Dense matter and the compressible liquid drop model

Abstract

We explore the equation of state of dense matter at densities up to nuclear matter density using the compressible liquid drop model. We consider two primary areas of application: the collapsing core of supernovae and the inner crust of a cooled neutron star. The model is generalized to include a refined description of the nuclear surface properties as well as a number of smaller physical effects. We also adapt it to accommodate droplet shapes other than the customary spherical clusters in order to study the phase character of matter in these astrophysical situatipns. We present the results of a Hartree-Fock finite-temperature calculation of nuclear surface and curvature thermodynamic potentials, using phenomenological forces. These are the requisite ingredients needed for the model. For our purposes, we calculate these properties over the complete range of proton fraction (0 to 0.5). The self-consistent method is exploited to extract an approximation for neutron evaporation rates from hot nuclear surfaces. Dense matter at fixed overall proton fraction of Yp = 0.3 is considered at densities up to nuclear saturation density at low temperatures. We lay the framework, however, to explore matter at temperatures that one would expect in the collapsing supernova core. Matter in beta equilibrium is considered at low temperatures; this is the character of the matter that one expects to exist in the inner crust of a cooled neutron star. We obtain for the first time the density range occupied by the non-spherical nuclear shapes.