A systematic study of giant quadrupole resonances with the subtracted second random--phase approximation: beyond--mean--field centroids and fragmentation

A systematic analysis of giant quadrupole resonances is performed for several nuclei, from $^{30}$Si to $^{208}$Pb, within the subtracted second random--phase--approximation (SSRPA) model in the framework of the energy--density--functional theory. Centroid energies and widths of the isoscalar giant quadrupole resonances are compared with the corresponding random--phase--approximation (RPA) values. We find lower SSRPA centroid energies compared to the RPA values leading, in general, to a better agreement with the experimental data. As far as the widths are concerned, we observe for both SSRPA and RPA cases a global attenuation of the single--particle Landau damping going from lighter to heavier nuclei and we obtain, systematically, larger widths in the SSRPA model compared to the RPA case. For some selected nuclei for which high--resolution ($p,p'$) experimental data are available, namely $^{40}$Ca, $^{90}$Zr, $^{120}$Sn, and $^{208}$Pb, the theoretical strength distributions are directly compared with the experimental spectra. We observe a significant improvement, with respect to RPA results, in the description of the spreading widths and of the fragmentation of the obtained spectra, due to the coupling between 1 particle-1 hole and 2 particle-2 hole configurations.