Abstract:
A phenomenological momentum-independent (MID) model is constructed to describe the equation of state (EOS) for isospin asymmetric nuclear matter, especially the density dependence of the nuclear symmetry energy $E_{\text{\textrm{sym}}}(\rho)$. This model can reasonably describe the general properties of the EOS for symmetric nuclear matter and the symmetry energy predicted by both the sophisticated isospin and momentum dependent MDI model and the Skyrme-Hartree-Fock approach. We find that there exists a nicely linear correlation between $K_{\mathrm{sym}}$ and $L$ as well as between $J_{0}/K_{0} $ and $K_{0}$, where $L$ and $K_{\mathrm{sym}}$ represent, respectively, the slope and curvature parameters of the symmetry energy at the normal nuclear density $\rho_{0}$ while $K_{0}$ and $J_{0}$ are, respectively, the incompressibility and the third-order derivative parameter of symmetric nuclear matter at $\rho_{0}$. These correlations together with the empirical constraints on $K_{0}$, $L$ and $E_{\text{\textrm{sym}}}(\rho_{0}) $ lead to an estimation of -477 MeV $\leq K_{\mathrm{sat,2}}\leq -241 $ MeV for the second-order isospin asymmetry expansion coefficient for the incompressibility of asymmetric nuclear matter at the saturation point.

Abstract:
We explore the systematics of the density dependence of nuclear matter symmetry energy in the ambit of microscopic calculations with various energy density functionals, and find that the symmetry energy from subsaturation density to supra-saturation density can be well determined by three characteristic parameters of the symmetry energy at saturation density $\rho_0 $, i.e., the magnitude $E_{\text{sym}}({\rho_0 })$, the density slope $L$ and the density curvature $K_{\text{sym}}$. This finding opens a new window to constrain the supra-saturation density behavior of the symmetry energy from its (sub-)saturation density behavior. In particular, we obtain $L=46.7 \pm 12.8$ MeV and $K_{\text{sym}}=-166.9 \pm 168.3$ MeV as well as $E_{\text{sym}}({2\rho _{0}}) \approx 40.2 \pm 12.8$ MeV and $L({2\rho _{0}}) \approx 8.9 \pm 108.7$ MeV based on the present knowledge of $E_{\text{sym}}({\rho_{0}}) = 32.5 \pm 0.5$ MeV, $E_{\text{sym}}({\rho_c}) = 26.65 \pm 0.2$ MeV and $L({\rho_c}) = 46.0 \pm 4.5$ MeV at $\rho_{\rm{c}}= 0.11$ fm$^{-3}$ extracted from nuclear mass and the neutron skin thickness of Sn isotopes. Our results indicate that the symmetry energy cannot be stiffer than a linear density dependence.In addition, we also discuss the quark matter symmetry energy since the deconfined quarks could be the right degree of freedom in dense matter at high baryon densities.

Abstract:
We summarize the current status on constraining the density dependence of the symmetry energy from terrestrial laboratory measurements and astrophysical observations. While the value $E_{sym}({\rho_{0}})$ and density slope $L$ of the symmetry energy at saturation density $\rho_{0}$ can vary largely depending on the data or methods, all the existing constraints are essentially consistent with $E_{sym}({\rho_{0}}) = 31 \pm 2$ MeV and $L = 50 \pm 20$ MeV. The determination of the supra-saturation density behavior of the symmetry energy remains a big challenge.

Abstract:
The bulk parameters characterizing the energy of symmetric nuclear matter and the symmetry energy defined at normal nuclear density $\rho_0 $ provide important information on the equation of state (EOS) of isospin asymmetric nuclear matter. While significant progress has been made in determining some lower order bulk characteristic parameters, such as the energy $E_0(\rho_0)$ and incompressibility $K_0$ of symmetric nuclear matter as well as the symmetry energy $E_{sym}(\rho_0)$ and its slope parameter $L$, yet the higher order bulk characteristic parameters are still poorly known. Here, we analyze the correlations between the lower and higher order bulk characteristic parameters within the framework of Skyrme Hartree-Fock energy density functional and then estimate the values of some higher order bulk characteristic parameters. In particular, we obtain $J_0=-355 \pm 95$ MeV and $I_0=1473 \pm 680$ MeV for the third-order and fourth-order derivative parameters of symmetric nuclear matter at $\rho_0 $ and $K_{sym} = -100 \pm 165$ MeV, $J_{sym} = 224 \pm 385$ MeV, $I_{sym} = -1309 \pm 2025$ MeV for the curvature parameter, third-order and fourth-order derivative parameters of the symmetry energy at $\rho_0 $, using the empirical constraints on $E_0(\rho_0)$, $K_0$, $E_{sym}(\rho_0)$, $L$, and the isoscalar and isovector nucleon effective masses. Furthermore, our results indicate that the three parameters $E_0(\rho_0)$, $K_0$, and $J_0$ can reasonably characterize the EOS of symmetric nuclear matter up to $2\rho_0 $ while the symmetry energy up to $2\rho_0 $ can be well described by $E_{sym}(\rho_0)$, $L$, and $K_{sym}$.

Abstract:
Within the Skyrme-Hartree-Fock (SHF) approach, we show that for a fixed mass number A, both the symmetry energy coefficient a_{sym}(A) in the semi-empirical mass formula and the nuclear matter symmetry energy E_{sym}(\rho_A) at a subsaturation reference density rho_A can be determined essentially by the symmetry energy E_{sym}(rho_0) and its density slope L at saturation density rho_0. Meanwhile, we find the dependence of a_{sym}(A) on E_{sym}(rho_0) or L is approximately linear and is very similar to the corresponding linear dependence displayed by E_{sym}(\rho_A), providing an explanation for the relation E_{sym}(\rho_A) \approx a_{sym}(A). Our results indicate that a value of E_{sym}(\rho_A) leads to a linear correlation between E_{sym}(rho_0) and L and thus can put important constraints on E_{sym}(rho_0) and L. Particularly, the values of E_{sym}(rho_0)= 30.5 +- 3 MeV and L= 52.5 +- 20 MeV are simultaneously obtained by combining the constraints from recently extracted E_{sym}(\rho_A=0.1 fm^{-3}) with those from recent analyses of neutron skin thickness of Sn isotopes in the same SHF approach.

Abstract:
The anisotropic flow of charged hadrons in asymmetric Cu+Au collisions at the Relativistic Heavy Ion Collider is studied in a multi-phase transport model. Compared with previous results for symmetric Au+Au collisions, charged hadrons produced around midrapidity in asymmetric collisions are found to have a stronger directed flow $v_{1}$ and their elliptic flow $% v_{2} $ is also more sensitive to the parton scattering cross section. While higher-order flows $v_{3}$ and $v_{4}$ are small at all rapidities, both $% v_{1}$ and $v_{2}$ in these collisions are appreciable and show an asymmetry in forward and backward rapidities.

Abstract:
We report results from a multiphase transport (AMPT) model on the rapidity and system size dependence of charged hadron anisotropic flows in nuclear collisions at the Relativistic Heavy Ion Collider (RHIC).

Abstract:
Nucleon-nucleon (NN) cross sections are evaluated in neutron-rich matter using a scaling model according to nucleon effective masses. It is found that the in-medium NN cross sections are not only reduced but also have a different isospin dependence compared with the free-space ones. Because of the neutron-proton effective mass splitting the difference between nn and pp scattering cross sections increases with the increasing isospin asymmetry of the medium. Within the transport model IBUU04, the in-medium NN cross sections are found to influence significantly the isospin transport in heavy-ion reactions. With the in-medium NN cross sections, a symmetry energy of $E_{sym}(\rho)\approx 31.6(\rho /\rho_{0})^{0.69}$ was found most acceptable compared with both the MSU isospin diffusion data and the presently acceptable neutron-skin thickness in $^{208}$Pb. The isospin dependent part $K_{asy}(\rho _{0})$ of isobaric nuclear incompressibility was further narrowed down to $-500\pm 50$ MeV. The possibility of determining simultaneously the in-medium NN cross sections and the symmetry energy was also studied. The proton transverse flow, or even better the combined transverse flow of neutrons and protons, can be used as a probe of the in-medium NN cross sections without much hindrance from the uncertainties of the symmetry energy.

Abstract:
Based on the phase-space information obtained from a multi-phase transport model within the string melting scenario for strange and antistrange quarks, we study the yields and transverse momentum spectra of $\phi $ mesons and $\Omega $ ($\Omega ^{-}+\bar{\Omega}^{+}$) baryons as well as their anisotropic flows in Au+Au collisions at RHIC using a dynamical quark coalescence model that includes the effect due to quark phase-space distributions inside hadrons. With current quark masses and fixing the $\phi $ and $\Omega $ radii from fitting measured yields, we first study the ratio of the yield of $\Omega $ baryons to that of $\phi $ mesons as well as their elliptic and fourth-order flows as functions of their transverse momentum. How the elliptic and fourth-order flows of $\phi $ mesons and $\Omega $ baryons are related to those of strange and antistrange quarks is then examined. The dependence of above results on $\phi $ and $\Omega $ radii as well as on the strange quark mass is also studied.

Abstract:
We explore effects of the light vector $U$-boson, which is weakly coupled to nucleons, on the transition density $\rho_{t}$ and pressure $P_{t}$ at the inner edge separating the liquid core from the solid crust of neutron stars. Three methods, i.e., the thermodynamical approach, the curvature matrix approach and the Vlasov equation approach are used to determine the transition density $\rho_{t}$ with the Skyrme effective nucleon-nucleon interactions. We find that the $\rho_{t}$ and $P_{t}$ depend on not only the ratio of coupling strength to mass squared of the $U$-boson $g^{2}/\mu ^{2}$ but also its mass $\mu $ due to the finite range interaction from the $U$-boson exchange. In particular, our results indicate that the $\rho_{t}$ and $P_{t}$ are sensitive to both $g^{2}/\mu ^{2}$ and $\mu $ if the $U$-boson mass $\mu $ is larger than about 2 MeV. Furthermore, we show that both $g^{2}/\mu ^{2}$ and $\mu $ can have significant influence on the mass-radius relation and the crustal fraction of total moment of inertia of neutron stars. In addition, we study the exchange term contribution of the $U$-boson based on the density matrix expansion method, and demonstrate that the exchange term effects on the nuclear matter equation of state as well as the $\rho_{t}$ and $P_{t}$ are generally negligible.