Analytical continuation from bound to resonant states in the Dirac equation with quadrupole-deformed potentials

Background: Resonances with pronounced single-particle characteristics are crucial for quantitative descriptions of exotic nuclei near and beyond the drip lines, and often impact halo formation and nucleon decay processes. Since the majority of nuclei are deformed, the interplay between deformation and orbital structure near threshold can lead to improved descriptions of exotic nuclei. Purpose: Develop a method to study single-particle resonant orbital structure in the Dirac equation with a quadrupole-deformed Woods-Saxon potential. Determine the structure evolution of bound and resonant levels with deformation in this scheme, and examine the impact on halo formation in loosely bound systems, with a focus on the recent halo candidate nucleus Mg37. Method: Analytical continuation of the coupling constant (ACCC) method is developed on the basis of the Dirac equation with a deformed Woods-Saxon potential. The scalar and vector terms in the deformed potential are determined by the energies of the valence neutron and nearby orbitals, which are extracted from a self-consistent relativistic Hartree-Bogoliubov (RHB) calculation with the PC-PK1 density functional. Results: We compare the energies and widths of resonant orbitals in the recent halo nucleus candidate Mg37 using the ACCC method based on the Dirac coupled-channel equations with those determined from the scattering phase shift (SPS) method. It is found that the results from the two methods agree well for narrow resonances, whereas the SPS method fails for broad resonances. Nilsson levels for bound and resonant orbitals from the ACCC method are calculated over a wide range of deformations and show some decisive hints of halo formation in Mg37. Conclusions: In our ACCC model for deformed potentials in the coupled-channel Dirac equations, the crossing of the configuration 1/2[321] and 5/2[312] orbitals at a deformation of approximately 0.5 enhances the probability to occupy the 1/2[321] orbital coming from 2p3/2 thereby explaining the recent observation of a p-wave one-neutron halo configuration in Mg37. The resonant 1/2[301] configuration plays a crucial role in halo formation in the magnesium isotopes beyond A=40 for a wide range of deformations larger than 0.2.