  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 $^{56}$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.
