Kazuhiro Oyamatsu

Relativistic equation of state of nuclear matter for supernova and neutron star

Abstract We construct the equation of state (EOS) of nuclear matter using the relativistic mean field (RMF) theory in the wide density, temperature range with various proton fractions for the use of supernova simulation and the neutron star calculations. We first construct the EOS of homogeneous nuclear matter. We use then the Thomas-Fermi approximation to describe inhomogeneous matter, where heavy nuclei are formed together with free nucleon gas. We discuss the results on free energy, pressure and entropy in the wide range of astrophysical interest. As an example, we apply the resulting EOS on the neutron star properties by using the Oppenheimer-Volkoff equation.We construct the equation of state (EOS) of nuclear matter using the relativistic mean field (RMF) theory in the wide density, temperature range with various proton fractions for the use of supernova simulation and the neutron star calculations. We first construct the EOS of homogeneous nuclear matter. We use then the Thomas-Fermi approximation to describe inhomogeneous matter, where heavy nuclei are formed together with free nucleon gas. We discuss the results on free energy, pressure and entropy in the wide range of astrophysical interest. As an example, we apply the resulting EOS on the neutron star properties by using the Oppenheimer-Volkoff equation.

Relativistic Equation of State of Nuclear Matter for Supernova Explosion

We construct the equation of state (EOS) of nuclear matter at finite temperature and density with various proton fractions within the relativistic mean field (RMF) theory for the use in the supernova simulations. The Thomas-Fermi approximation is adopted to describe the non-uniform matter where we consider nucleus, alpha-particle, proton and neutron in equilibrium. We treat the uniform matter and non-uniform matter consistently using the RMF theory. We tabulate the outcome as the pressure, free energy, entropy etc, with enough mesh points in wide ranges of the temperature, proton fraction, and baryon mass density.

Quantum molecular dynamics approach to the nuclear matter below the saturation density

Quantum molecular dynamics is applied to study the ground state properties of nuclear matter at subsaturation densities. Clustering effects are observed as to soften the equation of state at these densities. The structure of nuclear matter at subsaturation density shows some exotic shapes with variation of the density.

Can the equation of state of asymmetric nuclear matter be studied using unstable nuclei

Abstract The paper shows that nuclear radii and neutron skins do directly reflect the saturation density of asymmetric nuclear matter. The proton distributions in a nucleus have been found to be remarkably independent of the equation of state (EOS) of the asymmetric matter. It is the neutron distributions that are dependent on the EOS. Macroscopic model calculations have been performed over the entire range of the nuclear chart based on two popular phenomenological, but distinctively different, EOS: the SIII parameter set for the non-relativistic Skyrme Hartree-Fock theory and the TM1 parameter set in the relativistic mean field theory. The saturation density for a small proton fraction remains almost the same as the normal nuclear matter density for SIII EOS, but it becomes significantly small for the TM1 EOS. The key EOS parameters used to describe the saturation density are the density derivative of the symmetry energy and the incompressibility of symmetric nuclear matter, while the saturation energy is written using the symmetry energy alone as a good approximation. We conclude that a systematic experimental study of heavy unstable nuclei would enable us to determine the EOS of asymmetric nuclear matter at about the normal nuclear matter density with a fixed proton fraction down to about 0.3.

Symmetry energy at subnuclear densities and nuclei in neutron star crusts

Department of Materials Science, Kochi University, Akebono-cho, Kochi 780-8520, Japan(Dated: February 9, 2008)We examine how the properties of inhomogeneous nuclear matter at subnuclear densities dependon the density dependence of the symmetry energy. Using a macroscopic nuclear model we calculatethe size and shape of nuclei in neutron star matter at zero temperature in a way dependent onthe density dependence of the symmetry energy. We find that for smaller symmetry energy atsubnuclear densities, corresponding to larger density symmetry coefficient L, the charge number ofnuclei is smaller, and the critical density at which matter with nuclei or bubbles becomes uniform islower. The decrease in the charge number is associated with the dependence of the surface tensionon the nuclear density and the density of a sea of neutrons, while the decrease in the critical densitycan be generally understood in terms of proton clustering instability in uniform matter.

Saturation of Nuclear Matter and Radii of Unstable Nuclei

We systematically examine relations among the parameters characterizing the phenomenological equation of state (EOS) of nearly symmetric, uniform nuclear matter near the saturation density by comparing macroscopic calculations of radii and masses of stable nuclei with experimental data. The EOS parameters of interest here are the symmetry energy coefficient S0, the symmetry energy density derivative coefficient L and the incompressibility K0 at normal nuclear density. We estimate a range of (K0, L) from empirically reasonable values of the slope of the saturation line (the line joining the saturation points of nuclear matter at finite neutron excess) and find a strong correlation between S0 and L. In light of the uncertainties on the values of K0 and L, we perform macroscopic calculations of the radii of unstable nuclei expected to be produced in future facilities. We find that the matter radii depend appreciably on L, while being almost independent of K0. This dependence implies that if the matter radii are measured with an accuracy of ±0.01 fm for a sufficiently large number of neutron-rich nuclides to allow one to smooth out the expected staggering of the radii due to shell and pairing effects, it might be possible to derive the value of L within ±20 MeV.

Effect of superfluidity on neutron star oscillations

We consider how superfluidity of dripped neutrons in the crust of a neutron star affects the frequencies of the crust’s fundamental torsional oscillations. A nonnegligible superfluid part of dripped neutrons, which do not comove with nuclei, act to reduce the enthalpy density and thus enhance the oscillation frequencies. By assuming that the quasi-periodic oscillations observed in giant flares of soft gamma repeaters arise from the fundamental torsional oscillations and that the mass and radius of the neutron star is in the range of 1.4 6 M/M⊙ 6 1.8 and 10 km 6 R 6 14 km, we constrain the density derivative of the symmetry energy as 100 MeV 50 MeV, derived by ignoring the superfluidity.

Probing the equation of state of nuclear matter via neutron star asteroseismology.

We general-relativistically calculate the frequency of fundamental torsional oscillations of neutron star crusts, where we focus on the crystalline properties obtained from macroscopic nuclear models in a way that is dependent on the equation of state of nuclear matter. We find that the calculated frequency is sensitive to the density dependence of the symmetry energy, but almost independent of the incompressibility of symmetric nuclear matter. By identifying the lowest-frequency quasiperiodic oscillation in giant flares observed from soft gamma-ray repeaters as the fundamental torsional mode and allowing for the dependence of the calculated frequency on stellar models, we provide a lower limit of the density derivative of the symmetry energy as L≃50  MeV.

Neutron star profiles in the relativistic Brueckner-Hartree-Fock theory

Abstract We study the properties of neutron star matter and neutron stars in the relativistic Brueckner-Hartree-Fock (RBHF) theory. Adopting the equation of state (EOS) in the RBHF theory, we calculate the properties of neutron star matter under the beta equilibrium condition in a wide range of density. We perform the Thomas-Fermi calculation of neutron star matter in the crust region taking into account the change of nuclear shapes around the density, ϱ ∼ 10 14 g/cm 3 . We compare the results with the properties of dense matter in the non-relativistic many body theory. The qualitative feature of neutron star matter in the crust is consistent with previous works. The relativistic EOS of neutron star matter is found to be stiffer than the non-relativistic EOSs characteristically. We found that the proton fraction of neutron star matter in the high density region in the RBHF theory is quite large as compared with those found in the non-relativistic calculations and allow the direct Urca process, which is crucial for the rapid cooling of neutron stars, for relatively massive neutron stars.

Possible Origin of the Gamma-ray Discrepancy in the Summation Calculations of Fission Product Decay Heat

In order to identify the origin of the ubiquitous and long-standing discrepancy seen in the γ-ray component of the FP decay heat in the cooling time range 300-3,000 s, a comprehensive analysis of the differences between the summation calculations and the experiments has been carried out. There may be some missing of the β-strength in the high energy region of the FPs in the mass region A=100-110. Especially, 102Tc, 104Tc, 105Tc and 108Rh are potentially responsible for the γ-ray discrepancy seen in the three major fissioning nuclides, 235U, 238U and 239Pu, systematically. The β-strength functions are theoretically calculated in order to validate this possibility. It is proved that the chance for finding the additional β-strength required to solve the discrepancy is not so large but still exists, and the exact β-feed from Tc to the highly excited levels in Rb should be identified experimentally. Finally, the impact of the β-ray discrepancy on the reactor-core decay heat is evaluated quantitatively for the ...