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 varia- tional 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 consis- tent 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.
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