Splitting and Structure of the Giant Quadrupole Resonances in Deformed Nuclei

We have performed microscopic calculations of the low-lying and high-lying ${K}^{\ensuremath{\pi}}={0}^{+}, {1}^{+}, \mathrm{and} {2}^{+}$ states in deformed rare-earth nuclei. The centroids of the isoscalar giant quadrupole resonance in $^{160}\mathrm{Dy}$, $^{170}\mathrm{Yb}$, and $^{184}\mathrm{W}$ are at 11.58, 11.44, and 11.22 MeV, respectively. A broadening of these resonances due to the deformation is predicted which varies appreciably in the different nuclei. About 20% of the monopole strength is found in the same energy range.