Exotic Nuclei and Relativistic Mean-Field Theory

A relativistic mean-field model is used to study the ground-state properties of neutron-rich nuclei. Nonlinear isoscalar-isovector terms, unconstrained by present day phenomenology, are added to the model Lagrangian in order to modify the poorly known density dependence of the symmetry energy. These new terms soften the symmetry energy and reshape the theoretical neutron drip line without compromising the agreement with existing ground-state information. A strong correlation between the neutron radius of Pb-208 and the binding energy of valence orbitals is found: the smaller the neutron radius of Pb-208, the weaker the binding energy of the last occupied neutron orbital. Thus, models with the softest symmetry energy are the first ones to drip neutrons. Further, in anticipation of the upcoming one-percent measurement of the neutron radius of Pb-208 at the Thomas Jefferson Laboratory, a close relationship between the neutron radius of Pb-208 and neutron radii of elements of relevance to atomic parity-violating experiments is established. On the basis of relativistic mean field calculations, we demonstrate 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, Ar-46 and Hg-206, in which the presence of a pair of s-1/2 proton holes would cause the spin-orbit 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 Ca-48 and Pb-208. We also explore how partial occupancy of the s-1/2 proton orbits affects this quenching. 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.