Field-theoretical model for nuclear and neutron matter. I. Equation of state.

Abstract

We analyze a field-theoretical Lagrangian model for the many-body problem of baryonic matter. The Lagrangian describes the baryonic interaction through the exchange of \ensuremath{\sigma}, \ensuremath{\pi}, \ensuremath{\omega}, and \ensuremath{\rho} mesons, and contains various models studied in the literature as particular cases. The model is solved in the relativistic Hartree approximation using the technique of the covariant Wigner function. The vacuum fluctuation effects are considered and renormalized through a counterterm procedure. The equation of state is obtained in this renormalized Hartree approximation at finite temperature and in the presence of homogeneous and isotropic meson condensates. In a first particular case (the Serot model) the parameters of the model are determined in order to explain the nuclear saturation and symmetry energy of symmetric nuclear matter at nuclear density and to account for the expected low-density behavior of dense matter after the neutron drip in a phenomenological way. In this case the incompressibility of nuclear matter at the nuclear density is 460 MeV. A second determination of the parameters of the general model leads to a \ensuremath{\sigma} model with an explicit symmetry-breaking term and is coupled to the \ensuremath{\omega} and \ensuremath{\rho} mesons in a renormalizable way. The equation of state thus obtained explains accurately all the properties of nuclear matter at nuclear density. In particular, we obtain a nuclear incompressibility of 225 MeV. The analysis of the resulting energy density as a function of the meson condensates shows that the presence of homogeneous and isotropic pion condensates or abnormal states of Lee-Wick type in neutron matter at T=0 is energetically forbidden in this approximation.