Hiroaki Kanzawa

Variational calculation for the equation of state of nuclear matter at finite temperatures

Abstract An equation of state (EOS) for uniform nuclear matter is constructed at zero and finite temperatures with the variational method starting from the realistic nuclear Hamiltonian composed of the Argonne V18 and UIX potentials. The energy is evaluated in the two-body cluster approximation with the three-body-force contribution treated phenomenologically so as to reproduce the empirical saturation conditions. The obtained energies for symmetric nuclear matter and neutron matter at zero temperature are in fair agreement with those by Akmal, Pandharipande and Ravenhall, and the maximum mass of the neutron star is 2.2 M ⊙ . At finite temperatures, a variational method by Schmidt and Pandharipande is employed to evaluate the free energy, which is used to derive various thermodynamic quantities of nuclear matter necessary for supernova simulations. The result of this variational method at finite temperatures is found to be self-consistent.

Nonuniform Matter in Neutron Star Crusts Studied by the Variational Method with Thomas-Fermi Calculations

The equation of state (EOS) for neutron star (NS) crusts is studied in the Thomas-Fermi (TF) approximation using the EOS for uniform nuclear matter obtained by the variational method with the realistic nuclear Hamiltonian. The parameters associated with the nuclear three-body force, which are introduced to describe the saturation properties, are finely adjusted so that the TF calculations for isolated atomic nuclei reproduce the experimental data on masses and charge distributions satisfactorily. The resulting root-mean-square deviation of the masses from the experimental data for mass-measured nuclei is about 3 MeV. With the use of the nuclear EOS thus obtained, the nuclear species in the NS crust at zero temperature are determined. The predicted proton numbers of the nuclei in the NS crust are close to the gross behavior of the results obtained by Negele and Vautherin, while they are larger than those for the EOS obtained by Shen et al. owing to the difference in the symmetry energy. The density profile of NS is calculated with the constructed EOS. Subject Index: 204, 210, 241, 421, 423

The equation of state of asymmetric nuclear matter at zero and finite temperatures with the variational method

The equation of state (EOS) of asymmetric nuclear matter at zero and finite temperatures is constructed with the variational method, starting from the realistic nuclear Hamiltonian composed of the AV18 and UIX nuclear potentials. At zero temperature, the energy per nucleon of asymmetric nuclear matter is calculated in the two-body-cluster approximation with the three-body-force contribution treated somewhat phenomenologically so as to reproduce the empirical saturation conditions. At finite temperatures, the free energies per nucleon of asymmetric nuclear matter are obtained with an extension of the variational method by Schmidt and Pandharipande. Validity of the frozen-correlation approximation employed in this study is confirmed. The obtained free energies and related thermodynamic quantities for various densities, temperatures and proton fractions are essential ingredients in our project for constructing a new nuclear EOS table for supernova simulations.

Variational Calculation for the Equation of State of Hot Asymmetric Nuclear Matter

We calculate the equation of state (EOS) of asymmetric nuclear matter at finite temperatures with the cluster variational method based on the realistic nuclear Hamiltonian composed of the AV18 and UIX nuclear potentials. The free energy is calculated with an extension of the variational method proposed by Schmidt and Pandharipande. The obtained thermodynamic quantities such as entropy, internal energy, pressure and chemical potential derived from the free energy are reasonable. It is also found that the present variational calculation is self‐consistent. These thermodynamic quantities are essential ingredients in our project for constructing a new nuclear EOS applicable to supernova simulations.

Nuclear Many-Body Approach for Supernova EOS: Thomas-Fermi Calculations of Non-Uniform Nuclear Matter

An equation of state (EOS) for uniform nuclear matter is constructed at zero and finite temperatures with the variational method starting from the realistic nuclear Hamiltonian composed of the AV18 two-body potential and the UIX three-body potential. The maximum mass of the cold neutron star with this EOS is 2.2 M☉. Making use of uncertainty of the threebody nuclear force, adjustable parameters in the EOS are tuned so that the Thomas-Fermi calculations for β-stable nuclei reproduce the empirical data. The obtained EOS is appropriate for constructing a new nuclear EOS table for supernova simulations.

Variational Calculations for the Nuclear Equation of State toward Supernova Simulations

We construct an equation of state (EOS) for uniform nuclear matter at zero and finite temperatures with the variational method starting from the realistic nuclear Hamiltonian composed of the AV18 two‐body potential and the UIX three‐body interaction. Using the obtained EOS, we perform the Thomas‐Fermi calculation of atomic nuclei, and tune adjustable parameters in the EOS for uniform matter to reproduce empirical data of β‐stable nuclei, toward a nuclear EOS table for supernova simulations.

Equation of State of Nuclear Matter and the Nuclear Three‐Body Force

An equation of state (EOS) for uniform nuclear matter is constructed at zero and finite temperatures with the variational method starting from a realistic nuclear Hamiltonian composed of the AV18 two‐body potential and the UIX three‐nucleon interaction (TNI). The two‐body energy is calculated with a Jastrow wave function, and the TNI energy with the Fermi‐gas wave function. In this calculation, the Fujita‐Miyazawa (FM) 2π‐exchange term of the TNI energy is positive for symmetric nuclear matter. By taking into account the correlation between nucleons perturbatively, the expectation value of the FM term is modified to be negative in the low density region.

VARIATIONAL CALCULATION FOR THE NUCLEAR EQUATION OF STATE TOWARD SUPERNOVA EXPLOSIONS

The equation of state (EOS) is calculated for uniform nuclear matter at zero and finite temperatures with the variational method. Making use of uncertainty of the three-body nuclear force, adjustable parameters in the nuclear EOS are tuned so that the Thomas-Fermi calculations for β-stable nuclei with the EOS reproduce the empirical data. The calculated nuclear properties imply that larger symmetry energy of the EOS is preferable to reproduce the empirical β-stability line. The expectation value of the nuclear Hamiltonian caused by the 2π-exchange three-body nuclear force is uncertain and related to the symmetry energy.