Prediction of axially and triaxially deformed halo nuclei in the <italic>A</italic>≈40 mass region

<sec><p indent="0mm">The halo phenomenon has long been a frontier in experimental and theoretical nuclear physics research. Over nearly forty years of exploration, signals of halos have been identified in approximately 20 nuclei, with ³⁷Mg being the heaviest among them. The worldwide development of rare isotope beam facilities continues to advance the experimental exploration of new halo nuclei in the <italic>A</italic>≈40 mass region. Meanwhile, relevant theoretical predictions are increasingly desirable. </sec><sec> The relativistic density functional theory is a crucial tool for studying halo nuclei. The deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) is capable of describing deformed exotic nuclei by incorporating self-consistently axial deformation degrees of freedom, pairing correlations, and continuum effects. It has provided microscopic descriptions for several known halo nuclei, such as ³¹Ne and ³⁷Mg. The success of the DRHBc theory is further evidenced by the high-precision DRHBc mass table and related applications to various nuclear phenomena. The DRHBc theory has predicted the newly discovered nuclide ³⁹Na and the yet-to-be-synthesized ⁴²Mg as deformed halo nuclei. </sec><sec> It has been found that the lowering of the 2<italic>p</italic> orbitals in the spherical limit causes the collapse of the <italic>N</italic>=28 shell closure in ³⁹Na, leading to a well-deformed ground state. Pairing correlations, together with the mixing of <italic>pf</italic> components driven by deformation, result in the occupation of weakly bound or continuum <italic>p</italic>-wave neutron orbitals. Consequently, an oblate halo forms around the prolate core in ³⁹Na. </sec><sec> The experimental neutron separation energies and empirical matter radii of neutron-rich magnesium isotopes, along with the deformed <italic>p</italic>-wave halo characteristics of ³⁷Mg, are well reproduced by the DRHBc theory. A deformed neutron halo in ⁴²Mg is revealed through the analysis of angle-averaged densities as well as densities along and perpendicular to the symmetry axis for magnesium isotopes. It is shown that the deformation of a potential neutron halo depends essentially on the quantum numbers of the main components of the halo orbital(s). </sec><sec> The triaxial relativistic Hartree-Bogoliubov theory in continuum (TRHBc), which considers triaxiality, pairing correlations, and continuum effects, has been recently developed to explore triaxial halo nuclei. The TRHBc calculated neutron separation energies and charge radii for aluminum isotopes show good agreement with available experimental data. The heaviest observed odd-odd aluminum isotope, ⁴²Al, is predicted to be a triaxial halo nucleus with a novel shape decoupling, characterized by an exchange of intermediate and short axes from the well-deformed core to the super-deformed halo. </sec><sec> Combining nuclear reaction models with the DRHBc or TRHBc theory to provide a unified description of known halo nuclei and predict new ones, from structural properties to reaction dynamics, is a topic worthy of long-term exploration. Further applications of the DRHBc and TRHBc theories to other exotic phenomena near the dripline are also anticipated in the future. </sec>