Particle-vibrational coupling in covariant density-functional theory

A consistent combination of covariant density-functional theory and Landau-Migdal theory of finite fermi systems is presented. Both methods are in principle exact, but Landau-Migdal theory cannot describe ground-state properties and density-functional theory does not take into account the energy dependence of the self-energy and therefore fails to yield proper single-particle spectra as well as the coupling to complex configurations in the width of giant resonances. Starting from an energy functional, phonon energies and their vertices are calculated without any further parameters. They form the basis of particle-vibrational coupling leading to an energy dependence of the self-energy and an induced energy-dependent interaction in the response equation. A proper subtraction of the static phonon-coupling contribution from the induced interaction avoids double counting of this contribution. Applications in doubly magic nuclei and in a chain of superfluid nuclei show excellent agreement with experimental data.