Giant quadrupole resonances in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mrow/><mml:mn>208</mml:mn></mml:msup></mml:math>Pb, the nuclear symmetry energy, and the neutron skin thickness

Recent improvements in the experimental determination of properties of the isovector giant quadrupole resonance (IVGQR), as demonstrated in the $A=208$ mass region, may be instrumental for characterizing the isovector channel of the effective nuclear interaction. We analyze properties of the IVGQR in ${}^{208}$Pb, using both macroscopic and microscopic approaches. The microscopic method is based on families of nonrelativistic and covariant energy density functionals (EDF), characterized by a systematic variation of isoscalar and isovector properties of the corresponding nuclear matter equations of state. The macroscopic approach yields an explicit dependence of the nuclear symmetry energy at some subsaturation density, for instance $S(\ensuremath{\rho}=0.1$ fm${}^{\ensuremath{-}3})$, or the neutron skin thickness $\ensuremath{\Delta}{r}_{np}$ of a heavy nucleus, on the excitation energies of isoscalar and isovector GQRs. Using available data it is found that $S(\ensuremath{\rho}=0.1$ fm${}^{\ensuremath{-}3})=23.3\ifmmode\pm\else\textpm\fi{}0.6$ MeV. Results obtained with the microscopic framework confirm the correlation of the $\ensuremath{\Delta}{r}_{np}$ to the isoscalar and isovector GQR energies, as predicted by the macroscopic model. By exploiting this correlation together with the experimental values for the isoscalar and isovector GQR energies, we estimate $\ensuremath{\Delta}{r}_{np}=0.14\ifmmode\pm\else\textpm\fi{}0.03$ fm for ${}^{208}$Pb, and the slope parameter of the symmetry energy: $L=37\ifmmode\pm\else\textpm\fi{}18$ MeV.