LAUSR

The recently observed weakly bound $^{39}\mathrm{Na}$ provides a stringent theoretical constraint on the neutron drip line. We studied the properties of drip-line nuclei around $^{39}\mathrm{Na}$ with the Hartree-Fock-Bogoliubov method and various Skyrme interactions. We adopted the extended ${\mathrm{SkM}}_{\mathrm{ext}1}^{*}$ parametrization which can properly describe two-neutron separation energies of oxygen and fluorine isotopes and deformations at the center of ``island of inversion.'' Systematic calculations of drip lines of O, F, Ne, Na, Mg, and Al isotopes have been performed. We infer that $^{42}\mathrm{Mg}$ is weakly bound and $^{45}\mathrm{Al}$ is less weakly bound. $^{44}\mathrm{Mg}$ and $^{47}\mathrm{Al}$ could barely exist. We also demonstrated the deformed halo properties of $^{39}\mathrm{Na}$. Our studies could be valuable for experimental explorations of drip-line nuclei in the forthcoming Facility for Rare Isotope Beams (FRIB) and other rare-isotope beam facilities.