Saturation of nuclear matter and radii of unstable nuclei

We 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 the experimental data. The EOS parameters of interest here are the symmetry energy S_0, the symmetry energy density-derivative coefficient L and the incompressibility K_0 at the normal nuclear density. We find a constraint on the relation between K_0 and L from the empirically allowed values of the slope of the saturation line (the line joining the saturation points of nuclear matter at finite neutron excess), together with a strong correlation between S_0 and L. In the light of the uncertainties in the values of K_0 and L, we macroscopically calculate radii of unstable nuclei as expected to be produced in future facilities. We find that the matter radii depend strongly on L while being almost independent of K_0, a feature that will help to determine the L value via systematic measurements of nuclear size.Comment: 26 pages, 7 figure

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.Comment: 22 pages, LaTeX, 9 ps-figures, Submitted to Prog.Theor.Phy

Relativistic Equation of State for Core-Collapse Supernova Simulations

We construct the equation of state (EOS) of dense matter covering a wide range of temperature, proton fraction, and density for the use of core-collapse supernova simulations. The study is based on the relativistic mean-field (RMF) theory, which can provide an excellent description of nuclear matter and finite nuclei. The Thomas--Fermi approximation in combination with assumed nucleon distribution functions and a free energy minimization is adopted to describe the non-uniform matter, which is composed of a lattice of heavy nuclei. We treat the uniform matter and non-uniform matter consistently using the same RMF theory. We present two sets of EOS tables, namely EOS2 and EOS3. EOS2 is an update of our earlier work published in 1998 (EOS1), where only the nucleon degree of freedom is taken into account. EOS3 includes additional contributions from $\Lambda$ hyperons. The effect of $\Lambda$ hyperons on the EOS is negligible in the low-temperature and low-density region, whereas it tends to soften the EOS at high density. In comparison with EOS1, EOS2 and EOS3 have an improved design of ranges and grids, which covers the temperature range $T=0.1$--$10^{2.6}$ MeV with the logarithmic grid spacing $\Delta \log_{10}(T/\rm{[MeV]})=0.04$ (92 points including T=0), the proton fraction range $Y_p=0$--0.65 with the linear grid spacing $\Delta Y_p = 0.01$ (66 points), and the density range $\rho_B=10^{5.1}$--$10^{16}\,\rm{g\,cm^{-3}}$ with the logarithmic grid spacing $\Delta \log_{10}(\rho_B/\rm{[g\,cm^{-3}]}) = 0.1$ (110 points).Comment: 43 pages, 10 figure

Surface tension in a compressible liquid-drop model: Effects on nuclear density and neutron skin thickness

We examine whether or not the surface tension acts to increase the nucleon density in the nuclear interior within a compressible liquid-drop model. We find that it depends on the density dependence of the surface tension, which may in turn be deduced from the neutron skin thickness of stable nuclei.Comment: 4 pages, 1 figure, to be published in Physical Review

Relativistic Equation of State of Nuclear Matter for Supernova and Neutron Star

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.Comment: 15 pages, LaTeX, 14 ps-figures, accepted for publication in Nucl.Phys.

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.Comment: 21 pages of Latex (revtex), 9 Postscript figure

Non-uniform 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 use of the nuclear EOS thus determined, the nuclei in the crust of NS at zero temperature are calculated. The predicted proton numbers of the nuclei in the crust of NS are close to the gross behavior of the results by Negele and Vautherin, while they are larger than those for the EOS by Shen et al. due to the difference in the symmetry energy. The density profile of NS is calculated with the constructed EOS.Comment: 38 pages, 9 figures, accepted for publication in PT

Electron screening in the liquid-gas mixed phases of nuclear matter

Screening effects of electrons on inhomogeneous nuclear matter, which includes spherical, slablike, and rodlike nuclei as well as spherical and rodlike nuclear bubbles, are investigated in view of possible application to cold neutron star matter and supernova matter at subnuclear densities. Using a compressible liquid-drop model incorporating uncertainties in the surface tension, we find that the energy change due to the screening effects broadens the density region in which bubbles and nonspherical nuclei appear in the phase diagram delineating the energetically favorable shape of inhomogeneous nuclear matter. This conclusion is considered to be general since it stems from a model-independent feature that the electron screening acts to decrease the density at which spherical nuclei become unstable against fission and to increase the density at which uniform matter becomes unstable against proton clustering.Comment: 12 pages, 8 figures, accepted for publication in Physical Review