A benchmark experiment on ${}^{208}\mathrm{Pb}$ 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 $r_{\mathrm{skin}}={0.156}_{-0.021}^{+0.025}\mathrm{fm}$ in ${}^{208}\mathrm{Pb}$ 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.

The pygmy dipole resonance has been studied in the proton-magic nucleus Sn124 with the ($\alpha${}, $\alpha${}$'${}$\gamma${}) coincidence method at E$\alpha${}=136\,\,MeV. The comparison with results of photon-scattering experiments reveals a splitting into two components with different structure: one group of states which is excited in ($\alpha${}, $\alpha${}$'${}$\gamma${}) as well as in ($\gamma${}, $\gamma${}$'${}) reactions and a group of states at higher energies which is only excited in ($\gamma${}, $\gamma${}$'${}) reactions. Calculations with the self-consistent relativistic quasiparticle time-blocking approximation and the quasiparticle phonon model are in qualitative agreement with the experimental results and predict a low-lying isoscalar component dominated by neutron-skin oscillations and a higher-lying more isovector component on the tail of the giant dipole resonance.

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 single-particle 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 ${}^{208}\mathrm{Pb}$ and the corresponding distributions of the single-particle strength are discussed and compared with experimental data.

The self-consistent relativistic quasiparticle random-phase approximation (RQRPA) is extended by the quasiparticle-phonon coupling (QPC) model using the quasiparticle time blocking approximation (QTBA). The method is formulated in terms of the Bethe-Salpeter equation (BSE) in the two-quasiparticle space with an energy-dependent two-quasiparticle residual interaction. This equation is solved either in the basis of Dirac states forming the self-consistent solution of the ground state or in the momentum representation. Pairing correlations are treated within the Bardeen-Cooper-Schrieffer (BCS) model with a monopole-monopole interaction. The same NL3 set of the coupling constants generates the Dirac-Hartree-BCS single-quasiparticle spectrum, the static part of the residual two-quasiparticle interaction and the quasiparticle-phonon coupling amplitudes. A quantitative description of electric dipole excitations in the chain of tin isotopes ($Z=50$) with the mass numbers $A=100,106,114,116,120$, and 130 and in the chain of isotones with ($N=50$) ${}^{88}\mathrm{Sr}$, ${}^{90}\mathrm{Zr}$, ${}^{92}\mathrm{Mo}$ is performed within this framework. The RQRPA extended by the coupling to collective vibrations generates spectra with a multitude of $2q\otimes \mathrm{phonon}$ (two quasiparticles plus phonon) states providing a noticeable fragmentation of the giant dipole resonance as well as of the soft dipole mode (pygmy resonance) in the nuclei under investigation. The results obtained for the photo absorption cross sections and for the integrated contributions of the low-lying strength to the calculated dipole spectra agree very well with the available experimental data.

The electric dipole strength distribution in ${}^{44}\mathrm{C}\mathrm{a}$ 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 ${}^{40,48}\mathrm{C}\mathrm{a}$ 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.

The impact of particle-vibration coupling and polarization effects due to deformation and time-odd mean fields on single-particle spectra is studied systematically in doubly magic nuclei from low-mass ${}^{56}\mathrm{Ni}$ up to superheavy ones. Particle-vibration coupling is treated fully self-consistently within the framework of the 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.