## Abstract

We present the virial equation of state of low-density nuclear matter composed of neutrons, protons and alpha particles. The virial equation of state is model-independent, and therefore sets a benchmark for all nuclear equations of state at low densities. We calculate the second virial coefficients for nucleon-nucleon, nucleon-alpha and alpha-alpha interactions directly from the relevant binding energies and scattering phase shifts. The virial approach systematically takes into account contributions from bound nuclei and the resonant continuum, and consequently provides a framework to include strong-interaction corrections to nuclear statistical equilibrium models. The virial coefficients are used to make model-independent predictions for a variety of properties of nuclear matter over a range of densities, temperatures and compositions. Our results provide constraints on the physics of the neutrinosphere in supernovae. The resulting alpha particle concentration differs from all equations of state currently used in supernova simulations. Finally, the virial equation of state greatly improves our conceptual understanding of low-density nuclear matter.

Original language | English |
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Pages (from-to) | 55-79 |

Number of pages | 25 |

Journal | Nuclear Physics A |

Volume | 776 |

Issue number | 1-2 |

DOIs | |

State | Published - 18 Sep 2006 |

Externally published | Yes |

### Bibliographical note

Funding Information:We thank S. Karataglidis for the calculation of the nucleon–alpha phase shifts and A. Marek for providing us with tables of the LS, Shen and Wolff equations of state. This work is supported in part by the US DOE under Grant No. DE-FG02-87ER40365 and the NSF under Grant No. PHY-0244822.

### Funding

We thank S. Karataglidis for the calculation of the nucleon–alpha phase shifts and A. Marek for providing us with tables of the LS, Shen and Wolff equations of state. This work is supported in part by the US DOE under Grant No. DE-FG02-87ER40365 and the NSF under Grant No. PHY-0244822.

Funders | Funder number |
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National Science Foundation | |

U.S. Department of Energy | DE-FG02-87ER40365 |

Directorate for Mathematical and Physical Sciences | 0244822 |

## Keywords

- Clustering
- Equation of state
- Low-density nuclear matter
- Virial expansion