ASYMMETRIC NUCLEAR MATTER: A VARIATIONAL APPROACH

The effects of density dependence of the symmetry energy on the collective modes and dynamical instabilities of cold and warm nuclear and stellar matter are studied in the framework of relativistic mean-field hadron models. The existence of the collective isovector and possibly an isoscalar collective mode above saturation density is discussed. It is shown that soft equations of state do not allow for a high density isoscalar collective mode, however, if the symmetry energy is hard enough an isovector mode will not disappear at high densities. The crust-core transition density and pressure are obtained as a function of temperature for $\beta$-equilibrium matter with and without neutrino trapping. An estimation of the size of the clusters formed in the non-homogeneous phase as well as the corresponding growth rates and distillation effect is made. It is shown that cluster sizes increase with temperature, that the distillation effect close to the inner edge of the crust-core transition is very sensitive to the symmetry energy, and that, within a dynamical instability calculation, the pasta phase exists in warm compact stars up to 10 - 12 MeV.

Thermal impacts on the properties of nuclear matter and young neutron star

A set of density dependent nucleon-nucleon (N-N) interactions has been examined in nuclear matter calculations by varying spin-isospin contributions. Two sets of potentials have been considered. One having a density dependentσ-function type short range part followed by one term long range Gaussian part while the other having a density dependentσ-function part followed by two Gaussian terms. The strength parameters of the potential have been fitted to the saturation properties of nuclear matter, i.e. binding energy per particle of 15.5 MeV atk F=1.35 fm−1. Several sets of these two potentials have been generated by varying the strength parameterM of Majorana exchange operatorP M. It is seen thatM indirectly controls the spin, iso-spin contribution to the interaction potential and thus affects the nuclear matter properties such as compressibility and symmetry energy considerably, while variation of these quantities with the range parameterμ for givenM is moderate at lowM values while at higherM values it is quite large.

New equations of state for dense nuclear matter properties

Analytical expressions for the saturation density of asymmetric nuclear matter as well as its binding energy and incompressibility at saturation density are given up to fourth order in the isospin asymmetry $\ensuremath{\delta}=({\ensuremath{\rho}}_{n}\ensuremath{-}{\ensuremath{\rho}}_{p})/\ensuremath{\rho}$ using 11 characteristic parameters defined by the density derivatives of the binding energy per nucleon of symmetric nuclear matter, the symmetry energy ${E}_{\mathrm{sym}} (\ensuremath{\rho})$, and the fourth-order symmetry energy ${E}_{\mathrm{sym},4}(\ensuremath{\rho})$ at normal nuclear density ${\ensuremath{\rho}}_{0}$. Using an isospin- and momentum-dependent modified Gogny interaction (MDI) and the Skyrme-Hartree-Fock (SHF) approach with 63 popular Skyrme interactions, we have systematically studied the isospin dependence of the saturation properties of asymmetric nuclear matter, particularly the incompressibility ${K}_{\mathrm{sat}}(\ensuremath{\delta})={K}_{0}+{K}_{\mathrm{sat},2}{\ensuremath{\delta}}^{2}+{K}_{\mathrm{sat},4}{\ensuremath{\delta}}^{4}+O({\ensuremath{\delta}}^{6})$ at saturation density. Our results show that the magnitude of the higher order ${K}_{\mathrm{sat},4}$ parameter is generally small compared to that of the ${K}_{\mathrm{sat},2}$ parameter. The latter essentially characterizes the isospin dependence of the incompressibility at saturation density and can be expressed as ${K}_{\mathrm{sat},2}={K}_{\mathrm{sym}}\ensuremath{-}6L\ensuremath{-}\frac{{J}_{0}}{{K}_{0}}L$, where $L$ and ${K}_{\mathrm{sym}}$ represent, respectively, the slope and curvature parameters of the symmetry energy at ${\ensuremath{\rho}}_{0}$ and ${J}_{0}$ is the third-order derivative parameter of symmetric nuclear matter at ${\ensuremath{\rho}}_{0}$. Furthermore, we have constructed a phenomenological modified Skyrme-like (MSL) model that can reasonably describe the general properties of symmetric nuclear matter and the symmetry energy predicted by both the MDI model and the SHF approach. The results indicate that the higher order ${J}_{0}$ contribution to ${K}_{\mathrm{sat},2}$ generally cannot be neglected. In addition, it is found that there exists a nicely linear correlation between ${K}_{\mathrm{sym}}$ and $L$ as well as between ${J}_{0}/{K}_{0}$ and ${K}_{0}$. These correlations together with the empirical constraints on ${K}_{0},L,{E}_{\mathrm{sym}} ({\ensuremath{\rho}}_{0})$, and the nucleon effective mass lead to an estimate of ${K}_{\mathrm{sat},2}=\ensuremath{-}370\ifmmode\pm\else\textpm\fi{}120$ MeV.

During the last decade STAR experiment has studied the hot and dense nuclear matter produced in heavy ion collisions at RHIC. The study of quarkonia, such as J/ψ meson, production provides the information about properties of this nuclear matter. It is predicted that due to the Debye screening the quarkonia production is suppressed when Quark Gluon Plasma (QGP) is presented. In order to understand the properties of hot and dense nuclear matter, it is necessary to study the production of quarkonia in hadron-hadron, hadron-ion, and ion-ion collisions separately to distinguish cold nuclear matter effect, such as gluon shadowing, from the suppression due to the formation of QGP. Moreover, the J/ψ hadron azimuthal correlations allow to extract the fraction of J/ψ that originates from B-mesons. This proceedings presents recent J/ψ measurements at mid-rapidity in p+p, and Au+Au collisions at = 200 GeV at STAR, the fraction of J/ψ originates from B-mesons, and J/ψ eliptic flow v2 as a function of transverse momentum in Au+Au collisions in = 200 GeV at STAR.

Within the framework of the Dirac-Brueckner (DB) approach, the properties of dense nuclear and neutron matter are investigated using realistic nucleon-nucleon (NN) interactions which are derived from relativistic meson-field theory and describe the two-nucleon system quantitatively. Single-particle potentials, equations of state, nucleon effective masses, Landau parameters, and speeds of sound are calculated and analyzed as functions of density, for both nuclear and neutron matter. In the DB approach, the equation of state comes out stiffer than in the most sophisticated nonrelativistic calculation, but softer than in the Walecka model. Possible extensions of the present approach to nucleon-nucleus scattering and nucleus-nucleus collisions are also discussed.

We study the properties of nuclear matter with lattice nucleon-nucleon (NN) potential in the relativistic Brueckner-Hartree-Fock (RBHF) theory. To use this potential in such a microscopic many-body theory, we firstly have to construct a one-boson-exchange potential (OBEP) based on the latest lattice NN potential. Three mesons, pion, σ meson, and ω meson, are considered. Their coupling constants and cut-off momenta are determined by fitting the on-shell behaviors and phase shifts of the lattice force, respectively. Therefore, we obtain two parameter sets of the OBEP potential (named as LOBEP1 and LOBEP2) with these two fitting ways. We calculate the properties of symmetric and pure neutron matter with LOBEP1 and LOBEP2. In non-relativistic Brueckner-Hartree-Fock case, the binding energies of symmetric nuclear matter are around −3 and −5 MeV at saturation density, while it becomes −8 and −12 MeV in relativistic framework with 1S0, 3S1, and 3D1 channels using our two parameter sets. For the pure neutron matter, the equations of state in non-relativistic and relativistic cases are very similar due to only consideration 1S0 channel with isospin T = 1 case.

We calculate the properties of nuclear matter and neutron matter with charge dependent potentials using the Dirac-Brueckner approach. It turns out that the charge dependence of the NN interaction has no significant influence on the properties of nuclear matter and neutron matter.

The structure of nuclear systems derived from low momentum nucleon–nucleon potentials

The effective Skyrme interaction has been used extensively in mean-field models for several decades and many different parametrizations of the interaction have been proposed. All of these give similar agreement with the experimental observables of nuclear ground states as well as with the properties of infinite symmetric nuclear matter at the saturation density ${n}_{0}.$ However, when applied over a wider range of densities (up to $\ensuremath{\sim}{3n}_{0})$ they predict widely varying behavior for the observables of both symmetric and asymmetric nuclear matter. A particularly relevant example of naturally occurring asymmetric nuclear matter is the material of which neutron stars are composed. At around nuclear matter density, this can be well represented as a mixture of neutrons, protons, electrons, and muons $(n+p+e+\ensuremath{\mu}$ matter) in $\ensuremath{\beta}$-equilibrium, and these densities turn out to be the key ones for determining the properties of neutron-star models with masses near to the widely used ``canonical'' value of ${1.4M}_{\ensuremath{\bigodot}}.$ By constructing equations of state for neutron-star matter using the different Skyrme parametrizations, calculating corresponding neutron-star models and then comparing these with observational data, an additional constraint can be obtained for the values of the Skyrme parameters. Such a constraint is particularly relevant because the parametrizations are initially determined by fitting to the properties of doubly closed-shell nuclei and it is an open question how suitable they then are for nuclei with high values of isospin, such as those at the neutron drip-line and beyond. The neutron-star environment provides an invaluable testing ground for this. We have carried out an investigation of 87 different Skyrme parametrizations in order to examine how successful they are in predicting the expected properties of infinite nuclear matter and generating plausible neutron-star models. This is the first systematic study of the predictions of the various Skyrme parametrizations for the density dependence of the characteristic observables of nuclear matter; the density dependence of the symmetry energy for $\ensuremath{\beta}$-equilibrium matter turns out to be a crucial property for indicating which Skyrme parameter sets will apply equally well for finite nuclei and for neutron-star matter. Only 27 of the 87 parametrizations investigated pass the test of giving satisfactory neutron-star models and we present a list of these.

We review theoretical relations between macroscopic properties of neutron stars and microscopic quantities of nuclear matter, such as consistency of hadronic nuclear models and observed masses of neutron stars. The relativistic hadronic field theory, quantum hadrodynamics (QHD), and mean-field approximations of the theory are applied to saturation properties of symmetric nuclear and neutron matter. The equivalence between mean-field approximations and Hartree approximation is emphasized in terms of renormalized effective masses and effective coupling constants of hadrons. This is important to prove that the direct application of mean-field (Hartree) approximation to nuclear and neutron matter is inadequate to examine physical observables. The equations of state (EOS), binding energies of nuclear matter, self-consistency of nuclear matter, are reviewed, and the result of chiral Hartree-Fock approximation is shown. Neutron stars and history of nuclear astrophysics, nuclear model and nuclear matter, possibility of hadron and hadron-quark neutron stars are briefly reviewed. The hadronic models are very useful and practical for understanding astrophysical phenomena, nuclear matter and radiation phenomena of nuclei.

I have proposed two parameter sets, NLD1 and NLD2, for the Lagrangian with nonlinear derivative couplings in the relativistic mean-field theory. Properties of nuclear matter and finite nuclei are explored. It is shown that this Lagrangian model can lead to a softening of the equation of state and symmetry energy at high densities. Two trends for the high-density behavior of symmetry energy are obtained with NLD1 and NLD2. These two sets also give a much less repulsive Schr\"odinger equivalent optical potential at high nucleon energies compared to standard relativistic mean-field models and reproduce the experimental data very well. The study also shows that a good description of ground-state properties of nuclei is achieved with this Lagrangian.

The Korea-IBS-Daegu-SKKU energy density functional (KIDS-EDF) models, constructed from the perturbative expansion of the energy density in nuclear matter, have been successfully and widely applied in describing the properties of finite nuclei and infinite nuclear matter. In the present work, we extend the applications of the KIDS-EDF models to investigate the implications of the nucleon effective mass and nuclear symmetry energy for the properties of neutron stars (NSs) and neutrino interaction with the NS constituent matter in the linear response approximation (LRA). At fixed neutrino energy and momentum transfer, we analyze the total differential cross section of neutrinos, the neutrino mean free path (NMFP), and the NS mass-radius (M-R) relations. Remarkable results are given by the KIDS0-m*87 and SLy4 models, in which ${M}_{n}^{*}/M\ensuremath{\lesssim}1$, and their NMFPs are quite higher in comparison with those obtained from the KIDS0, KIDS-A, and KIDS-B models, which result in ${M}_{n}^{*}/M\ensuremath{\gtrsim}1$. For the KIDS0, KIDS-A, and KIDS-B models, we obtain $\ensuremath{\lambda}\ensuremath{\lesssim}{R}_{\text{NS}}$, indicating that these models could predict the slow NS cooling and neutrino trapping in NSs. In contrast, the KIDS0-m*87 and SLy4 models yield $\ensuremath{\lambda}\ensuremath{\gtrsim}{R}_{\text{NS}}$ and thus we expect faster NS cooling and a small possibility of neutrino trapping within NSs. We also calculate the NMFP as a function of the neutrino energy and the nuclear matter density and find that the NMFP decreases as the density and neutrino energy increase, which is consistent with the result obtained in the Brussels-Montreal Skyrme (BSk17 and BSk18) models at saturation density.

In order to predict properties of asymmetric nuclear matter, we construct a relativistic mean field (RMF) model consisting of one-meson exchange (OME) terms and point coupling (PC) terms. In order to determine the density dependent parameters of this model, we use properties of isospin symmetric nuclear matter in combination with the information on nucleon-nucleon scattering data, which are given in the form of the density dependent G-matrix derived from Brueckner calculations based on the Tamagaki potential. We show that the medium- and long-range components of this G-matrix can be described reasonably well by our effective OME interaction. In order to take into account the short-range part of the nucleon-nucleon interaction, which cannot be described well in this manner, a point coupling term is added. Its analytical form is taken from a model based on chiral perturbation theory. It contains only one additional parameter, which does not depend on the density. It is, together with the parameters of the OME potentials adjusted to the equation of state of symmetric nuclear matter. We apply this model for the investigation of asymmetric nuclear matter and find that the results for the symmetry energy as well as for the equation of state of pure neutron matter are in good agreement with either experimental data or with presently adopted theoretical predictions. In order to test the model at higher density, we use its equation of state for an investigation of properties of neutron stars.