Neutron halo and spin-orbit splitting in some neutron-rich nuclei

The density-dependent relativistic mean-field theory with $\sigma$, $\omega$, and $\rho$ mesons, as a parameter-free calculation, has been used to study the ground-state properties of ${}_{}{}^{12,14}{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{30,32}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{60,62}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{122,124}{}_{}{}^{}\mathrm{Zr}$. A special emphasis is placed on the influence of the $\rho$ tensor coupling on the neutron halo and on the spin-orbit splitting. It is shown for the first time that the inclusion of the $\rho$ tensor coupling will lead to the isospin-dependent spin-orbit splitting although the binding energy and the radius of these nuclei are insensitive to it.