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.

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The Extended Theory of Finite Fermi Systems is based on the conventional Landau-Migdal theory and includes the coupling to the low-lying phonons in a consistent way. The phonons give rise to a fragmentation of the single-particle strength and to a compression of the single-particle spectrum. Both effects are crucial for a quantitative understanding of nuclear structure properties. We demonstrate the effects on the electric dipole states in 208 Pb (which possesses 50% more neutrons then protons) where we calculated the low-lying non-collective spectrum as well as the high-lying collective resonances. Below 8 MeV, where one expects the so called isovector pygmy resonances, we also find a strong admixture of isoscalar strength that comes from the coupling to the high-lying isoscalar electric dipole resonance, which we obtain at about 22 MeV. The transition density of this resonance is very similar to the breathing mode, which we also calculated. We shall show that the extended theory is the correct approach for self-consistent calculations, where one starts with effective Lagrangians and effective Hamiltonians, respectively, if one wishes to describe simultaneously collective and non-collective properties of the nuclear spectrum. In all cases for which experimental data exist the agreement with the present theory results is good.

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Within a microscopic approach which takes into account RPA configurations, the single-particle continuum and more complex 1p1h ⊗ phonon configurations isoscalar and isovector M1 excitations for the unstable nuclei 56,78 Ni and 100,132 Sn are calculated. For comparison, the experimentally known M1 excitations in 40 Ca and 208 Pb have also been calculated. In the latter nuclei good agreement in the centroid energy, the total transition strength and the resonance width is obtained. With the same parameters we predict the magnetic excitations for the unstable nuclei. The strength is sufficiently concentrated to be measurable in radioactive beam experiments. New features are found for the very neutron rich nucleus 78 Ni and the neutron deficient nucleus 100 Sn.

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The isoscalar E2 giant resonance in Ca has been calculated within a microscopic approach which takes into account, in addition to the random-phase-approximation configurations, one-particleone-hole (lplh)phouon configurations and the continuum.We reproduce the observed shift of a considerable part of the E2 strength to lower energies which gives rise to a nearly uniform distribution. If we add the EO strength calculated within the same approach, then we obtain good agreement with a recent electron scattering experiment, which is a further strong indication for low-lying EO strength. PACS numbers: 24.30.Cz, 21.10.Re, 27.40.+z The isoscalar E2 giant resonance in Ca has been investigated in many experiments (see [1 -5], and references therein). A fine structure has been found in (p, p') experiments with an energy resolution of 70 eV [3], which is a challenge for the microscopic theory of giant resonances. It has also been observed that the isoscalar E2 strength in Ca is split into two major peaks with energies of 14 and 18 MeV [1 -5]. The strength is divided in approximately equal parts around these values. In an (n, n', c) experiment [1,2] one observed (50~10)% of the E2 (b, T = 0) energy weighted sum rule (EWSR) in the 10 -16 MeV interval and in a (p, p') experiment [3] 24.9% of the E2 EWSR was observed in the 13.2-16.0 MeV interval. In the following we will concentrate our discussion on the splitting of the isoscalar giant quadrupole resonance (GQR). So far there is no theoretical explanation for these facts. The random phase approximation (RPA) calculations give only one peak at about 18 MeV [6]. The inclusion of additional "pure" two-particletwo-hole 2p2h configurations [7,8] does not explain the data. Inclusion of lp1hphonon configurations [9] [without treatment of all the ground state correlations (GSC) induced by the 1plhephonon configurations] does not give a quantitative explanation, as was noticed by van der Woude [1].Here we show that the observed low-lying E2 strength in Ca is connected with more global and general properties of nuclei in the ground state, i.e. , the correlations of the ground state (GSC). These correlations also have a strong inhuence on the excited states, and they are caused by a consistent treatment of configurations more complex than those which are accounted for by the RPA. There are two kinds of GSC. The first kind is a generalization of the well known RPA ground state correlations which give rise to a redistribution of the strength but do not generate new transitions. The second class of GSC modifies the ground state in such a way that new transitions appear between the correlated ground state and 1plhphonon configurations. In this sense our method is qualitatively different from the RPA approach. We shall demonstrate that this effect is important and that its inclusion gives an explanation of the above-mentioned experimental data in Ca.Although we discuss here 4 Ca only, the results are much more general. We expect the same effects in all lighter nuclei. This may be the...