A universal fate for spin-orbit partners in the weak-binding regime?

Over the past decade or so, experimental data on single-neutron energies in neutron-rich nuclei around N = 20 and 28 have become available. From this body of data, a smooth decrease in the separation of the 2p_3/2-2p_1/2 spin-orbit splittings is observed as they approach zero binding. This behavior is at odds with the well-accepted scaling, with mass, of measured spin-orbit splittings across the chart of nuclides for well-bound states as established by Mairle [Phys. Lett. B 304, 39 (1993)], but is well described by the calculations of the single-particle energies approaching the zero-binding threshold in a finite mean-field potential. We present the contrast between experimental data, the mean-field description, and the trends established by Mairle for both well-bound and weakly bound systems across the nuclear chart, with a focus on neutron spin-orbit partners. These trends appear to be universal.