Nuclear Schwinger-Dyson formalism applied to finite baryon density. II. Numerical calculations and medium effects of meson self-energies

Numerical results based on coupled equations of the nuclear Schwinger-Dyson (NSD) without and with the sigma-omega meson mixing under a bare-vertex approximation are shown. Comparisons between NSD and traditional methods such as the mean field theory (MFT) or Hartree-Fock (HF) are made. It is shown that higher order effects beyond HF are important because they modify properties of mesons in the nuclear medium. Because of a large negative of a scalar meson self-energy, the scalar meson in NSD without the mixing works more attractively than that in HF. From a comparison between NSD without and with the meson mixing, mixing ring energies are extracted and it is shown that the mixing works repulsively and the ring energy with the mixing cancels partially the ring energy without the mixing. Nevertheless, NSD leads to smaller couplings than MFT or HF, i.e., ${\mathit{g}}^{\mathit{S}}$=8.714, ${\mathit{g}}^{\mathit{V}}$=10.678 in the nonmixed calculation, and ${\mathit{g}}^{\mathit{S}}$=7.590, ${\mathit{g}}^{\mathit{V}}$=8.462 in the mixed calculation. The NSD with the meson mixing gives a smaller incompressibility k=386 MeV than the other models. It is also shown that MFT or HF approximation is able to simulate the saturation curve of the binding energy of NSD without the mixing if their couplings are refitted so as to reproduce the experimental saturation point, however, MFT or HF cannot simulate the saturation curve of NSD with the meson mixing even if their coupling constants are adjusted.