We investigate the role of the pion in Covariant Density Functional Theory. Starting from conventional Relativistic Mean Field (RMF) theory with a non-linear coupling of the $\sigma$-meson and without exchange terms we add pions with a pseudo-vector coupling to the nucleons in relativistic Hartree-Fock approximation. In order to take into account the change of the pion field in the nuclear medium the effective coupling constant of the pion is treated as a free parameter. It is found that the inclusion of the pion to this sort of density functionals does not destroy the overall description of the bulk properties by RMF. On the other hand, the non-central contribution of the pion (tensor coupling) does have effects on single particle energies and on binding energies of certain nuclei.Comment: 12 pages, 5 figure

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We investigate the connection between relativistic mean field models and the bare nucleon-nucleon interaction by using a realistic interaction in the nuclear medium. Starting from a nonrelativistic bare potential and by employing a G-matrix formalism we derive an effective interaction in the nuclear medium that depends on its density. We show that its medium-and long-range components can be described to a good extent by an effective density-dependent one-boson-exchange (OBE) potential. For a good fit of the OBE to the G-matrix potential the following degrees of freedom have been found to be necessary: an isoscalar scalar S (σ-meson), an isoscalar vector V (ω-meson), an isovector scalar T S (δmeson), an isovector vector T V (ρ-meson), and an isovector pseudoscalar P S (π-meson) Yukawa field. This allows us to extract the mass and the coupling strength of the various mesons at different densities of nuclear matter. In such a way, we investigate the densitydependence of these parameters and the influence of many-body and multi-scattering effects. We find that with increasing density of the nuclear medium m σ is constant to a good approximation, m δ decreases quite strongly, while m ω and m ρ decrease rather weakly. The coupling strengths of the fields also show a rather weak decreasing tendency. Furthermore it turns out that the extracted values of the meson fields masses and couplings are rather consistent with the parameters of effective mesons of recent RMF phenomenologies. Finally, we find that the tensor force of the bare nucleon-nucleon interaction is essential to explain the dominance of the σ-field for the attraction. This makes RMF models more consistent with ab initio calculations. † deceased

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