Global investigation of the fine structure of the isoscalar giant quadrupole resonance

Fine structure in the region of the isoscalar giant quadrupole resonance (ISGQR) in Ni-58, Y-89, Zr-90, Sn-120, Er-166, and Pb-208 has been observed in high-energy-resolution (Delta E-1/2 similar or equal to 35-50 keV) inelastic proton scattering measurements at E-0 = 200 MeV at iThemba LABS. Calculations of the corresponding quadrupole excitation strength functions performed within models based on the random-phase approximation (RPA) reveal similar fine structure when the mixing of one-particle one-hole states with two-particle two-hole states is taken into account. A detailed comparison of the experimental data is made with results from the quasiparticle-phonon model (QPM) and the extended time-dependent Hartree-Fock (ETDHF) method. For Pb-208, additional theoretical results from second RPA and the extended theory of finite Fermi systems (ETFFS) are discussed. A continuous wavelet analysis of the experimental and the calculated spectra is used to extract dominant scales characterizing the fine structure. Although the calculations agree with qualitative features of these scales, considerable differences are found between the model and experimental results and amongst different models. Within the framework of the QPM and ETDHF calculations it is possible to decompose the model spaces into subspaces approximately corresponding to different damping mechanisms. It is demonstrated that characteristic scales mainly arise from the collective coupling of the ISGQR to low-energy surface vibrations.