Nuclear collective excitations within the UCOM framework: RPA and beyond

Correlated Hamiltonians derived from realistic nucleon-nucleon interactions within the Unitary Correlation Operator Method (UCOM) are employed in studies of nuclear collective excitations within random phase approximation (RPA) models. First, a standard, self-consistent, first-order Hartree-Fock+RPA is used. The properties of the giant monopole resonance are reproduced reasonably well, whereas the energies of the giant dipole and quadrupole resonances are overestimated by several MeV. The results reflect the properties of the UCOM Hamiltonian as an effective interaction and demonstrate the importance of residual long-range correlations and higher-order effects. The effect of explicit RPA correlations built in the ground state is examined within a renormalized RPA version and is found to be rather small. By contrast, the coupling to second-order configurations, as described within Second RPA, are found essential for the description of giant resonances using the UCOM Hamiltonian. (orig.)