A benchmark experiment on (208)Pb shows that polarized proton inelastic scattering at very forward angles including 0° is a powerful tool for high-resolution studies of electric dipole (E1) and spin magnetic dipole (M1) modes in nuclei over a broad excitation energy range to test up-to-date nuclear models. The extracted E1 polarizability leads to a neutron skin thickness r(skin) = 0.156(-0.021)(+0.025) fm in (208)Pb derived within a mean-field model [Phys. Rev. C 81, 051303 (2010)], thereby constraining the symmetry energy and its density dependence relevant to the description of neutron stars.

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 Relativistic Mean Field (RMF) approach describing the motion of independent particles in effective meson fields is extended by a microscopic theory of particle vibrational coupling. It leads to an energy dependence of the relativistic mass operator in the Dyson equation for the singleparticle propagator. This equation is solved in the shell-model of Dirac states. As a result of the dynamics of particle-vibrational coupling we observe a noticeable increase of the level density near the Fermi surface. The shifts of the single-particle levels in the odd nuclei surrounding 208 Pb and the corresponding distributions of the single-particle strength are discussed and compared with experimental data.

The impact of particle-vibration coupling and polarization effects due to deformation and timeodd mean fields on single-particle spectra is studied systematically in doubly magic nuclei from low mass 56 Ni up to superheavy ones. Particle-vibration coupling is treated fully self-consistently within the framework of relativistic particle-vibration coupling model. Polarization effects due to deformation and time-odd mean field induced by odd particle are computed within covariant density functional theory. It has been found that among these contributions the coupling to vibrations makes a major impact on the single-particle structure. The impact of particle-vibration coupling and polarization effects on calculated single-particle spectra, the size of the shell gaps, the spin-orbit splittings and the energy splittings in pseudospin doublets is discussed in detail; these physical observables are compared with experiment. Particle-vibration coupling has to be taken into account when model calculations are compared with experiment since this coupling is responsible for observed fragmentation of experimental levels; experimental spectroscopic factors are reasonably well described in model calculations.