Reduced spin-orbit splitting in 35Si: Weak binding or density-depletion effect?

The reduction of the neutron spin-orbit (SO) splitting 2p3/2−2p1/2 between the 41Ca and 35Si isotones is a unique feature throughout the chart of nuclides, as the SO splitting usually increases with decreasing A. The way it is reduced, either gradually between 41Ca and 35Si or abruptly between 37S and 35Si, as well as the origin of its reduction, whether from the weak binding energy of the p states or from the sudden depletion in the central proton density moving to 35Si, are subject of debate. The results reported here using the self-consistent Covariant Energy Density Functional calculations with the DD-ME2 parametrization rather point to an abrupt, local decrease in 35Si, and to the large dominance of the central density depletion effect. It is concluded that weak binding, central density depletion as well as correlations must be taken into account to fully evaluate the amplitude and causes of this SO splitting reduction. To broaden the scope of the present work, discussions also include the recent experimental results of proton and neutron SO splittings around 132Sn and 56Ni.