Relativistic mean field models and nucleon-nucleon interactions

Abstract

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 TS (δ-meson), an isovector vector TV (ρ-meson), and an isovector pseudoscalar PS (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 density-dependence of these parameters and the influence of many-body and multi-scattering effects. We find that with increasing density of the nuclear medium mσ is constant to a good approximation, m δ decreases quite strongly, while mω and mρ 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.