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

TL;DR

This study links the neutron skin thickness in lead-208 to the energy difference between specific nuclear resonances, providing new constraints on nuclear symmetry energy parameters through microscopic calculations and experimental data comparison.

Contribution

It introduces a linear correlation between AGDR-IAS energy difference and neutron skin thickness using a microscopic approach with Skyrme functionals, refining constraints on symmetry energy.

Findings

Neutron skin thickness Delta(R) = 0.204 ± 0.009 fm

Symmetry energy at saturation J = 31.4 ± 0.5 MeV

Slope parameter L = 76.4 ± 5.4 MeV

Abstract

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.