Directed and elliptic flows of neutrons and light charged particles were measured for the reaction 197Au+197Au at 400 MeV/nucleon incident energy within the ASY-EOS experimental campaign at the GSI laboratory. The detection system consisted of the Large Area Neutron Detector LAND, combined with parts of the CHIMERA multidetector, of the ALADIN Time-of-flight Wall, and of the Washington-University Microball detector. The latter three arrays were used for the event characterization and reaction-plane reconstruction. In addition, an array of triple telescopes, KRATTA, was used for complementary measurements of the isotopic composition and flows of light charged particles. From the comparison of the elliptic flow ratio of neutrons with respect to charged particles with UrQMD predictions, a value \gamma = 0.72 \pm 0.19 is obtained for the power-law coefficient describing the density dependence of the potential part in the parametrization of the symmetry energy. It represents a new and more stringent constraint for the regime of supra-saturation density and confirms, with a considerably smaller uncertainty, the moderately soft to linear density dependence deduced from the earlier FOPI-LAND data. The densities probed are shown to reach beyond twice saturation.

Results of the ASY-EOS experiment at GSI: The symmetry energy at suprasaturation density

Systematics of azimuthal asymmetries in heavy ion collisions in the 1AGeV regime

Simulations by transport codes are indispensable to extract valuable physical information from heavy-ion collisions. In order to understand the origins of discrepancies among different widely used transport codes, we compare 15 such codes under controlled conditions of a system confined to a box with periodic boundary, initialized with Fermi-Dirac distributions at saturation density and temperatures of either 0 or 5 MeV. In such calculations, one is able to check separately the different ingredients of a transport code. In this second publication of the code evaluation project, we only consider the two-body collision term;i.e., we perform cascade calculations. When the Pauli blocking is artificially suppressed, the collision rates are found to be consistent for most codes (to within 1% or better) with analytical results, or completely controlled results of a basic cascade code. In order to reach that goal, it was necessary to eliminate correlations within the same pair of colliding particles that can be present depending on the adopted collision prescription. In calculations with active Pauli blocking, the blocking probability was found to deviate from the expected reference values. The reason is found in substantial phase-space fluctuations and smearing tied to numerical algorithms and model assumptions in the representation of phase space. This results in the reduction of the blocking probability in most transport codes, so that the simulated system gradually evolves away from the Fermi-Dirac toward a Boltzmann distribution. Since the numerical fluctuations are weaker in the Boltzmann-Uehling-Uhlenbeck codes, the Fermi-Dirac statistics is maintained there for a longer time than in the quantum molecular dynamics codes. As a result of this investigation, we are able to make judgements about the most effective strategies in transport simulations for determining the collision probabilities and the Pauli blocking. Investigation in a similar vein of other ingredients in transport calculations, like the mean-field propagation or the production of nucleon resonances and mesons, will be discussed in the future publications.

https://link.aps.org/accepted/10.1103/PhysRevC.97.034625

Comparison of heavy-ion transport simulations: Collision integral in a box

Many neutron star properties, such as the proton fraction, reflect the symmetry energy contributions to the equation of state that dominate when neutron and proton densities differ strongly. To constrain these contributions at suprasaturation densities, we measure the spectra of charged pions produced by colliding rare isotope tin (Sn) beams with isotopically enriched Sn targets. Using ratios of the charged pion spectra measured at high transverse momenta, we deduce the slope of the symmetry energy to be 42<L<117  MeV. This value is slightly lower but consistent with the L values deduced from a recent measurement of the neutron skin thickness of ^{208}Pb.

Probing the Symmetry Energy with the Spectral Pion Ratio.

The general idea of information entropy provided by C.E. Shannon "hangs over everything we do" and can be applied to a great variety of problems once the connection between a distribution and the quantities of interest is found. The Shannon information entropy essentially quantify the information of a quantity with its specific distribution, for which the information entropy based methods have been deeply developed in many scientific areas including physics. The dynamical properties of heavy-ion collisions (HICs) process make it difficult and complex to study the nuclear matter and its evolution, for which Shannon information entropy theory can provide new methods and observables to understand the physical phenomena both theoretically and experimentally. To better understand the processes of HICs, the main characteristics of typical models, including the quantum molecular dynamics models, thermodynamics models, and statistical models, etc, are briefly introduced. The typical applications of Shannon information theory in HICs are collected, which cover the chaotic behavior in branching process of hadron collisions, the liquid-gas phase transition in HICs, and the isobaric difference scaling phenomenon for intermediate mass fragments produced in HICs of neutron-rich systems. Even though the present applications in heavy-ion collision physics are still relatively simple, it would shed light on key questions we are seeking for. It is suggested to further develop the information entropy methods in nuclear reactions models, as well as to develop new analysis methods to study the properties of nuclear matters in HICs, especially the evolution of dynamics system.

Shannon Information Entropy in Heavy-ion Collisions

The updated ultrarelativistic quantum molecular dynamics (UrQMD) model, a microscopic transport model, is used to study the directed and elliptic collective flows and the nuclear stopping in Au$+$Au collisions at incident energies covered by INDRA and lower-energy FOPI experiments It is seen clearly that these observables are sensitive to both the potential terms (including isoscalar and isovector parts as well as the momentum dependent term) in the equation of state (EoS) and the collision term [including the Pauli blocking and the medium-modified nucleon-nucleon elastic cross section (NNECS)] The momentum modifications of both, the mean-field potentials and the density dependent NNECS, are found to affect the collectivity of heavy-ion collisions At INDRA energies ($\ensuremath{\leqslant}$$150$ MeV/nucleon) the dynamic transport with a soft EoS with momentum dependence and with the momentum-modified density-dependent NNECS describes the directed flow exhibited by hydrogen isotopes ($Z=1$) emitted at midrapidity fairly well

Nonequilibrium dynamics in heavy-ion collisions at low energies available at the GSI Schwerionen Synchrotron

The influence of the density-dependent symmetry energy on the balance energy (Ebal) of directed flow from heavy ion collisions (HICs) at incident energies covered by INDRA and MSU experiments is studied, using the updated version of the ultrarelativistic quantum molecular dynamics (UrQMD) model, especially adapted to low-energy heavy ion collisions (HICs). Four mass-symmetric reactions with total mass numbers between 192 and 394 are chosen for investigating the influence of the symmetry energy on the system-mass dependence of Ebal. The results show that the uncertainty in the density dependence of the symmetry potential causes changes of Ebal of the order of several MeV, depending on the type of particle considered. The Ebal of neutrons from HICs is particularly sensitive to the density dependence of the symmetry potential energy, while the system-mass dependence of Ebal of Z = 1 particles is not.

Influence of the symmetry energy on the balance energy of the directed flow

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Nonequilibrium dynamics in heavy-ion collisions at low energies available at the GSI Schwerionen Synchrotron

Influence of the symmetry energy on the balance energy of the directed flow