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Directed and elliptic flow (1999)

Sven Soff Steffen A. Bass Marcus Bleicher Horst Stöcker Walter Greiner

We compare microscopic transport model calculations to recent data on the directed and elliptic flow of various hadrons in 2 - 10 A GeV Au+Au and Pb (158 A GeV) Pb collisions. For the Au+Au excitation function a transition from the squeeze-out to an in-plane enhanced emission is consistently described with mean field potentials corresponding to one incompressibility. For the Pb (158 A GeV) Pb system the elliptic flow prefers in-plane emission both for protons and pions, the directed flow of protons is opposite to that of the pions, which exhibit anti-flow. Strong directed transverse flow is present for protons and Lambdas in Au (6 A GeV) Au collisions as well. Both for the SPS and the AGS energies the agreement between data and calculations is remarkable.

Microscopic analysis of thermodynamic parameters from 160 MeV/n - 160 GeV/n (1997)

Marcus Bleicher Steffen A. Bass Mohamed Belkacem Jörg Brachmann Mathias Brandstetter Christoph Ernst Lars Gerland Jens Konopka Sven Soff Christian Spieles Henning Weber Horst Stöcker Walter Greiner

Microscopic 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 reaction stages of highest density and during the expansion show that the system does not reach global equilibrium. Even if a considerable amount of equilibration is assumed, the connection of the measurable final state to the macroscopic parameters, e.g. the temperature, of the transient ''equilibrium'' state remains ambiguous.

Reaction dynamics in Pb+Pb at the CERN/SPS: from partonic degrees of freedom to freeze-out (1998)

Steffen A. Bass Henning Weber Christoph Ernst Marcus Bleicher Mohamed Belkacem Larissa V. Bravina Sven Soff Horst Stöcker Walter Greiner Christian Spieles

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.

Local thermal and chemical equilibration and the equation of state in relativistic heavy ion collisions (1998)

Larissa V. Bravina Mathias Brandstetter Mark I. Gorenstein Eugene E. Zabrodin Mohamed Belkacem Marcus Bleicher Steffen A. Bass Christoph Ernst M. Hofmann Sven Soff Horst Stöcker Walter Greiner

Thermodynamical variables and their time evolution are studied for central relativistic heavy ion collisions from 10.7 to 160 AGeV in the microscopic Ultrarelativistic Quantum Molecular Dynamics model (UrQMD). The UrQMD model exhibits drastic deviations from equilibrium during the early high density phase of the collision. Local thermal and chemical equilibration of the hadronic matter seems to be established only at later stages of the quasi-isentropic expansion in the central reaction cell with volume 125 fm 3. Baryon energy spectra in this cell are reproduced by Boltzmann distributions at all collision energies for t > 10 fm/c with a unique rapidly dropping temperature. At these times the equation of state has a simple form: P = (0.12 - 0.15) Epsilon. At SPS energies the strong deviation from chemical equilibrium is found for mesons, especially for pions, even at the late stage of the reaction. The final enhancement of pions is supported by experimental data.

Equation of state, spectra and composition of hot and dense infinite hadronic matter in a microscopic transport model (1998)

Mohamed Belkacem Mathias Brandstetter Steffen A. Bass Marcus Bleicher Larissa V. Bravina Mark I. Gorenstein Jens Konopka Ludwig Neise Christian Spieles Sven Soff Henning Weber Horst Stöcker Walter Greiner

Equilibrium properties of infinite relativistic hadron matter are investigated using the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) model. The simulations are performed in a box with periodic boundary conditions. Equilibration times depend critically on energy and baryon densities. Energy spectra of various hadronic species are shown to be isotropic and consistent with a single temperature in equilibrium. The variation of energy density versus temperature shows a Hagedorn-like behavior with a limiting temperature of 130 +/- 10 MeV. Comparison of abundances of different particle species to ideal hadron gas model predictions show good agreement only if detailed balance is implemented for all channels. At low energy densities, high mass resonances are not relevant; however, their importance raises with increasing energy density. The relevance of these different conceptual frameworks for any interpretation of experimental data is questioned.

Local thermodynamical equilibrium and the equation of state of hot, dense matter created in Au+Au collisions at AGS (1998)

Larissa V. Bravina Mark I. Gorenstein Mohamed Belkacem Steffen A. Bass Marcus Bleicher Mathias Brandstetter M. Hofmann Sven Soff Christian Spieles Henning Weber Horst Stöcker Walter Greiner

Local kinetic and chemical equilibration is studied for Au+Au collisions at 10.7 AGeV in the microscopic Ultrarelativistic Quantum Molecular Dynamics model (UrQMD). The UrQMD model exhibits dramatic deviations from equilibrium during the high density phase of the collision. Thermal and chemical equilibration of the hadronic matter seems to be established in the later stages during a quasiisentropic expansion, observed in the central reaction cell with volume 125 fm3. For t > 10 fm/c the hadron energy spectra in the cell are nicely reproduced by Boltzmann distributions with a common rapidly dropping temperature. Hadron yields change drastically and at the late expansion stage follow closely those of an ideal gas statistical model. The equation of state seems to be simple at late times: P = 0.12 Epsilon. The time evolution of other thermodynamical variables in the cell is also presented.

Microscopic models for ultrarelativistic heavy ion collisions (1998)

Steffen A. Bass Mohamed Belkacem Marcus Bleicher Mathias Brandstetter Larissa V. Bravina Christoph Ernst Lars Gerland M. Hofmann S. Hofmann Jens Konopka Guangjun Mao Ludwig Neise Sven Soff Christian Spieles Henning Weber L. A. Winckelmann Horst Stöcker Walter Greiner Christoph Hartnack Jörg Aichelin N. Amelin

In this paper, the concepts of microscopic transport theory are introduced and the features and shortcomings of the most commonly used ansatzes are discussed. In particular, the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) transport model is described in great detail. Based on the same principles as QMD and RQMD, it incorporates a vastly extended collision term with full baryon-antibaryon symmetry, 55 baryon and 32 meson species. Isospin is explicitly treated for all hadrons. The range of applicability stretches from E lab < 100$ MeV/nucleon up to E lab> 200$ GeV/nucleon, allowing for a consistent calculation of excitation functions from the intermediate energy domain up to ultrarelativistic energies. The main physics topics under discussion are stopping, particle production and collective flow.

Are we close to the QGP? - Hadrochemical vs. microscopic analysis of particle production in ultrarelativistic heavy ion collisions (1997)

Steffen A. Bass Mohamed Belkacem Mathias Brandstetter Marcus Bleicher Lars Gerland Jens Konopka Ludwig Neise Christian Spieles Sven Soff Henning Weber Horst Stöcker Walter Greiner

Ratios of hadronic abundances are analyzed for pp and nucleus-nucleus collisions at sqrt(s)=20 GeV using the microscopic transport model UrQMD. Secondary interactions significantly change the primordial hadronic cocktail of the system. A comparison to data shows a strong dependence on rapidity. Without assuming thermal and chemical equilibrium, predicted hadron yields and ratios agree with many of the data, the few observed discrepancies are discussed.

The disappearance of flow (1995)

Sven Soff Steffen A. Bass Christoph Hartnack Horst Stöcker Walter Greiner

We investigate the disappearance of collective flow in the reaction plane in heavy-ion collisions within a microscopic model (QMD). A systematic study of the impact parameter dependence is performed for the system Ca+Ca. The balance energy strongly increases with impact parameter. Momentum dependent interactions reduce the balance energies for intermediate impact parameters b ~ 4.5 fm. Dynamical negative flow is not visible in the laboratory frame but does exist in the contact frame for the heavy system Au+Au. For semi-peripheral collisions of Ca+Ca with b ~ 6.5 fm a new two-component flow is discussed. Azimuthal distributions exhibit strong collectiv flow signals, even at the balance energy.

Antiflow of nucleons at the softest point of the EoS (1999)

Jörg Brachmann Sven Soff Adrian Dumitru Horst Stöcker Joachim A. Maruhn Walter Greiner Dirk-Hermann Rischke

Report-no: UFTP-492/1999 Journal-ref: Phys.Rev. C61 (2000) 024909 We investigate flow in semi-peripheral nuclear collisions at AGS and SPS energies within macroscopic as well as microscopic transport models. The hot and dense zone assumes the shape of an ellipsoid which is tilted by an angle Theta with respect to the beam axis. If matter is close to the softest point of the equation of state, this ellipsoid expands predominantly orthogonal to the direction given by Theta. This antiflow component is responsible for the previously predicted reduction of the directed transverse momentum around the softest point of the equation of state.

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