Collective Correlations in Spherical Nuclei and the Structure of Giant Resonances

The theory of collective correlations in nuclei is formulated for giant resonances interacting with surface vibrations. The giant dipole states are treated in the particle-hole framework, while the surface vibrations are described by the collective model. Consequently, this treatment of nuclear structure goes beyond both the common particle-hole model (including its various improvements which take ground-state correlations into account) and the pure collective model. The interaction between giant resonances and surface degrees of freedom as known from the dynamic collective theory is formulated in the particle-hole language. Therefore, the theory contains the particle-hole structures and the most important "collective intermediate" structures of giant resonances. Detailed calculations are performed for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, and ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$. A good detailed agreement between theory and experiment is obtained for all these nuclei, although only ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$ is in the region where one would expect the theory to work well ($50<A<\mathrm{}110\mathrm{}$).