Although ab initio calculations of relativistic Brueckner theory lead to large scalar isovector fields in nuclear matter, at present, successful versions of covariant density functional theory neglect the interactions in this channel. A new high-precision density functional DD-ME$\delta${} is presented which includes four mesons, $\sigma${}, $\omega${}, $\delta${}, and $\rho${}, with density-dependent meson-nucleon couplings. It is based to a large extent on microscopic ab initiocalculations in nuclear matter. Only four of its parameters are determined by adjusting to binding energies and charge radii of finite nuclei. The other parameters, in particular the density dependence of the meson-nucleon vertices, are adjusted to nonrelativistic and relativistic Brueckner calculations of symmetric and asymmetric nuclear matter. The isovector effective mass mp*$-${}mn* derived from relativistic Brueckner theory is used to determine the coupling strength of the $\delta${} meson and its density dependence.

The tilted axis cranking formalism is implemented in relativistic mean field (RMF) theory. It is used for a microscopic description of magnetic rotation in the framework of covariant density functional theory. We assume that the rotational axis is in the $\mathit{xz}$ plane and consider systems with the two symmetries $\mathcal{P}$ (space reflection) and ${\mathcal{P}}_y\mathcal{T}$ (a combination of a reflection in the $y$ direction and time reversal). A computer code based on these symmetries is developed, and first applications are discussed for the nucleus ${}^{142}\mathrm{Gd}$: the rotational band based on the configuration $\pi h_{11/2}^2\otimes \nu h_{11/2}^{-2}$ is investigated in a fully microscopic and self-consistent way. The results are compared with available data, such as spectra and electromagnetic transition ratios $B(M1)/B(E2)$. The relation between rotational velocity and angular momentum are discussed in detail together with the shears mechanism characteristic of magnetic rotation.

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.

We use covariant density functional theory beyond mean field in order to describe neutrinoless double-beta decay in a fully relativistic way. The dynamic effect We use covariant density functional theory beyond mean field in order to describe neutrinoless double-beta decay in a fully relativistic way. The dynamic effect

Covariant Density functional theory is used as a basis for a microscopic description of spectroscopic properties of quantum phase transitions in nuclei. Since it is well known that the mean field approximation breaks down in transitional nuclei, where configuration mixing and fluctuations connected with broken symmetries play an important role, a theory is developed which uses the Relativistic Generator Coordinate Method to perform configuration mixing calculations of angular momentum and particle number projected wave functions. As applications with show 3D-calculations of the spectrum of low-lying collective states in the nucleus ²⁴Mg. This method can also be used to study the behavior of characteristic physical quantities as a function of the physical control parameter, the number of nucleons, in the region of quantum phase transitions.