Nuclear collisions can compress nuclear matter to densities achieved within neutron stars and within core-collapse supernovae. These dense states of matter exist momentarily before expanding. We analyzed the flow of matter to extract pressures in excess of 1034 pascals, the highest recorded under laboratory-controlled conditions. Using these analyses, we rule out strongly repulsive nuclear equations of state from relativistic mean field theory and weakly repulsive equations of state with phase transitions at densities less than three times that of stable nuclei, but not equations of state softened at higher densities because of a transformation to quark matter.

Determination of the Equation of State of Dense Matter

This article combines two talks given by the authors and is based on Works done in collaboration with G.E. Brown and D.P. Min on kaon condensation in dense baryonic medium treated in chiral perturbation theory using heavy-baryon formalism. It contains, in addition to what was recently published, astrophysical backgrounds for kaon condensation discussed by Brown and Bethe, a discussion on a renormalization-group analysis to meson condensation worked out together with H.K. Lee and S.J. Sin, and the recent results of K.M. Westerberg in the bound-state approach to the Skyrme model. Negatively charged kaons are predicted to condense at a critical density 2 {approx_lt} {rho}/{rho}o {approx_lt} 4, in the range to allow the intriguing new phenomena predicted by Brown and Bethe to take place in compact star matter.

Kaon condensation in dense stellar matter

The structure of neutron stars is considered from theoretical and observational perspectives. We demonstrate an important aspect of neutron star structure: the neutron star radius is primarily determined by the behavior of the pressure of matter in the vicinity of nuclear matter equilibrium density. In the event that extreme softening does not occur at these densities, the radius is virtually independent of the mass and is determined by the magnitude of the pressure. For equations of state with extreme softening or those that are self-bound, the radius is more sensitive to the mass. Our results show that in the absence of extreme softening, a measurement of the radius of a neutron star more accurate than about 1 km will usefully constrain the equation of state. We also show that the pressure near nuclear matter density is primarily a function of the density dependence of the nuclear symmetry energy, while the nuclear incompressibility and skewness parameters play secondary roles. In addition, we show that the moment of inertia and the binding energy of neutron stars, for a large class of equations of state, are nearly universal functions of the star's compactness. These features can be understood by considering two analytic, yet realistic, solutions of Einstein's equations, by, respectively, Buchdahl and Tolman. We deduce useful approximations for the fraction of the moment of inertia residing in the crust, which is a function of the stellar compactness and, in addition, the pressure at the core-crust interface.

Neutron Star Structure and the Equation of State(Nuclear Astrophysics,New Frontiers in QCD 2010-Exotic Hadron Systems and Dense Matter-)

Binding energy of symmetric nuclear matter can be accessed straightforwardly with the textbook mass-formula and a sample of nuclear masses. We show that, with a minimally modified formula (along the lines of the droplet model), the symmetry energy of nuclear matter can be accessed nearly as easily. Elementary considerations for a macroscopic nucleus show that the surface tension needs to depend on asymmetry. That dependence modifies the surface energy and implies the emergence of asymmetry skin. In the mass formula, the volume and surface and (a)symmetry energies combine as energies of two connected capacitors, with the volume and surface capacitances proportional to the volume and area, respectively. The net asymmetry partitions itself into volume and surface contributions in proportion to the capacitances. A combination of data on skin sizes and masses constrains the volume symmetry parameter to 27 MeV≲ α ≲31 MeV and the volume-to-surface symmetry-parameter ratio to 2.0≲ α / β ≲2.8. In Thomas–Fermi theory, the surface asymmetry-capacitance stems from a drop of the symmetry energy per nucleon S with density. We establish limits on the drop at half of normal density, to 0.57≲ S ( ρ 0 /2)/ S ( ρ 0 )≲0.83. In considering the feeding of surface by an asymmetry flux from interior, we obtain a universal condition for the collective asymmetry oscillations, in terms of the asymmetry-capacitance ratio.

Surface Symmetry Energy

Momentum and density dependence of single-nucleon potential uτ (k, ρ, β) is analyzed using a density dependent finite range effective interaction of the Yukawa form. Depending on the choice of the strength parameters of exchange interaction, two different trends of the momentum dependence of nuclear symmetry potential are noticed which lead to two opposite types of neutron and proton effective mass splitting. The 2nd-order and 4th-order symmetry energy of isospin asymmetric nuclear matter are expressed analytically in terms of the single-nucleon potential. Two distinct behavior of the density dependence of 2nd-order and 4th-order symmetry energy are observed depending on neutron and proton effective mass splitting. It is also found that the 4th-order symmetry energy has a significant contribution towards the proton fraction of β-stable npeμ matter at high densities.

Nuclear symmetry energy in terms of single-nucleon potential and its effect on the proton fraction of β -stable npeμ matter

A phenomenological momentum dependent interaction (MDI) is considered to describe the equation of state (EOS) for isospin asymmetric nuclear matter (ANM), where the density dependence of the nuclear symmetry is the basic input. In this interaction, the symmetry energy shows soft dependence of density. Within the nonrelativistic mean field approach we calculate the nuclear matter fourth-order symmetry energy Esym, 4(ρ). Our result shows that the value of Esym, 4(ρ) at normal nuclear matter density ρ0( = 0.161 fm-3) is less than 1 MeV conforming the empirical parabolic approximation to the EOS of ANM at ρ0. Then the higher-order effects of the isospin asymmetry on the saturation density ρsat(β), binding energy per nucleon Ksat(β) and isobaric incompressibility Ksat(β) of ANM is being studied, where is the isospin asymmetry. We have found that the fourth-order isospin asymmetry β cannot be neglected, while calculating these quantities. Hence the second-order Ksat, 2 parameter basically characterizes the isospin dependence of the incompressibility of ANM at saturation density.

Isospin dependence of the saturation properties of asymmetric nuclear matter in nonrelativistic mean field model

Role of symmetry potential in nuclear symmetry energy and its density slope parameter

Using a simple density-dependent finite-range effective interaction having Yukawa form, the density dependence of isoscalar and isovector effective masses is studied. The isovector effective mass is found to be different for different pairs of like and unlike nucleons. Using HVH theorem, the neutron-proton effective mass splitting is represented in terms of symmetry energy and its density slope. It is again observed that the neutron-proton effective mass splitting has got a positive value when isoscalar effective mass is greater than the isovector effective mass and has a negative value for the opposite case. Furthermore, the neutron-proton effective mass splitting is found to have a linear dependence on asymmetry β. The second-order symmetry potential has a vital role in the determination of density slope of symmetry energy but it does not have any contribution on neutron-proton effective mass splitting. The finite-range effective interaction is compared with the SLy2, SKM, f−, f0, and f+ forms of interactions.

Neutron-Proton Effective Mass Splitting in Terms of Symmetry Energy and Its Density Slope ∗

We analyze the relation between the symmetry energy coefficient asym(A) of finite nuclei with mass number A in the semi-empirical mass formula. The nuclear matter symmetry energy Esym(ρA) at refere...

Neutron skin thickness of finite nuclei with finite range effective interaction in droplet model

An extended nuclear mass formula has been used by considering the bulk, surface and coulomb contributions to the nuclear mass. In this mass formula, the fourth-order symmetry energy coefficient asy...

B. Sahoo

Papers

Isospin dependence of the saturation properties of asymmetric nuclear matter in nonrelativistic mean field model

Role of symmetry potential in nuclear symmetry energy and its density slope parameter

Neutron-Proton Effective Mass Splitting in Terms of Symmetry Energy and Its Density Slope ∗

Neutron skin thickness of finite nuclei with finite range effective interaction in droplet model

The fourth-order symmetry energy of nuclear matter and symmetry energy coefficients of finite nuclei using extended semi-empirical mass formula