The predictive power of the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) for nuclear mass is examined in the superheavy region, $102\le Z\le 120$. The accuracy of predicting the 10 (56) measured (measured and empirical) masses is 0.635 (0.642) MeV, in comparison with 0.515 (1.360) MeV by WS4 and 0.910 (2.831) MeV by FRDM. Possible stability against multineutron emission beyond the two-neutron drip line is explored by the DRHBc theory, which takes into account simultaneously the deformation effects, the pairing correlations, and the continuum effects. Nuclei stable against two- and multineutron emissions beyond the two-neutron drip line are predicted in ${}_{106}\mathrm{Sg}, {}_{108}\mathrm{Hs}, {}_{110}\mathrm{Ds}$, and ${}_{112}\mathrm{Cn}$ isotopic chains, forming a peninsula of stability adjacent to the nuclear mainland. This stability is mainly due to the deformation which significantly affects the shell structure around the Fermi surface. The pairing correlations and continuum influence the stability peninsula in a self-consistent way.

Possible bound nuclei beyond the two-neutron drip line in the $50\le Z\le 70$ region are investigated by using the deformed relativistic Hartree-Bogoliubov theory in continuum with density functional PC-PK1. Bound nuclei beyond the drip lines of ${}_{56}\mathrm{Ba}$, ${}_{58}\mathrm{Ce}$, ${}_{62}\mathrm{Sm}$, ${}_{64}\mathrm{Gd}$, and ${}_{66}\mathrm{Dy}$ are predicted, forming peninsulas of stability in the nuclear landscape. Near these peninsulas, several multineutron emitters are predicted. The underlying mechanism of the peninsulas of stability is investigated by studying the total energy, Fermi surface, quadrupole deformation, and the single-neutron spectrum in the canonical basis. It is found that the deformation effect is crucial for forming the peninsulas of stability, and pairing correlations are also essential in specific cases. The dependence on the deformation evolution is also discussed. The decay rates of multineutron radioactivity in Ba and Sm isotopic chains are estimated by using the direct decay model.

The Woods-Saxon basis has achieved great success in both nonrelativistic and covariant density functional theories in recent years. Due to its nonanalytical nature, however, applications of the Woods-Saxon basis are numerically complicated and computationally time consuming. In this paper, based on the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), we check in detail the convergence with respect to the basis space in the Dirac sea. An optimized Dirac Woods-Saxon basis is proposed, whose corresponding potential is close to the nuclear mean field. It is shown that the basis space of the optimized Dirac Woods-Saxon basis required for convergence is substantially reduced compared with the original one. In particular, it does not need to contain the bases from continuum in the Dirac sea. The application of the optimized Woods-Saxon basis would greatly reduce computing resource for large-scale density functional calculations.

The dominance of prolate over oblate ground-state deformations has been a well-known empirical fact. With the state-of-the-art deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) and taking Te, Xe, and Ba isotopes with neutron number $82⩽N⩽126$ as examples, a self-consistent and microscopic study of the prolate-shape dominance is given. According to the calculated potential-energy curves, most of these isotopes have both prolate and oblate minima and prefer prolate in the ground state, while the small amount of oblate ground-state shapes mainly appear after the major shell is half filled. It is also found that the prolate-shape dominance enhances with the proton number increasing from 52 to 56. The dominance and its enhancement can be well understood by the microscopic canonical single-particle energies obtained in the DRHBc theory, in good agreement with the schematic interpretation based on the Nilsson diagram. Finally, pairing correlations are found to bring more energy displacements to oblate minima on average but do not play a decisive role in prolate-shape dominance.

More and more halo nuclei or candidates have been identified or suggested in experiments in recent years. It was declared that the halo structure of ${}^{22}\mathrm{Al}$ is revealed by the large isospin asymmetry in ${}^{22}\mathrm{Si}/{}^{22}\mathrm{O}$ mirror Gamow-Teller transitions [ Phys. Rev. Lett. 125, 192503 (2020)]. We highlight that a significant mirror asymmetry already exists between wave functions of the likely unbound nucleus ${}^{22}\mathrm{Si}$ and the doubly magic nucleus ${}^{22}\mathrm{O}$, which largely explains the observed asymmetry in the transitions. Furthermore, these transitions involve only the $1^{+}$ excited states of the daughter nuclei ${}^{22}\mathrm{Al}$ and ${}^{22}\mathrm{F}$. The $1^{+}$ state of ${}^{22}\mathrm{Al}$ cannot be considered a halo state due to its proton-unbound nature. An analysis of the spin parity suggests that a weakly bound $2s_{1/2}$ valence proton in the ground state of ${}^{22}\mathrm{Al}$ is improbable. To investigate the shell structure for the ground state of ${}^{22}\mathrm{Al}$, we employ the state-of-the-art deformed and triaxial relativistic Hartree-Bogoliubov theories in continuum. We find that a small $s$-wave component of $5\%$ appears for the weakly bound valence proton in ${}^{22}\mathrm{Al}$ only when triaxial deformation is considered. While the examination of densities and rms radii indicates that this small $s$-wave component is insufficient to form a discernible proton halo in ${}^{22}\mathrm{Al}$, slightly larger $2s_{1/2}$ occupations have been reported in other recent theoretical results. The question of how many low-$\ell$ components are sufficient to form a proton halo in the presence of the Coulomb barrier remains open. Thus, future measurements of reaction or interaction cross sections and momentum distributions of breakup fragments are highly desirable to verify whether ${}^{22}\mathrm{Al}$ is a halo nucleus.