Symmetry Energy Constraints from Giant Resonances: A Theoretical Overview

Abstract: Giant resonances encapsulate the dynamic response of the nuclear ground state to external perturbations. As such, they offer a unique view of the nucleus that is often not accessible otherwise. Although interesting in their own right, giant resonances are also enormously valuable in providing stringent constraints on the equation of state of asymmetric matter. We this view in mind, we focus on two modes of excitation that are essential in reaching this goal: the isoscalar giant monopole resonance (GMR) and the isovector giant dipole resonance (GDR). GMR energies in heavy nuclei are sensitive to the symmetry energy because they probe the incompressibility of neutron-rich matter. Unfortunately, access to the symmetry energy is hindered by the relatively low neutron-proton asymmetry of stable nuclei. Thus, the measurement of GMR energies in exotic nuclei is strongly encouraged. In the case of the GDR, we find the electric dipole polarizability of paramount importance. Indeed, the electric dipole polarizability appears as one of two laboratory observables -- with the neutron-skin thickness being the other -- that are highly sensitive to the density dependence of the symmetry energy. Finally, we identify the softness of skin and the nature of the pygmy resonance as important unsolved problems in nuclear structure.