  The reduction of the neutron spin-orbit splitting $2p_{3/2} - 2p_{1/2}$
between the $^{41}$Ca and $^{35}$Si isotones is a unique feature throughout the
chart of nuclides, as the spin-orbit splitting usually increases with $A$.
Moreover, its way of decrease, gradual between $^{41}$Ca and $^{35}$Si or
abrupt between $^{37}$S and $^{35}$Si, as well as its origin, caused by the
weak binding energy of the $p$ states or by the sudden central proton density
depletion in $^{35}$Si, 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 $^{35}$Si,
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
spin-orbit reduction.

Nuclear Theory;Nuclear Experiment