Deformed relativistic Hartree-Bogoliubov theory in continuum with a point-coupling functional: Examples of even-even Nd isotopes

Background: The study of exotic nuclei far from the $\ensuremath{\beta}$ stability line is stimulated by the development of radioactive ion beam facilities worldwide and brings opportunities and challenges to existing nuclear theories. Including self-consistently the nuclear superfluidity, deformation, and continuum effects, the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) has turned out to be successful in describing both stable and exotic nuclei. Due to several challenges, however, the DRHBc theory has only been applied to study light nuclei so far.Purpose: The aim of this work is to develop the DRHBc theory based on the point-coupling density functional and examine its possible application for all even-even nuclei in the nuclear chart by taking Nd isotopes as examples.Method: The nuclear superfluidity is taken into account via Bogoliubov transformation. Densities and potentials are expanded in terms of Legendre polynomials to include the axial deformation degrees of freedom. Sophisticated relativistic Hartree-Bogoliubov equations in coordinate space are solved in a Dirac Woods-Saxon basis to consider the continuum effects.Results: Numerical convergence for energy cutoff, angular momentum cutoff, Legendre expansion, pairing strength, and (un)constrained calculations are confirmed for the DRHBc theory from light nuclei to heavy nuclei. The ground-state properties of even-even Nd isotopes are calculated with the successful density functional PC-PK1 and compared with the spherical nuclear mass table based on the relativistic continuum Hartree-Bogoliubov (RCHB) theory as well as the available data. The calculated binding energies are in very good agreement with the existing experimental values with a rms deviation of $0.958\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$, which is remarkably smaller than $8.301\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$ in the spherical case. The predicted proton and neutron drip-line nuclei for Nd isotopes are respectively $^{120}\mathrm{Nd}$ and $^{214}\mathrm{Nd}$, in contrast with $^{126}\mathrm{Nd}$ and $^{228}\mathrm{Nd}$ in the RCHB theory. The experimental quadrupole deformations and charge radii are reproduced well. An interesting decoupling between the oblate shape ${\ensuremath{\beta}}_{2}=\ensuremath{-}0.273$ contributed by bound states and the nearly spherical one ${\ensuremath{\beta}}_{2}=0.047$ contributed by continuum is found in $^{214}\mathrm{Nd}$. Contributions of different single-particle states to the total neutron density are investigated and an exotic neutron skin phenomenon is suggested for $^{214}\mathrm{Nd}$. The proton radioactivity beyond the proton drip line is discussed and $^{114}\mathrm{Nd}, ^{116}\mathrm{Nd}$, and $^{118}\mathrm{Nd}$ are predicted to be candidates for two-proton or even multiproton radioactivity.Conclusions: The DRHBc theory based on the point-coupling density functional is developed and detailed numerical checks are performed. The techniques to construct the DRHBc mass table for even-even nuclei are explored and extended for all even-even nuclei in the nuclear chart by taking Nd isotopes as examples. The available experimental data are reproduced well. The deformation and continuum effects on drip-line nuclei, exotic neutron skin, and proton radioactivity are presented.