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.

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.

We have constructed a nuclear equation of state (EOS) that includes a full nuclear ensemble for use in core-collapse supernova simulations. It is based on the EOS for uniform nuclear matter that two of the authors derived recently, applying a variational method to realistic two-and there-body nuclear forces. We have extended the liquid drop model of heavy nuclei, utilizing the mass formula that accounts for the dependences of bulk, surface, Coulomb and shell energies on density and/or temperature. As for light nuclei, we employ a quantum-theoretical mass evaluation, which incorporates the Pauli-and self-energy shifts. In addition to realistic nuclear forces, the inclusion of in-medium effects on the full ensemble of nuclei makes the new EOS one of the most realistic EOS's, which covers a wide range of density, temperature and proton fraction that supernova simulations normally encounter. We make comparisons with the FYSS EOS, which is based on the same formulation for the nuclear ensemble but adopts the relativistic mean field (RMF) theory with the TM1 parameter set for uniform nuclear matter. The new EOS is softer than the FYSS EOS around and above nuclear saturation densities. We find that neutron-rich nuclei with small mass numbers are more abundant in the new EOS than in the FYSS EOS because of the larger saturation densities and smaller symmetry energy of nuclei in the former. We apply the two EOS's to 1D supernova simulations and find that the new EOS gives lower electron fractions and higher temperatures in the collapse phase owing to the smaller symmetry energy. As a result, the inner core has smaller masses for the new EOS. It is more compact, on the other hand, due to the softness of the new EOS and bounces at higher densities. It turns out that the shock wave generated 2 by core bounce is a bit stronger initially in the simulation with the new EOS. The ensuing outward propagations of the shock wave in the outer core are very similar in the two simulations, which may be an artifact, though, caused by the use of the same tabulated electron capture rates for heavy nuclei ignoring differences in the nuclear composition between the two EOS's in these computations.where the values of the constants, σ 0 = 1.15 MeV/fm 3 and S s = 45.8 MeV, are adopted from Lattimer and Swesty [17]. We may

A new scenario for neutron-star cooling is suggested by the correspondence between pion condensation, induced by critical spin-isospin fluctuations, and the metal-insulator phase transition in a 2D electron gas. Above the threshold density for pion condensation, the neutron single-particle spectrum acquires an insulating gap that quenches neutron contributions to neutrino production. In the liquid phase just below the transition, the fluctuations play dual roles by (i) creating a multisheeted neutron Fermi surface that extends to low momenta and activates the normally forbidden direct Urca cooling mechanism, and (ii) amplifying the nodeless P-wave neutron superfluid gap while suppressing S-wave pairing. Lighter stars without a pion-condensed core undergo slow cooling, whereas enhanced cooling occurs in heavier stars via direct Urca emission from a thin shell of the interior.

We investigate the effects of the odd-state part of bare ΛΛ interactions on the structure of neutron stars (NSs) by constructing equations of state (EOSs) for uniform nuclear matter containing Λ and Σ − hyperons with use of the cluster variational method. The isoscalar part of the Argonne v18 two-nucleon potential and the Urbana IX three-nucleon potential are employed as the interactions between nucleons, whereas, as the bare ΛN and even-state ΛΛ interactions, two-body central potentials that are determined so as to reproduce the experimental data on single-and double-Λ hypernuclei are adopted. In addition, the Σ − N interaction is constructed so as to reproduce the empirical single-particle potential of Σ − in symmetric nuclear matter. Since the odd-state part of the ΛΛ interaction is not known owing to lack of experimental data, we construct four EOSs of hyperonic nuclear matter, each with a different odd-state part of the ΛΛ interaction. The EOS obtained for NS matter becomes stiffer as the odd-state ΛΛ interaction becomes more repulsive, and correspondingly the maximum mass of NSs increases. It is interesting that the onset density of Σ − depends strongly on the repulsion of the odd-state ΛΛ interaction. Furthermore, we take into account the three-baryon repulsive force to obtain results that are consistent with observational data on heavy NSs.