Systematic study of deformed nuclei at the drip lines and beyond

An improved prescription for choosing a transformed harmonic-oscillator (THO) basis for use in configuration-space Hartree-Fock-Bogoliubov (HFB) calculations is presented. The new $\text{HFB}+\text{THO}$ framework that follows accurately reproduces the results of coordinate-space HFB calculations for spherical nuclei, including those that are weakly bound. Furthermore, it is fully automated, facilitating its use in systematic investigations of large sets of nuclei throughout the periodic table. As a first application, we have carried out calculations using the Skyrme force SLy4 and volume pairing, with exact particle-number projection following application of the Lipkin-Nogami prescription. Calculations were performed for all even-even nuclei from the proton drip line to the neutron drip line having proton numbers $Z=2,4,\dots{},108$ and neutron numbers $N=2,4,\dots{},188$. We focus on nuclei near the neutron drip line and find that there exist numerous particle-bound even-even nuclei (i.e., nuclei with negative Fermi energies) that have at the same time negative two-neutron separation energies. This phenomenon, which was earlier noted for light nuclei, is attributed to bound shape isomers beyond the drip line.