### Abstract

An equation of state (EOS) for uniform asymmetric nuclear matter (ANM) is constructed at zero and finite temperatures by the variational method starting from the nuclear Hamiltonian that is composed of the Argonne v18 and Urbana IX potentials. At zero temperature, the two-body energy is calculated with the Jastrow wave function in the two-body cluster approximation which is supplemented by Mayer's condition and the healing-distance condition so as to reproduce the result by Akmal, Pandharipande and Ravenhall. The energy caused by the three-body force is treated somewhat phenomenologically so that the total energy reproduces the empirical saturation conditions. The masses and radii of neutron stars obtained with the EOS are consistent with recent observational data. At finite temperatures, thermodynamic quantities such as free energy, internal energy, entropy, pressure and chemical potentials are calculated with an extension of the method by Schmidt and Pandharipande. The validity of the frozen-correlation approximation employed in this work is confirmed as compared with the result of the fully minimized calculation. The quadratic proton-fraction-dependence of the energy of ANM is confirmed at zero temperature, whereas the free energy of ANM deviates from the quadratic proton-fraction-dependence markedly at finite temperatures. The obtained EOS of ANM will be an important ingredient of a new nuclear EOS for supernova numerical simulations.

Original language | English |
---|---|

Pages (from-to) | 53-73 |

Number of pages | 21 |

Journal | Nuclear Physics A |

Volume | 902 |

DOIs | |

Publication status | Published - 2013 Mar 5 |

### Fingerprint

### Keywords

- Neutron stars
- Nuclear EOS
- Nuclear matter
- Supernovae
- Variational method

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Variational study for the equation of state of asymmetric nuclear matter at finite temperatures.** / Togashi, H.; Takano, Masatoshi.

Research output: Contribution to journal › Article

*Nuclear Physics A*, vol. 902, pp. 53-73. https://doi.org/10.1016/j.nuclphysa.2013.02.014

}

TY - JOUR

T1 - Variational study for the equation of state of asymmetric nuclear matter at finite temperatures

AU - Togashi, H.

AU - Takano, Masatoshi

PY - 2013/3/5

Y1 - 2013/3/5

N2 - An equation of state (EOS) for uniform asymmetric nuclear matter (ANM) is constructed at zero and finite temperatures by the variational method starting from the nuclear Hamiltonian that is composed of the Argonne v18 and Urbana IX potentials. At zero temperature, the two-body energy is calculated with the Jastrow wave function in the two-body cluster approximation which is supplemented by Mayer's condition and the healing-distance condition so as to reproduce the result by Akmal, Pandharipande and Ravenhall. The energy caused by the three-body force is treated somewhat phenomenologically so that the total energy reproduces the empirical saturation conditions. The masses and radii of neutron stars obtained with the EOS are consistent with recent observational data. At finite temperatures, thermodynamic quantities such as free energy, internal energy, entropy, pressure and chemical potentials are calculated with an extension of the method by Schmidt and Pandharipande. The validity of the frozen-correlation approximation employed in this work is confirmed as compared with the result of the fully minimized calculation. The quadratic proton-fraction-dependence of the energy of ANM is confirmed at zero temperature, whereas the free energy of ANM deviates from the quadratic proton-fraction-dependence markedly at finite temperatures. The obtained EOS of ANM will be an important ingredient of a new nuclear EOS for supernova numerical simulations.

AB - An equation of state (EOS) for uniform asymmetric nuclear matter (ANM) is constructed at zero and finite temperatures by the variational method starting from the nuclear Hamiltonian that is composed of the Argonne v18 and Urbana IX potentials. At zero temperature, the two-body energy is calculated with the Jastrow wave function in the two-body cluster approximation which is supplemented by Mayer's condition and the healing-distance condition so as to reproduce the result by Akmal, Pandharipande and Ravenhall. The energy caused by the three-body force is treated somewhat phenomenologically so that the total energy reproduces the empirical saturation conditions. The masses and radii of neutron stars obtained with the EOS are consistent with recent observational data. At finite temperatures, thermodynamic quantities such as free energy, internal energy, entropy, pressure and chemical potentials are calculated with an extension of the method by Schmidt and Pandharipande. The validity of the frozen-correlation approximation employed in this work is confirmed as compared with the result of the fully minimized calculation. The quadratic proton-fraction-dependence of the energy of ANM is confirmed at zero temperature, whereas the free energy of ANM deviates from the quadratic proton-fraction-dependence markedly at finite temperatures. The obtained EOS of ANM will be an important ingredient of a new nuclear EOS for supernova numerical simulations.

KW - Neutron stars

KW - Nuclear EOS

KW - Nuclear matter

KW - Supernovae

KW - Variational method

UR - http://www.scopus.com/inward/record.url?scp=84874565986&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84874565986&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysa.2013.02.014

DO - 10.1016/j.nuclphysa.2013.02.014

M3 - Article

AN - SCOPUS:84874565986

VL - 902

SP - 53

EP - 73

JO - Nuclear Physics A

JF - Nuclear Physics A

SN - 0375-9474

ER -