We review an extension of Migdal's Theory of Finite Fermi Systems which has been developed and applied to collective vibrations in closed shell nuclei in the past ten years. This microscopic approach is based on a consistent use of the Green function method. Here one considers in a consistent way more complex 1p1h⊗phonon configurations beyond the RPA correlations. Moreover, these configurations are not only included in the excited states but also explicitly in the ground states of nuclei. The method has been applied to the calculation of the strength distribution and transition densities of giant electric and magnetic resonances in stable and unstable magic nuclei. Using these microscopic transition densities, cross sections for inelastic electron and alpha scattering have been calculated and compared with the available experimental data. The method also allows one to extract in a consistent way the magnitude of the strength of the various multipoles in the energy regions in which several multipoles overlap. We compare the microscopic transition densities, the strength distributions and the various multipole strengths with their values extracted phenomenologically.

The electric dipole strength distribution in 44Ca has been measured up to 10 MeV in high resolution photon scattering experiments for the first time. The data obtained have been compared to earlier measurements on (40,48)Ca in order to view the evolution of the electric pygmy dipole resonance (PDR). Calculations that were performed within the framework of the microscopic extended theory of finite Fermi systems, which adds contributions of the quasiparticle-phonon coupling to random phase approximation calculations, give a qualitative agreement with the experimental data for all three isotopes. We have shown that it is necessary to include this coupling to describe the PDR.

We have calculated the strength distributions of the giant monopole resonance in the even-A tin isotopes (A = 112 − 124) which were recently measured in inelastic α-scattering. The calculations were performed within two microscopic models: the quasiparticle random phase approximation (QRPA) and the quasiparticle time blocking approximation which is an extension of the QRPA including quasiparticle-phonon coupling. We used a self-consistent calculational scheme based on the HF+BCS approximation. The single-particle continuum was exactly included on the RPA level. The self-consistent mean field and the effective interaction were derived from the Skyrme energy functional. In the calculations, two Skyrme force parametrizations were used. The T5 parametrization with comparatively low value of the incompressibility of infinite nuclear matter (K ∞ = 202 MeV) gives theoretical results in good agreement with the experimental data including the resonance widths.

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