependent meson-nucleon coupling strengths. With the newly obtained RMF Lagrangian DD-LZ1, satisfactory descriptions can be obtained for the bulk properties of nuclear matter and finite nuclei. In particular, significant improvements on describing the single-particle spectra are achieved by DD-LZ1. In particular, the spurious shell closures and , commonly found in previous RMF calculations, are eliminated by the new effective interaction DD-LZ1, and consistently the pseudo-spin symmetry (PSS) around the Fermi levels is reasonably restored for both low-l and high-l orbits. Moreover, the description of nuclear masses is also notably improved by DD-LZ1, as compared to the other RMF Lagrangians.

Background: One fascinating frontier in nuclear physics is the study of exotic nuclei. The deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), which simultaneously includes the nuclear superfluidity, deformation, and continuum effects, can provide proper descriptions for both stable and exotic nuclei. In a previous work [Zhang et al., Phys. Rev. C 102, 024314 (2020)], the DRHBc theory based on the point-coupling density functionals was developed and the DRHBc calculation, previously accessible only for light nuclei, was extended for all even-even nuclei in the nuclear chart. The ground-state properties for the even-even nuclei with $8\le Z\le 120$ from the DRHBc calculations have been summarized [Zhang et al., At. Data Nucl. Data Tables 144, 101488 (2022)].

Starting from the Bonn potential, the relativistic Brueckner-Hartree-Fock (RBHF) equations are solved for nuclear matter in the full Dirac space, which provides a unique way to determine the single-particle potentials and avoids the approximations applied in the RBHF calculations in the Dirac space with positive-energy states (PESs) only. The uncertainties of the RBHF calculations in the Dirac space with PESs only are investigated, and the importance of RBHF calculations in the full Dirac space is demonstrated. In the RBHF calculations in the full Dirac space, the empirical saturation properties of symmetric nuclear matter are reproduced, and the obtained equation of state agrees with the results based on the relativistic Green's function approach up to the saturation 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 {${}^{34}\mathrm{Si},{}^{34}\mathrm{Ca}$} commonly by the selected Lagrangians, due to the persistence of $Z\left(N\right)=14$ subshell gaps above which the $\pi \left(\nu \right)2s_{1/2}$ states are not occupied. However, for the popular candidate ${}^{46}\mathrm{Ar}$, 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.