Constraints on the Neutron Skin and the Symmetry Energy from the Anti-analog Giant Dipole Resonance in 208Pb

We investigate the impact of the neutron-skin thickness Delta(R) on the energy difference between the anti-analog giant dipole resonance (AGDR), E(AGDR), and the isobaric analog state (IAS), E(IAS), in a heavy nucleus such as 208Pb. For guidance, we first develop a simple and analytic, yet physical, approach based on the Droplet Model that linearly connects the energy difference E(AGDR)-E(IAS) with Delta(R). To test this correlation on more fundamental grounds, we employ a family of systematically varied Skyrme energy density functionals where variations on the value of the symmetry energy at saturation density J are explored. The calculations have been performed within the fully self consistent Hartree-Fock (HF) plus charge-exchange random phase approximation (RPA) framework. We confirm the linear correlation within our microscopic apporach and, by comparing our results with available experimental data in 208Pb, we find that our analysis is consistent with Delta(R) = 0.204 \pm 0.009 fm, J = 31.4 \pm 0.5 MeV and a slope parameter of the symmetry energy at saturation of L = 76.4 \pm 5.4 MeV - the attached errors correspond to a lower-limit estimate of the systematic plus experimental uncertainties. These results are in agreement with those extracted from different experimental data albeit, L and Delta(R) are somewhat large when compared to previous estimations based on giant resonance studies.