Exploration of the ground state properties of neutron-rich sodium isotopes using the deformed relativistic mean field theory in complex momentumrepresentations with BCS pairings*

Abstract

This study explores the ground-state characteristics of neutron-rich sodium isotopes, encompassing two-neutron separation energies, root-mean-square radii, quadrupole moments of proton and neutron distributions, single-particle levels of bound and resonant states, neutron density distributions, and shapes. Simultaneously, special attention is given to the distinctive physical phenomena associated with these isotopes. The deformed relativistic mean field theory in complex momentum representations with BCS pairings (DRMF-CMR-BCS), employed in our work, provides resonant states with real physics, offering insights into deformed halo nuclei. Four effective interactions (NL3, NL3$^{*}$, PK1, and NLSH) were considered to assess the influence of continuum and deformation effects on halo structures. Calculations for odd-even nuclei $^{35-43}$Na revealed the dependence on the chosen effective interaction and the number of considered resonant states. Neutron occupation patterns near the Fermi surface, particularly in orbitals $1/2^{-}_3$ and $3/2^{-}_2$, were found to play a crucial role in halo formation. The study provided detailed insights into the density distributions, shape evolution, and structure of neutron-rich sodium isotopes, contributing valuable information to the field of nuclear physics.