Isovector Monopole Resonance

Abstract

We present a theoretical study of the three isospin channels of the isovector giant monopole resonance (IVGMR) within self-consistent Skyrme Hartree-Fock plus Random-Phase Approximation. A modified charge-exchange monopole operator is introduced to remove the dominant isobaric-analog-state contribution, thereby isolating the genuine radial isovector response. We derive the associated non-energy- and energy-weighted sum rules and establish approximate relations between the charge-exchange and non-charge-exchange strengths. The relative locations of the three IVGMR centroids are interpreted in terms of Coulomb displacement energies, the neutron-proton mass difference, and the finite-nucleus symmetry potential. Calculations for \(^{48}\)Ca, \(^{90}\)Zr, and \(^{208}\)Pb show that the non-charge-exchange centroid is accurately approximated by the average of the two charge-exchange centroids in medium-heavy and heavy nuclei. Using a broad set of Skyrme energy-density functionals, we find that the centroid energies of the three channels display a weak model dependence for a fixed nucleus, whereas the non-charge-exchange monopole polarizability exhibits a clear sensitivity to the density dependence of the symmetry energy. These results clarify the isospin structure of the IVGMR and support its use as a complementary probe of isovector nuclear properties.