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. One of the primary motivations for the study of exotic nuclei is to search for novel shell structure effects. A large amount of attention has been paid to the possibility that the spin-orbit force on high-j neutron orbits weakens in nuclei near the neutron drip line [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. The neutron magic numbers for stable nuclei rely on the effect of the strong spin-orbit force on high-j orbits, so the weakening of this force has the potential to change the neutron magic numbers in neutron-rich nuclei. The possibility of the narrowing or collapse of the N = 28 major shell closure in neutron-rich nuclei near 42 Si has attracted considerable attention because these isotopes are becoming accessible to experiments [15,16,17,18]. The two most important reasons generally given for the decline of the spin-orbit force on high-j neutron orbits near the neutron drip line are the large neutron surface diffuseness and the influence of the continuum in these nuclei [19,20].In the present communication, we predict a novel shell structure effect having to do with spin-orbit splitting in low-j neutron orbits -namely, p orbits. The dramatic decrease in the spin-orbit splitting described here is not caused by the neutron density near the nuclear surface, but rather by the proton density in the nuclear interior. The two nuclei for which we make specific predictions, 46 Ar and 206 Hg, are exotic but within two protons of the valley of stability. We make these predictions using the relativistic mean field theory, which has also been used to study the spin-orbit splitting of high-j orbits in exotic nuclei [4,8,9,11,13].The relativistic mean field calculation reported here is identical to the calculation used in Ref.[21] to predict the properties of neutron-rich nuclei over a wide mass range. The model used in Ref.[21] is based on a Lagrangian developed in Refs. [22,23] that includes novel nonlinear couplings between the isoscalar and isovector mesons. These new terms, which supplement the phenomenologically successful Lagrangians of Refs. [24,25,26], modify the density dependence of the symmetry energy without changing ground state properties that are well established experimentally. Modifications to the poorly known density dependence of t...
