Spin-orbit coupling characterizes quantum systems such as atoms, nuclei, hypernuclei, quarkonia, etc., and is essential for understanding their spectroscopic properties. Depending on the system, the effect of spin-orbit coupling on shell structure is
large in nuclei, small in quarkonia, perturbative in atoms. In the standard non-relativistic reduction of the single-particle Dirac equation, we derive a universal rule for the relative magnitude of the spin-orbit effect that applies to very different quantum systems, regardless of whether the spin-orbit coupling originates from the strong or electromagnetic interaction. It is shown that in nuclei the near equality of the mass of the nucleon and the difference between the large repulsive and attractive potentials explains the fact that spin-orbit splittings are comparable to the energy spacing between major shells. For a specific ratio between the particle mass and the effective potential whose gradient determines the spin-orbit force, we predict the occurrence of giant spin-orbit energy splittings that dominate the single-particle excitation spectrum.
Excited states in $^{28}$Na have been studied using the $beta$-decay of implanted $^{28}$Ne ions at GANIL/LISE as well as the in-beam $gamma$-ray spectroscopy at the NSCL/S800 facility. New states of positive (J$^{pi}$=3,4$^+$) and negative (J$^{pi}$
=1-5$^-$) parity are proposed. The former arise from the coupling between 0d$_{5/2}$ protons and a 0d$_{3/2}$ neutron, while the latter are due to couplings with 1p$_{3/2}$ or 0f$_{7/2}$ neutrons. While the relative energies between the J$^{pi}$=1-4$^+$ states are well reproduced with the USDA interaction in the N=17 isotones, a progressive shift in the ground state binding energy (by about 500 keV) is observed between $^{26}$F and $^{30}$Al. This points to a possible change in the proton-neutron 0d$_{5/2}$-0d$_{3/2}$ effective interaction when moving from stability to the drip line. The presence of J$^{pi}$=1-4$^-$ negative parity states around 1.5 MeV as well as of a candidate for a J$^{pi}$=5$^-$ state around 2.5 MeV give further support to the collapse of the N=20 gap and to the inversion between the 0f$_{7/2}$ and 1p$_{3/2}$ levels below Z=12. These features are discussed in the framework of Shell Model and EDF calculations, leading to predicted negative parity states in the low energy spectra of the $^{26}$F and $^{25}$O nuclei.
