Triaxial relativistic Hartree-Bogoliubov theory in continuum for exotic nuclei

A triaxial relativistic Hartree-Bogoliubov theory in continuum (TRHBc) has been developed to incorporate triaxial deformation, pairing correlations, and continuum effects in a fully microscopic and self-consistent way, aiming for a reliable description of triaxial exotic nuclei with extreme neutron-to-proton ratios. The TRHBc formalism is presented in detail, and its numerical implementation is benchmarked against the results from the axially deformed relativistic Hartree-Bogoliubov theory in continuum and the TRHB theory in harmonic oscillator expansion. The TRHBc theory is applied to investigate the aluminum isotopes systematically, and the available data are well reproduced for the binding energies, one- and two-neutron separation energies, and charge radii. The nuclei near the one-neutron drip line, $^{40}$Al and $^{42}$Al, are found to be triaxially deformed with one-neutron separation energies below 1 MeV. Possible neutron halos in the triaxial nuclei $^{40}$Al and $^{42}$Al are explored by examining the single-particle levels around the Fermi surface, including their composition and contribution to the total neutron density. The existence of neutron halos in $^{40}$Al and $^{42}$Al is also supported by the halo scale, which is comparable to other halo nuclei well-established previously. More importantly, the mechanism for the halo formation in $^{40}$Al is revealed to be the triaxial deformation, which results in the decoupling of the halo orbitals from those of the core.