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- Current status of quark gluon plasma signals (2001)
- Compelling evidence for the creation of a new form of matter has been claimed to be found in Pb+Pb collisions at SPS. We discuss the uniqueness of often proposed experimental signatures for quark matter formation in relativistic heavy ion collisions. It is demonstrated that so far none of the proposed signals like J/psi meson production/suppression, strangeness enhancement, dileptons, and directed flow unambigiously show that a phase of deconfined matter has been formed in SPS Pb+Pb collisions. We emphasize the need for systematic future measurements to search for simultaneous irregularities in the excitation functions of several observables in order to come close to pinning the properties of hot, dense QCD matter from data.

- Equilibrium and non-equilibrium effects in relativistic heavy ion collisions (1999)
- The hypothesis of local equilibrium (LE) in relativistic heavy ion collisions at energies from AGS to RHIC is checked in the microscopic transport model. We find that kinetic, thermal, and chemical equilibration of the expanding hadronic matter is nearly reached in central collisions at AGS energy for t >_ fm/c in a central cell. At these times the equation of state may be approximated by a simple dependence P ~= (0.12-0.15) epsilon. Increasing deviations of the yields and the energy spectra of hadrons from statistical model values are observed for increasing bombarding energies. The origin of these deviations is traced to the irreversible multiparticle decays of strings and many-body (N >_ 3) decays of resonances. The violations of LE indicate that the matter in the cell reaches a steady state instead of idealized equilibrium. The entropy density in the cell is only about 6% smaller than that of the equilibrium state.

- Microscopic calculations of stopping and flow from 160AMeV to 160AGeV (1996)
- The behavior of hadronic matter at high baryon densities is studied within Ultrarelativistic Quantum Molecular Dynamics (URQMD). Baryonic stopping is observed for Au+Au collisions from SIS up to SPS energies. The excitation function of flow shows strong sensitivities to the underlying equation of state (EOS), allowing for systematic studies of the EOS. Effects of a density dependent pole of the rho-meson propagator on dilepton spectra are studied for different systems and centralities at CERN energies.

- Chemical freeze-out parameters at RHIC from microscopic model calculations (2001)
- The relaxation of hot nuclear matter to an equilibrated state in the central zone of heavy-ion collisions at energies from AGS to RHIC is studied within the microscopic UrQMD model. It is found that the system reaches the (quasi)equilibrium stage for the period of 10-15 fm/c. Within this time the matter in the cell expands nearly isentropically with the entropy to baryon ratio S/A = 150 - 170. Thermodynamic characteristics of the system at AGS and at SPS energies at the endpoints of this stage are very close to the parameters of chemical and thermal freeze-out extracted from the thermal fit to experimental data. Predictions are made for the full RHIC energy square root s = 200$ AGeV. The formation of a resonance-rich state at RHIC energies is discussed.

- Local equilibrium in heavy ion collisions. Microscopic model versus statistical model analysis (1999)
- The assumption of local equilibrium in relativistic heavy ion collisions at energies from 10.7 AGeV (AGS) up to 160 AGeV (SPS) is checked in the microscopic transport model. Dynamical calculations performed for a central cell in the reaction are compared to the predictions of the thermal statistical model. We find that kinetic, thermal and chemical equilibration of the expanding hadronic matter are nearly approached late in central collisions at AGS energy for t >= 10 fm/c in a central cell. At these times the equation of state may be approximated by a simple dependence P ~= (0.12-0.15) epsilon. Increasing deviations of the yields and the energy spectra of hadrons from statistical model values are observed for increasing energy, 40 AGeV and 160 AGeV. These violations of local equilibrium indicate that a fully equilibrated state is not reached, not even in the central cell of heavy ion collisions at energies above 10 AGeV. The origin of these findings is traced to the multiparticle decays of strings and many-body decays of resonances.

- Extracting the equation of state from a microscopic non-equilibrium model (1996)
- We study the thermodynamic properties of infinite nuclear matter with the Ultrarelativistic Quantum Molecular Dynamics (URQMD), a semiclassical transport model, running in a box with periodic boundary conditions. It appears that the energy density rises faster than T4 at high temperatures of T approx. 200 - 300 MeV. This indicates an increase in the number of degrees of freedom. Moreover, We have calculated direct photon production in Pb+Pb collisions at 160 GeV/u within this model. The direct photon slope from the microscopic calculation equals that from a hydrodynamical calculation without a phase transition in the equation of state of the photon source.

- Collective flow in heavy ion reactions and the properties of excited nuclear matter (1996)
- Quantum Molecular Dynamics (QMD) calculations of central collisions between heavy nuclei are used to study fragment production and the creation of collective flow. It is shown that the final phase space distributions are compatible with the expectations from a thermally equilibrated source, which in addition exhibits a collective transverse expansion. However, the microscopic analyses of the transient states in the intermediate reaction stages show that the event shapes are more complex and that equilibrium is reached only in very special cases but not in event samples which cover a wide range of impact parameters as it is the case in experiments. The basic features of a new molecular dynamics model (UQMD) for heavy ion collisions from the Fermi energy regime up to the highest presently available energies are outlined.

- Signatures of dense hadronic matter in ultrarelativistic heavy ion reactions (1996)
- The behavior of hadronic matter at high baryon densities is studied within Ultrarelativistic Quantum Molecular Dynamics (URQMD). Baryonic stopping is observed for Au+Au collisions from SIS up to SPS energies. The excitation function of flow shows strong sensitivities to the underlying equation of state (EOS), allowing for systematic studies of the EOS. Dilepton spectra are calculated with and without shifting the rho pole. Except for S+Au collisions our calculations reproduce the CERES data.

- Reaction dynamics in Pb+Pb at the CERN/SPS: from partonic degrees of freedom to freeze-out (1998)
- We analyze the reaction dynamics of central Pb+Pb collisions at 160 GeV/nucleon. First we estimate the energy density pile-up at mid-rapidity and calculate its excitation function: The energy density is decomposed into hadronic and partonic contributions. A detailed analysis of the collision dynamics in the framework of a microscopic transport model shows the importance of partonic degrees of freedom and rescattering of leading (di)quarks in the early phase of the reaction for E >= 30 GeV/nucleon. The energy density reaches up to 4 GeV/fm 3, 95% of which are contained in partonic degrees of freedom. It is shown that cells of hadronic matter, after the early reaction phase, can be viewed as nearly chemically equilibrated. This matter never exceeds energy densities of 0.4 GeV/fm 3, i.e. a density above which the notion of separated hadrons loses its meaning. The final reaction stage is analyzed in terms of hadron ratios, freeze-out distributions and a source analysis for final state pions.

- Strangeness dynamics in relativistic nucleus-nucleus collision (2003)
- We investigate hadron production as well as transverse hadron spectra in nucleus-nucleus collisions from 2 A.GeV to 21.3 A.TeV within two independent transport approaches (UrQMD and HSD) that are based on quark, diquark, string and hadronic degrees of freedom. The comparison to experimental data demonstrates that both approaches agree quite well with each other and with the experimental data on hadron production. The enhancement of pion production in central Au+Au (Pb+Pb) collisions relative to scaled pp collisions (the 'kink') is well described by both approaches without involving any phase transition. However, the maximum in the K+/Pi+ ratio at 20 to 30 A.GeV (the 'horn') is missed by ~ 40%. A comparison to the transverse mass spectra from pp and C+C (or Si+Si) reactions shows the reliability of the transport models for light systems. For central Au+Au (Pb+Pb) collisions at bombarding energies above ~ 5 A.GeV, however, the measured K +/- m-theta-spectra have a larger inverse slope parameter than expected from the calculations. The approximately constant slope of K+/-spectra at SPS (the 'step') is not reproduced either. Thus the pressure generated by hadronic interactions in the transport models above ~ 5 A.GeV is lower than observed in the experimental data. This finding suggests that the additional pressure - as expected from lattice QCD calculations at finite quark chemical potential and temperature - might be generated by strong interactions in the early pre-hadronic/partonic phase of central Au+Au (Pb+Pb) collisions.