Hot and dense matter beyond relativistic mean field theory

Abstract

Properties of hot and dense matter are calculated in the framework of quantum hadro-dynamics by including contributions from two-loop (TL) diagrams arising from the exchange of iso-scalar and iso-vector mesons between nucleons. Our extension of mean-field theory (MFT) employs the same five density-independent coupling strengths which are calibrated using the empirical properties at the equilibrium density of iso-spin symmetric matter. Results of calculations from the MFT and TL approximations are compared for conditions of density, temperature, and proton fraction encountered in astrophysics applications involving compact objects. The TL results for the equation of state (EOS) of cold pure neutron matter at sub- and near-nuclear densities agree well with those of modern quantum Monte Carlo and effective field-theoretical approaches. Although the high-density EOS in the TL approximation for neutron-star matter is substantially softer than its MFT counterpart, it is able to support a $2M_\odot$ neutron star required by recent precise determinations. In addition, radii of $1.4M_\odot$ stars are smaller by $\sim 1$ km than obtained in MFT. In contrast to MFT, the TL results also give a better account of the single-particle or optical potentials extracted from analyses of medium-energy proton-nucleus and heavy-ion experiments. In degenerate conditions, the thermal variables are well reproduced by results of Landau's Fermi-Liquid theory in which density-dependent effective masses feature prominently. The ratio of the thermal components of pressure and energy density expressed as $\Gamma_{th}=1+(P_{th}/\epsilon_{th})$, often used in astrophysical simulations, exhibits a stronger dependence on density than on proton fraction and temperature in both MFT and TL calculations. The prominent peak of $\Gamma_{th}$ at supra-nuclear density found in MFT is, however, suppressed in TL calculations.