Nuclear matter at a HIRFL-CSR energy regime

We report some recent progress in constraining the symmetry energy E-sym(rho) at high densities using high-energy heavy-ion collisions. Circumstantial evidence of a soft E-sym(rho) at supra-saturation density is obtained by comparing the pion ratio pi(-)/pi(+) measured recently with FOPI at GSI and the IBUU04 model calculations. Detailed studies indicate that the power of determining the E-sym(rho)from pi(-)/pi(+) is enhanced with decreasing the beam energy to near the pion production threshold, showing a correlation to the increasing nuclear stopping. Among several heavy-ion reaction facilities in the world, the cooling storage ring (HIRFL-CSR), newly commissioned at Lanzhou, delivering heavy-ion beams up to 1 A GeV, to be coupled with advanced detectors will contribute significantly to further studies of the equation of state of asymmetric nuclear matter.

Superfluidity in dense nuclear matter

We discuss the onset of superfluidity in neutron stars, where the model of nuclear matter is realized in a high-density and asymmetry state. In particular, we present the study of the effects of microscopic three-body forces on the proton pairing in the 1S0 channel and neutron pairing in 3PF1 channel for β-stable neutron star matter. It is found that the main effects of three-body forces are to shrink the domain of existence of the 1S0 below the threshold of the direct URCA process and to stretch the density range of the 3PF1 pairing in a broad domain so to cover most part of the neutron-star core.

Isospin dependence of nucleon (PF2)-P-3 superfluidity in asymmetric nuclear matter

We have investigated the isospin dependence of the neutron and proton (PF2)-P-3 superfluidity in isospin-asymmetric nuclear matter within the framework of the Brueckner-Hartree-Fock approach and the BCS theory. We show that the (PF2)-P-3 neutron and proton pairing gaps depend sensitively on isospin asymmetry of asymmetric nuclear matter. As the isospin asymmetry increases, the neutron (PF2)-P-3 superfluidity becomes stronger and the peak value of the neutron (PF2)-P-3 pairing gap increases rapidly. The isospin dependence of the proton (PF2)-P-3 superfluidity is shown to be opposite to the neutron one. The proton (PF2)-P-3 superfluidity becomes weaker at a higher asymmetry and it even vanishes at high enough asymmetries. At high asymmetries, the neutron (PF2)-P-3 superfluidity turns out to be much stronger than the proton one, implying that the neutron (PF2)-P-3 superfluidity is dominated in the highly asymmetric dense interior of neutron stars.

Hot Nuclear Matter Equation of State and Finite Temperature Kaon Condensation

We perform a systematic calculation of the equation of state of asymmetric nuclear matter at finite temperature within the framework of the Brueckner-Hartree-Fock approach with a microscopic three-body force. When applying it to the study of hotka on condensed matter, we find that the thermal effect is more profound in comparison with normal matter, in particular around the threshold density. Also, the increase of temperature makes the equation of state slightly stiffer through suppression of kaon condensation.

Neutron-proton bremsstrahlung from intermediate energy heavy-ion reactions as a probe of the nuclear symmetry energy?

Hard photons from neutron-proton bremsstrahlung in intermediate energy heavy-ion reactions are examined as a potential probe of the nuclear symmetry energy within a transport model. Effects of the symmetry energy on the yields and spectra of hard photons are found to be generally smaller than those due to the currently existing uncertainties of both the in-medium nucleon-nucleon cross sections and the photon production probability in the elementary process pn -> pn gamma. Very interestingly, nevertheless, the ratio of hard photon spectra R-1/2(gamma) from two reactions using isotopes of the same element is not only approximately independent of these uncertainties but also quite sensitive to the symmetry energy. For the head-on reactions of Sn-132 + Sn-124 and Sn-112 + Sn-112 at E-beam/A = 50 MeV, for example, the R-1/2(gamma) displays a rise up to 15% when the symmetry energy is reduced by about 20% at rho = 1.3 rho(0) which is the maximum density reached in these reactions. (C) 2008 Elsevier B.V. All rights reserved.

Deconfinement phase Transition including perturbative QCD corrections in (proto)neutron star matter

Deconfinement phase transition and neutrino trapping in (proto)neutron star matter are investigated in a chiral hadronic model (also referred to as the FST model) for the hadronic phase (HP) and in the color-flavor-locked (CFL) quark model for the deconfined quark phase. We include a perturbative QCD correction parameter alpha(s) in the CFL quark matter equation of states. It is shown that the CFL quark core with K-0 condensation forms in neutron star matter with the large value of alpha(s). If the small value of alpha(s) is taken, hyperons suppress the CFL quark phase and the HP is dominant in the high-density region of (proto)neutron star matter. Neutrino trapping makes the fraction of the CFL quark matter decrease compared with those without neutrino trapping. Moreover, increasing the QCD correction parameter alpha(s) or decreasing the bag constant B and the strange quark mass m(s) can make the fraction of the CFL quark matter increase, simultaneously, the fraction of neutrino in protoneutron star matter increases, too. The maximum masses and the corresponding radii of (proto)neutron stars are not sensitive to the QCD correction parameter alpha(s).

Differential isospin-fractionation in dilute asymmetric nuclear matter

The differential isospin-fractionation (IsoF) during the liquid-gas phase transition in dilute asymmetric nuclear matter is studied as a function of nucleon momentum. Within a self-consistent thermal model it is shown that the neutron/proton ratio of the gas phase becomes smaller than that of the liquid phase for energetic nucleons, although the gas phase is overall more neutron-rich. Clear indications of the differential IsoF consistent with the thermal model predictions are demonstrated within a transport model for heavy-ion reactions. Future comparisons with experimental data will allow us to extract critical information about the momentum dependence of the isovector strong interaction.

Phase transition to color-flavor-locked matter and condensation of Goldstone bosons in neutron star matter

Deconfinement phase transition and condensation of Goldstone bosons in neutron star matter are investigated in a chiral hadronic model (also referred as to the FST model) for the hadronic phase (HP) and in the color-flavor-locked (CFL) quark model for the deconfined quark phase. It is shown that the hadronic-CFL mixed phase (MP) exists in the center of neutron stars with a small bag constant, while the CFL quark matter cannot appear in neutron stars when a large bag constant is taken. Color superconductivity softens the equation of state (EOS) and decreases the maximum mass of neutron stars compared with the unpaired quark matter. The K-0 condensation in the CFL phase has no remarkable contribution to the EOS and properties of neutron star matter. The EOS and the properties of neutron star matter are sensitive to the bag constant B, the strange quark mass m(s) and the color superconducting gap Delta. Increasing B and m(s) or decreasing Delta can stiffen the EOS which results in the larger maximum masses of neutron stars.

Properties of proto-neutron star and effect of three-body forces

Within the Brueckner-Hartree-Fock framework, the equation of state and the properties of newborn neutron stars are investigated by adopting a realistic nucleon-nucleon interaction AV(18) supplemented with a microscopic three-body force or a phenomenological three-body force. The maximum mass of newborn neutron star and the proton fraction in the newborn beta-stable neutron-star matter are calculated. The neutrino-trapping and the three-body force effects are discussed, and the interplay between the effects of the trapped neutrino and the three-body force are especially explored. It is shown that neutrino trapping considerably affects the proton abundance and the equation of state of the newborn neutron star in both cases with and without the three-body forces. The effect of neutrino trapping remarkably enhances the proton abundance, and the contribution of the three-body force makes the equation of state of the newborn neutron star much stiffer at high densities and consequently increases the proton abundance strongly. The trapped neutrinos significantly reduce the influence of the three-body force on the proton abundance in newborn neutron stars.

Double neutron/proton ratio of nucleon emissions in isotopic reaction systems as a robust probe of nuclear symmetry energy

The double neutron/proton ratio of nucleon emissions taken from two reaction systems using four isotopes of the same element, namely, the neutron/proton ratio in the neutron-rich system over that in the more symmetric system, has the advantage of reducing systematically the influence of the Coulomb force and the normally poor efficiencies of detecting low energy neutrons. The double ratio thus suffers less systematic errors. Within the IBUU04 transport model the double neutron/proton ratio is shown to have about the same sensitivity to the density dependence of nuclear symmetry energy as the single neutron/proton ratio in the neutron-rich system involved. The double neutron/proton ratio is therefore more useful for further constraining the symmetry energy of neutron-rich matter.

The effect of the scalar-isovector meson field on hyperon-rich neutron star matter

We investigate the effect of the calar-isovector delta-meson field on the equation of state (EOS) and composition of hyperonic neutron star matter, and the properties of hyperonic neutron stars within the frame work of the relativistic mean field theory. The influence of the delta-field turns out to be quite different and generally weaker for hyperonic neutron star matter as compared to that for npe mu neutron star matter. We find that inclusion of the delta-field enhances the strangeness content slightly and consequently moderately softens the EOS of neutron star matter in its hyperonic phase. As for the composition of hyperonic star matter, the effect of the delta-field is shown to shift the onset of the negatively-charged (positively-charged) hyperons to slightly lower (higher) densities and to enhance (reduce) their abundances. The influence of the delta-field on the maximum mass of hyperonic neutron stars is found to be fairly weak, where as inclusion of the delta-field turns out to enhance sizably both the radii and the moments of inertia of neutron stars with given masses. It is also shown that the effects of the delta-field on the properties of hyperonic neutron stars remain similar in the case of switching off the Sigma hyperons.

System size and beam energy effects on probing the high-density behavior of nuclear symmetry energy with pion ratio

Based on the isospin-and momentum-dependent hadronic transport model IBUU04, we have investigated the pi(-)/pi(+) ratio in the following three reactions: Ca-48+Ca-48, Sn-124 +Sn-124 and Au-197+Au-197 with nearly the same isospin asymmetry but different masses, at the bombarding energies from 0.25 to 0.6 A GeV. It is shown that the sensitivity of probing the E-sym (rho) with pi(-)/pi(+) increases with increasing the system size or decreasing the beam energy, showing a correlation to the degree of isospin fractionation. Therefore, with a given isospin asymmetry, heavier system at energies near the pion threshold is preferential to study the behavior Of nuclear symmetry energy at supra-saturation densities.

Recent Progress in Constraining the Equation of State of Dense Neutron-Rich Nuclear Matter with Heavy-Ion Reactions

The nuclear symmetry energy E-sym(rho) is the most uncertain part of the Equation of State (EOS) of dense neutron-rich nuclear matter. In this talk, we discuss the underlying physics responsible for the uncertain E-sym(rho) especially at supra-saturation densities, the circumstantial evidence for a super-soft E-sym(rho) from analyzing pi(-)/pi(+) ratio in relativistic heavy-ion collisions and its impacts on astrophysics and cosmology.

Effects of elastic and inelastic NN scattering cross sections on pi(-)/pi(+) ratios in heavy-ion collisions at intermediate energies

Based on the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model and the scaling model according to nucleon effective mass, effects of elastic and inelastic NN scattering cross sections on pi(-)/pi(+) in the neutron-rich reaction of Ca-48 + Ca-48 at a beam energy of 400 MeV/nucleon are studied. It is found that cross-section effects of both NN elastic and inelastic scatterings affect Delta(1232), pi(-) and pi(+) production, as well as the value of pi(-)/pi(+).

Dynamics of strangeness production in heavy-ion collisions near threshold energies

Within the framework of the improved isospin-dependent quantum molecular dynamics (ImIQMD) model, the dynamics of strangeness (K-0,K-+, Lambda, and Sigma(-,0,+)) production in heavy-ion collisions near threshold energies is investigated systematically, with the strange particles considered to be produced mainly by inelastic collisions of baryon-baryon and pion-baryon. Collisions in the region of suprasaturation densities of the dense baryonic matter formed in heavy-ion collisions dominate the yields of strangeness production. Total multiplicities as functions of incident energies and collision centralities are calculated with the Skyrme parameter SLy6. The excitation function of strangeness production is analyzed and also compared with the KaoS data for K+ production in the reactions C-12 + C-12 and Au-197 + Au-197.