  On the basis of relativistic mean field calculations, we predict that the
spin-orbit splitting of $p_{3/2}$ and $p_{1/2}$ neutron orbits depends
sensitively on the magnitude of the proton density near the center of the
nucleus, and in particular on the occupation of $s_{1/2}$ proton orbits. We
focus on two exotic nuclei, $^{46}$Ar and $^{206}$Hg, in which the presence of
a pair of $s_{1/2}$ proton holes is predicted to cause the splitting between
the $p_{3/2}$ and $p_{1/2}$ neutron orbits near the Fermi surface to be much
smaller than in the nearby doubly-magic nuclei $^{48}$Ca and $^{208}$Pb. We
note that these two exotic nuclei depart from the long-standing paradigm of a
central potential proportional to the ground state baryon density and a
spin-orbit potential proportional to the derivative of the central potential.
