Nuclear symmetry energy: constraints from giant quadrupole resonances and parity violating electron scattering

The nuclear symmetry energy is a basic ingredient of the nuclear equation of state: it accounts for the energy cost per nucleon to convert all protons into neutrons in symmetric nuclear matter. Experimental and theoretical efforts are being devoted to the study of observables that can shed light on the properties of the nuclear symmetry energy. We present our new results on the excitation energy and polarizability of the Isovector Giant Quadrupole Resonance (IVGQR), which has been the object of new experimental investigation. We also present our theoretical analysis on the parity violating asymmetry at the kinematics of the Lead Radius Experiment (PREx) and highlight its relation with the density dependence of the symmetry energy. Most results deal with ²⁰⁸Pb nucleus