# Statistical Model for a Complete Supernova Equation of State

## TL;DR

This paper introduces a comprehensive statistical model for the supernova equation of state that accounts for nuclear composition, phase transitions, and cluster distributions, improving the accuracy of supernova simulations.

## Contribution

It presents a novel statistical model incorporating nuclear distributions, shell effects, and excluded volume corrections for supernova matter EOS, applicable across all relevant densities.

## Key findings

- Light clusters significantly influence the EOS and composition.
- Shell effects cause narrow peaks around neutron magic numbers at low temperatures.
- The model's EOS closely matches existing models, with notable differences near phase transition regions.

## Abstract

A statistical model for the equation of state (EOS) and the composition of supernova matter is presented with focus on the liquid-gas phase transition of nuclear matter. 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 nuclear structure calculations which are based on the same nuclear Lagrangian. For known nuclei experimental data is used directly. Excluded volume effects are implemented in a thermodynamic consistent way so that the transition to uniform nuclear matter at large densities can be described. Thus the model can be applied at all densities relevant for supernova simulations, i.e. rho=10^5 - 10^15 g/cm^3, and it is possible to calculate a complete supernova EOS table. The model allows to investigate the role of shell effects, which lead to narrow-peaked distributions around the neutron magic numbers for low temperatures. At larger temperatures the distributions become broad. The significance of the statistical treatment and the nuclear distributions for the composition is shown. We find that the contribution of light clusters is very important and is only poorly represented by alpha-particles alone. The results for the EOS are systematically compared to two commonly used models for supernova matter which are based on the single nucleus approximation. Apart from the composition, in general only small differences of the different EOSs are found. The differences are most pronounced around the (low-density) liquid-gas phase transition line where the distribution of light and intermediate clusters has an important effect. Possible extensions and improvements of the model are discussed.