A new table of the nuclear equation of state (EOS) based on realistic nuclear potentials is constructed for core-collapse supernova numerical simulations. Adopting the EOS of uniform nuclear matter constructed by two of the present authors with the cluster variational method starting from the Argonne v18 and Urbana IX nuclear potentials, the Thomas-Fermi calculation is performed to obtain the minimized free energy of a Wigner-Seitz cell in non-uniform nuclear matter. As a preparation for the Thomas-Fermi calculation, the EOS of uniform nuclear matter is modified so as to remove the effects of deuteron cluster formation in uniform matter at low densities. Mixing of alpha particles is also taken into account following the procedure used by Shen et al. ( , 2011. The critical densities with respect to the phase transition from non-uniform to uniform phase with the present EOS are slightly higher than those with the Shen EOS at small proton fractions. The critical temperature with respect to the liquid-gas phase transition decreases with the proton fraction in a more gradual manner than in the Shen * Corresponding author Email address: hajime.togashi@riken.jp (H. Togashi)Preprint submitted to Nuclear Physics A March 23, 2017EOS. Furthermore, the mass and proton numbers of nuclides appearing in non-uniform nuclear matter with small proton fractions are larger than those of the Shen EOS. These results are consequences of the fact that the density derivative coefficient of the symmetry energy of our EOS is smaller than that of the Shen EOS.

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We have constructed a new equation of state (EOS) for dense nuclear matter based on a variational many-body theory. For the homogeneous phase, the free energy is calculated by the cluster variational method with the realistic nuclear Hamiltonian composed of the Argonne v18 two-nucleon and Urbana IX three-nucleon potentials. For the inhomogeneous phase, the Thomas-Fermi approximation is adopted so as to construct the EOS of non-uniform matter which is consistent with that of uniform phase. It is found that the obtained EOS shows the higher critical temperature and larger mass numbers of nuclides in neutron-rich nuclear matter, as compared with the Shen EOS. We tabulate the present EOS in wade ranges of the temperature, proton fraction, and baryon density. Using the resultant EOS table, we finally perform the calculation of protoneutron star structures and the simple supernova simulation to investigate the properties of our EOS.

We propose a new nuclear equation of state (EOS) for numerical simulations of core-collapse supernovae (SNe) using the variational many-body theory with realistic nuclear forces. Starting from the nuclear Hamiltonian composed of the Argonne v18 two-body potential and Urbana IX three-body potential, we first construct the EOS of uniform nuclear matter by the cluster variational method. The obtained free energies of pure neutron matter and symmetric nuclear matter are in good agreement with those of Fermi hypernetted chain variational calculations. Moreover, the mass-radius relation of neutron stars derived from this EOS at zero temperature is consistent with recent observational data. Using the free energies of uniform nuclear matter based on the realistic nuclear Hamiltonian, we then construct the EOS for non-uniform nuclear matter by the Thomas-Fermi calculation. The obtained phase diagram of hot nuclear matter is reasonable as compared with the Shen EOS, and thermodynamic quantities in the non-uniform phase with the present EOS are similar to those with the Shen EOS. Finally, the present EOS is applied to a spherically symmetric adiabatic numerical simulation of SNe. We confirm that our EOS is successfully applied to this hydrodynamics simulation. It is also seen that the present EOS in a relatively large proton fraction is softer than the Shen EOS, which is consistent with the fact that the incompressibility of the present EOS is smaller than that of the Shen EOS.