Abstract
The energy of the charge-exchange anti-analogue giant dipole resonance (AGDR) has been calculated using the state-of-the-art fully self-consistent relativistic proton–neutron quasiparticle random-phase approximation based on the relativistic Hartree–Bogoliubov model. It is shown that the AGDR centroid energy is very sensitively related to the corresponding neutron-skin thickness. The AGDR excitation energy has also been used to calculate the symmetry energy at saturation and the slope of the symmetry energy, resulting in more stringent constraints than most of the previous studies.