Field theoretical model for nuclear and neutron matter: Thermal effects.

Abstract

A field theoretical model for the analysis of relativistic nuclear and neutron matter, obtained elsewhere, is studied at nonzero temperature. The Lagrangian describing the microdynamics has been introduced by coupling the nucleons (protons and neutrons) to the \ensuremath{\sigma}, \ensuremath{\pi}, \ensuremath{\omega}, and \ensuremath{\rho} meson fields in a renormalizable way. The model is solved in the renormalized Hartree approximation and the free parameters in the Lagrangian are determined in such a way that the empirical properties of symmetric nuclear matter at nuclear density are accurately fitted by the resulting equation of state. We obtain, in particular, a nuclear incompressibility of 225 MeV. The equilibrium neutron star configurations obtained elsewhere with this equation of state, are in very good agreement with the observational evidence. For symmetric nuclear matter, we obtain the behavior of the first-order phase transition and bound states with temperature and we show the corresponding phase diagrams. For neutron matter we obtain the behavior of the various state variables with temperature. These results are useful in the analysis of relativistic heavy ion collisions and have been applied in calculations of neutron star structure, stability, and cooling. In order to facilitate use of the pure neutron matter equation of state at finite temperature in astrophysical calculations, we give a polynomial fit of the corresponding isotherms.