Directed and elliptic flows of neutrons and light charged particles were measured for the reaction 197 Au+ 197 Au 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, 2 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 γ = 0.72 ± 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.

Neutron-proton elliptic flow difference and ratio have been shown to be promising observables in the attempt to constrain the density dependence of the symmetry energy above the saturation point from heavy-ion collision data. Their dependence on model parameters like microscopic nucleon-nucleon cross-sections, compressibility of nuclear matter, optical potential, and symmetry energy parametrization is thoroughly studied. By using a parametrization of the symmetry energy derived from the momentum dependent Gogny force in conjunction with the T\'{u}bingen QMD model and comparing with the experimental FOPI/LAND data for 197Au+197Au collisions at 400 MeV/nucleon, a moderately stiff, x=-1.35 +/- 1.25, symmetry energy is extracted, a result that agrees with that of a similar study that employed the UrQMD transport model and a momentum independent power-law parametrization of the symmetry energy. This contrasts with diverging results extracted from the FOPI $\pi^{-}/\pi^{+}$ ratio available in the literature

The charged pion multiplicity ratio in intermediate energy central heavy-ion collisions has been proposed as a suitable observable to constrain the high density dependence of the isovector part of the equation of state. A comparison of various transport model predictions with existing experimental data has led, however, to contradictory results. Using an upgraded version of the Tübingen QMD transport model, which allows the conservation of energy at a local or global level by accounting for the potential energy of hadrons in two-body collisions and leading thus to particle production threshold shifts, we demonstrate that compatible constraints for the symmetry energy stiffness can be extracted from pion multiplicity and elliptic flow observables. However, pion multiplicities and ratios are proven to be highly sensitive to the yet unknown isovector part of the in-medium ∆(1232) potential which hinders, at present, the extraction of meaningful information on the high density dependence of the symmetry energy. A solution to this problem together with the inclusion of contributions presently neglected, such as in-medium pion potentials and retardation effects, are needed for a final verdict on this topic.

We employ an isospin dependent version of the QMD transport model to study the influence of the isospin dependent part of the nuclear matter equation of state and in-medium nucleon-nucleon cross-sections on the dynamics of heavy-ion collisions at intermediate energies. We find that the extraction of useful information on the isospin-dependent part of the equation of state of nuclear matter from proton or neutron elliptic flows is obstructed by their sensitivity to model parameters and in-medium values of nucleon-nucleon crosssections. Opposite to that, neutron-proton elliptic flow difference shows little dependence on those variables while its dependence on the isospin asymmetric EoS is enhanced, making it more suitable for a model independent constraining of the high-density behaviour of asy-EoS. Comparison with existing experimental FOPI-LAND neutron-hydrogen data can be used to set an upper limit to the softness of asy-EoS. Successful constraining of the asy-EoS via neutron-proton elliptic flow difference will require experimental data of higher accuracy than presently available.

A QMD transport model that employs a modified momentum dependent interaction (MDI2) potential, supplemented by a phase-space coalescence model fitted to FOPI experimental multiplicities of free nucleons and light clusters is used to study the density dependence of the symmetry energy above the saturation point by a comparison with experimental elliptic flow ratios measured by the FOPI-LAND and ASYEOS collaborations in 197 Au+ 197 Au collisions at 400 MeV/nucleon impact energy. A previous calculation using the same model has proven that neutron-to-proton and neutron-to-charged particles elliptic flow ratios probe on average different densities allowing in principle the extraction of both the slope L and curvature Ksym parameters of the symmetry energy. To make use of this result a Gogny interaction inspired potential is modified by the addition of a density-dependent, momentum-independent term, while enforcing a close description of the empirical nucleon optical potential, allowing independent modifications of L and Ksym. Comparing theoretical predictions with experimental data for neutron-to-proton and neutron-tocharged particles elliptic flow ratios the following constraint is extracted: L=85±22(exp)±20(th)±12(sys) MeV and Ksym=96±315(exp)±170(th)±166(sys) MeV. Theoretical errors include effects due to uncertainties in the isoscalar part of the equation of state, value of the isovector neutron-proton effective mass splitting, in-medium effects on the elastic nucleon-nucleon cross-sections, Pauli blocking algorithm variants and scenario considered for the conservation of the total energy of the system. Systematical uncertainties are generated by the inability of the transport model to reproduce experimental light-cluster-to-proton multiplicity ratios. A value for L free of systematical theoretical uncertainties can be extracted from the neutron-to-proton elliptic flow ratio alone: L=84±30(exp)±19(th) MeV. It is demonstrated that elliptic flow ratios reach a maximum sensitivity on the Ksym parameter in heavy-ion collisions of about 250 MeV/nucleon impact energy, allowing a reduction of its experimental component of uncertainty to about 150 MeV. PACS. 21.65.Mn Nuclear matter equations of state -21.65.Cd Nuclear matter asymmetric matter -25.75.Ld Collective flow, relativistic collisions -25.70.-z Heavy-ion nuclear reactions, low and intermediate energy

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The charged pion multiplicity ratio in intermediate energy heavy-ion collisions, a probe of the density dependence of symmetry energy above the saturation point, has been proven in a previous study to be extremely sensitive to the strength of the isovector ∆(1232) potential in nuclear matter. As there is no knowledge, either from theory or experiment, about the magnitude of this quantity, the extraction of constraints on the slope of the symmetry energy at saturation by using exclusively the mentioned observable is hindered at present. It is shown that, by including the ratio of average pT of charged pions pin the list of fitted observables, the noted problem can be circumvented. A realistic description of this observable requires accounting for the interaction of pions with the dense nuclear matter environment by the incorporation of the so called S-wave and P -wave pion optical potentials. This is performed within the framework of a quantum molecular dynamics transport model that enforces the conservation of the total energy of the system. It is shown that constraints on the slope of the symmetry energy at saturation density and the strength of the ∆(1232) potential can be simultaneously extracted. A symmetry energy with a value of the slope parameter L > 50 MeV is favored, at 1σ confidence level, from a comparison with published FOPI experimental data. A precise constraint will require experimental data more accurate than presently available, particularly for the charged pion multiplicity ratio, and better knowledge of the density and momentum dependence of the pion potential for the whole range of these two variables probed in intermediate energy heavy-ion collisions.

The in-medium spectral functions of ρ and ω mesons and the broadening of nucleon resonances at finite baryon density are calculated self-consistently by combining a resonance dominance model for the vector meson production with an extended vector meson dominance model. The influence of the in-medium modifications of the vector meson properties on the dilepton spectrum in heavy-ion collisions is investigated. The dilepton spectrum is generated for the C+C reaction at 2.0A GeV and compared with recent HADES Collaboration data. The collision dynamics is then described by the Tübingen relativistic quantum molecular dynamics transport model. We find that an iterative calculation of the vector meson spectral functions that takes into account the broadening of the nucleon resonances due to their increased in-medium decay branchings is convergent and provides a reasonable description of the experimental data in the mass region 0.45 ≤ M ≤ 0.75 GeV. On the other side, the theoretical calculations slightly underestimate the region m π ≤ M ≤ 0.4 GeV. Popular in-medium scenarios such as a schematic collisional broadening and dropping vector mesons masses are discussed as well.