Covariant density functional theory, which has so far been applied only within the framework of static and time dependent mean field theory is extended to include Particle-Vibration Coupling (PVC) in a consistent way. Starting from a conventional energy functional we calculate the lowlying collective vibrations in Relativistic Random Phase Approximation (RRPA) and construct an energy dependent self-energy for the Dyson equation. The resulting Bethe-Salpeter equation in the particle-hole (ph) channel is solved in the Time Blocking Approximation (TBA). No additional parameters are used and double counting is avoided by a proper subtraction method. The same energy functional, i.e. the same set of coupling constants, generates the Dirac-Hartree singleparticle spectrum, the static part of the residual ph-interaction and the particle-phonon coupling vertices. Therefore a fully consistent description of nuclear excited states is developed. This method is applied for an investigation of damping phenomena in the spherical nuclei with closed shells 208 Pb and 132 Sn. Since the phonon coupling terms enrich the RRPA spectrum with a multitude of ph⊗phonon components a noticeable fragmentation of the giant resonances is found, which is in full agreement with experimental data and with results of the semi-phenomenological non-relativistic approach.

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The problem of the microscopic description of excited states of the even-even open-shell atomic nuclei is considered. A model is formulated which allows one to go beyond the quasiparticle random phase approximation. The physical content of the model is determined by the quasiparticle time blocking approximation (QTBA) which enables one to include contributions of the two-quasiparticle and the two-phonon configurations, while excluding (blocking) more complicated intermediate states. In addition, the QTBA ensures consistent treatment of ground state correlations in the Fermi systems with pairing. The model is based on the generalized Green function formalism (GGFF) in which the normal and the anomalous Green functions are treated in a unified way in terms of the components of generalized Green functions in a space that is double the size of the usual single-particle space. Modification of the GGFF is considered in the case when the many-body nuclear Hamiltonian contains two-, three-, and other many-particle effective forces.

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A two-phonon version of the relativistic quasiparticle time blocking approximation (RQTBA-2) represents a new class of many-body models for nuclear structure calculations based on the covariant energy density functional. As a fully consistent extension of the relativistic quasiparticle random phase approximation (RQRPA), the two-phonon RQTBA implies a fragmentation of nuclear states over two-quasiparticle and two-phonon configurations. This leads, in particular, to a splitting-out of the lowest 1 − state as a member of the two-phonon [2 + ⊗3 − ] quintuplet from the RQRPA pygmy dipole mode, thus establishing a physical mixing between these three modes.The inclusion of the two-phonon configurations in the model space allows to describe the positions and the reduced transition probabilities of the lowest 1 − states in isotopes 116,120 Sn as well as the low-energy fraction of the dipole strength without any adjustment procedures. The model is also applied to the low-lying dipole strength in neutron-rich 68,70,72 Ni isotopes. Recent experimental data for 68 Ni are reproduced fairly well.The theoretical description of nuclear low-lying dipole strength remains among the most important problems in nuclear structure and nuclear astrophysics [1]. Measurements of the dipole strength by means of high resolution nuclear resonance fluorescence [2,3,4,5,6,7] resolve the fine structure of the spectra below the neutron threshold. Unique spectroscopic information about neutron-rich medium-mass and heavy nuclei have been obtained in recent experiments with Coulomb dissociation [8,9] and virtual photon scattering [10]. This offers

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.

The extended RPA theories are analyzed from the point of view of the problem of stability of their solutions. Three kinds of such theories are considered: the second RPA and two versions of the quasiparticle-phonon coupling model within the time-blocking approximation: the model including 1p1h⊗phonon configurations and the two-phonon model. It is shown that stability is ensured by making use of the subtraction method proposed previously to solve double counting problem in these theories. This enables one to generalize the famous Thouless theorem proved in the case of the RPA. These results are illustrated by an example of schematic model.

In this paper we propose a generalization of the density functional theory. The theory leads to single-particle equations of motion with a quasilocal mean-field operator, which contains a quasiparticle position-dependent effective mass and a spin-orbit potential. The energy density functional is constructed using the extended Thomas-Fermi approximation and the ground-state properties of doubly magic nuclei are considered within the framework of this approach. Calculations were performed using the finite-range Gogny D1S forces and the results are compared with the exact Hartree-Fock calculations.