Probing the equation of state of neutron-rich matter with intermediate energy heavy-ion collisions

Nuclear reactions induced by stable and/or radioactive neutron-rich nuclei provide the opportunity to pin down the equation of state of neutron-rich matter, especially the density ($\rho$) dependence of its isospin-dependent part, i.e., the nuclear symmetry energy $E_{\rm sym}$. A conservative constraint, $32(\rho /\rho_{0})^{0.7} < E_{\rm sym}(\rho ) < 32(\rho /\rho _{0})^{1.1}$, around the nuclear matter saturation density $\rho_0$ has recently been obtained from the isospin diffusion data in intermediate energy heavy-ion collisions. We review this exciting result and discuss its consequences and implications on nuclear effective interactions, radii and cooling mechanisms of neutron stars.Comment: 10 pages. Invited talks at (1) International Workshop on Nuclear Multifragmentation, Nov. 28-Dec. 1, 2005, Catania, Italy and (2) XXIX Symposium on Nuclear Physics, Jan. 3-6, 2006, Cocoyoc, Morelos, Mexic

Nuclear matter symmetry energy and the neutron skin thickness of heavy nuclei

Correlations between the thickness of the neutron skin in finite nuclei and the nuclear matter symmetry energy are studied in the Skyrme Hartree-Fock model. From the most recent analysis of the isospin diffusion data in heavy-ion collisions based on an isospin- and momentum-dependent transport model with in-medium nucleon-nucleon cross sections, a value of $L=88\pm 25$ MeV for the slope of the nuclear symmetry energy at saturation density is extracted, and this imposes stringent constraints on both the parameters in the Skyrme effective interactions and the neutron skin thickness of heavy nuclei. Predicted thickness of the neutron skin is $0.22\pm 0.04$ fm for $$Pb, $0.29\pm 0.04$ fm for $^{132}$Sn, and $0.22\pm 0.04$ fm for $$Sn.Comment: 6 pages, 4 figures, 1 table, revised version, to appear in PR

Constraining the Skyrme effective interactions and the neutron skin thickness of nuclei using isospin diffusion data from heavy ion collisions

Recent analysis of the isospin diffusion data from heavy-ion collisions based on an isospin- and momentum-dependent transport model with in-medium nucleon-nucleon cross sections has led to the extraction of a value of $L=88\pm 25$ MeV for the slope of the nuclear symmetry energy at saturation density. This imposes stringent constraints on both the parameters in the Skyrme effective interactions and the neutron skin thickness of heavy nuclei. Among the 21 sets of Skyrme interactions commonly used in nuclear structure studies, the 4 sets SIV, SV, G$_\sigma$, and R$_\sigma$ are found to give $L$ values that are consistent with the extracted one. Further study on the correlations between the thickness of the neutron skin in finite nuclei and the nuclear matter symmetry energy in the Skyrme Hartree-Fock approach leads to predicted thickness of the neutron skin of $0.22\pm 0.04$ fm for $^{208}$Pb, $0.29\pm 0.04$ fm for $^{132}$Sn, and $0.22\pm 0.04$ fm for $^{124}$Sn.Comment: 10 pages, 4 figures, 1 Table, Talk given at 1) International Conference on Nuclear Structure Physics, Shanghai, 12-17 June, 2006; 2) 11th China National Nuclear Structure Physics Conference, Changchun, Jilin, 13-18 July, 200

Determination of the stiffness of the nuclear symmetry energy from isospin diffusion

With an isospin- and momentum-dependent transport model, we find that the degree of isospin diffusion in heavy ion collisions at intermediate energies is affected by both the stiffness of the nuclear symmetry energy and the momentum dependence of the nucleon potential. Using a momentum dependence derived from the Gogny effective interaction, recent experimental data from NSCL/MSU on isospin diffusion are shown to be consistent with a nuclear symmetry energy given by $E_{\text{sym}}(\rho)\approx 31.6(\rho /\rho_{0})^{1.05}$ at subnormal densities. This leads to a significantly constrained value of about -550 MeV for the isospin-dependent part of the isobaric incompressibility of isospin asymmetric nuclear matter.Comment: 4 pages, 4 figures, 1 table, revised version, to appear in PR

Equation of state of the hot dense matter in a multi-phase transport model

Within the framework of a multi-phase transport model, we study the equation of state and pressure anisotropy of the hot dense matter produced in central relativistic heavy ion collisions. Both are found to depend on the hadronization scheme and scattering cross sections used in the model. Furthermore, only partial thermalization is achieved in the produced matter as a result of its fast expansion

Effect of symmetry energy on two-nucleon correlation functions in heavy-ion collisions induced by neutron-rich nuclei

Using an isospin-dependent transport model, we study the effects of nuclear symmetry energy on two-nucleon correlation functions in heavy ion collisions induced by neutron-rich nuclei. We find that the density dependence of the nuclear symmetry energy affects significantly the nucleon emission times in these collisions, leading to larger values of two-nucleon correlation functions for a symmetry energy that has a stronger density dependence. Two-nucleon correlation functions are thus useful tools for extracting information about the nuclear symmetry energy from heavy ion collisions.Comment: Revised version, to appear in Phys. Rev. Let

Circumstantial evidence for a soft nuclear symmetry energy at supra-saturation densities

Within an isospin- and momentum-dependent hadronic transport model it is shown that the recent FOPI data on the $\pi^-/\pi^+$ ratio in central heavy-ion collisions at SIS/GSI energies (Willy Reisdorf {\it et al.}, NPA {\bf 781}, 459 (2007)) provide circumstantial evidence suggesting a rather soft nuclear symmetry energy \esym at $\rho\geq 2\rho_0$ compared to the Akmal-Pandharipande-Ravenhall prediction. Some astrophysical implications and the need for further experimental confirmations are discussed.Comment: Version to appear in Phys. Rev. Let

Transition Density and Pressure at the Inner Edge of Neutron Star Crusts

Using the nuclear symmetry energy that has been recently constrained by the isospin diffusion data in intermediate-energy heavy ion collisions, we have studied the transition density and pressure at the inner edge of neutron star crusts, and they are found to be 0.040 fm$^{-3}$ $\leq \rho_{t}\leq 0.065$ fm$^{-3}$ and 0.01 MeV/fm$^{3}$ $\leq P_{t}\leq 0.26$ MeV/fm$^{3}$, respectively, in both the dynamical and thermodynamical approaches. We have also found that the widely used parabolic approximation to the equation of state of asymmetric nuclear matter gives significantly higher values of core-crust transition density and pressure, especially for stiff symmetry energies. With these newly determined transition density and pressure, we have obtained an improved relation between the mass and radius of neutron stars.Comment: 7 pages, 3 figures, proceeding of "The International Workshop on Nuclear Dynamics in Heavy-Ion Reactions and the Symmetry Energy (IWND2009)

Partonic effects on anisotropic flows at RHIC

We report recent results from a multiphase transport (AMPT) model on the azimuthal anisotropies of particle momentum distributions in heavy ion collisions at the Relativistic Heavy Ion Collider. These include higher-order anisotropic flows and their scaling, the rapidity dependence of anisotropic flows, and the elliptic flow of charm quarks.Comment: 7 pages, 5 figures, talk given at "Hot Quarks 2004", July 18-24, 2004, Taos Valley, NM, US

Constraining properties of neutron stars with heavy-ion reactions in terrestrial laboratories

Heavy-ion reactions provide a unique means to investigate the equation of state (EOS) of neutron-rich nuclear matter, especially the density dependence of the nuclear symmetry energy $E_{sym}(\rho)$. The latter plays an important role in understanding many key issues in both nuclear physics and astrophysics. Recent analyses of heavy-ion reactions have already put a stringent constraint on the $E_{sym}(\rho)$ around the saturation density. This subsequently allowed us to constrain significantly the radii and cooling mechanisms of neutron stars as well as the possible changing rate of the gravitational constant G.Comment: 6 pages. Talk given at the Nuclear Physics in Astrophysics III, Dresden, Germany, March 26-31, 2007. To appear in a special volume of J. of Phys.