Constraints on the neutron skin and symmetry energy from the anti-analog giant dipole resonance in $^208\mathrmPb$

We investigate the impact of the neutron skin thickness, ΔR np , 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 Pb 208 . 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 ΔR np . 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 approach and we can compare our results with available experimental data in Pb 208 in order to extract a preferred value for ΔR np and, in turn, for the symmetry energy parameters. Averaging the results from two available experimental data, our analysis gives ΔR np = 0.236±0.018 fm, J = 33.2±1.0 MeV, and a slope parameter of the symmetry energy at saturation L = 97.3±11.2 MeV. The errors include the experimental uncertainties and a lower-limit estimate of model uncertainties. These results are consistent with those extracted from different experimental data albeit L and ΔR np are somewhat large when compared to previous estimations based on giant resonance studies. Possible hints whether model dependence can explain this difference are provided.