Giant Quadrupole Resonance in Deformed Nuclei

With use of the ordinary quadrupole-quadrupole (Q-Q) interaction, a total splitting of the $K=0, 1, 2$ components in the giant quadrupole resonance (GQR) of about 6 MeV is predicted for deformed ${}_{}{}^{154}{}_{}{}^{}\mathrm{Sm}$. A 0.8±0.3-MeV broadening of the GQR is observed for ${}_{}{}^{154}{}_{}{}^{}\mathrm{Sm}$ relative to spherical ${}_{}{}^{144}{}_{}{}^{}\mathrm{Sm}$ with inelastic $\alpha$ scattering. A model requiring rigorous self-consistency is proposed which modifies the Q-Q interaction, reduces the predicted splitting to about 2 MeV, and removes inconsistencies in the strength of the interaction for $K=0\mathrm{}$ and $K=2\mathrm{}$ components in low-lying $\beta$ and $\gamma$ bands.