A statistical model for a complete supernova equation of state

A statistical model for the equation of state and the composition of supernova matter is presented. It consists of an ensemble of nuclei and interacting nucleons in nuclear statistical equilibrium. A relativistic mean field model is applied for the nucleons. The masses of the nuclei are taken from experimental data and from nuclear structure calculations. Excluded volume effects are implemented in a thermodynamic consistent way so that the transition to uniform nuclear matter can be described. Thus the model can be applied at all densities relevant for supernova simulations, i.e. image, and it is possible to calculate a complete supernova equation of state table. The importance of the nuclear distributions for the composition is shown and the role of shell effects is investigated. We find a significant contribution of light clusters which is only poorly represented by α-particles alone. The equation of state is systematically compared to two commonly used models for supernova matter which are based on the single nucleus approximation. In general only small differences are found. These are most pronounced around the (low-density) liquid–gas phase transition line where the distribution of light and intermediate clusters has an important effect.