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The disappearance of flow
(1995)
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.
We make predictions for the kaon interferometry measurements in Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC). A first order phase transition from a thermalized Quark-Gluon-Plasma (QGP) to a gas of hadrons is assumed for the transport calculations. The fraction of kaons that are directly emitted from the phase boundary is considerably enhanced at large transverse momenta K T ~ 1 GeV/c. In this kinematic region, the sensitivity of the R out/R side ratio to the QGP-properties is enlarged. Here, the results of the 1-dimensional correlation analysis are presented. The extracted interferometry radii, depending on K-Theta, are not unusually large and are strongly affected by momentum resolution effects.
We calculate the kaon HBT radius parameters for high energy heavy ion collisions, assuming a first order phase transition from a thermalized Quark-Gluon-Plasma to a gas of hadrons. At high transverse momenta K_T ~ 1 GeV/c direct emission from the phase boundary becomes important, the emission duration signal, i.e., the R_out/R_side ratio, and its sensitivity to T_c (and thus to the latent heat of the phase transition) are enlarged. Moreover, the QGP+hadronic rescattering transport model calculations do not yield unusual large radii (R_i<9fm). Finite momentum resolution effects have a strong impact on the extracted HBT parameters (R_i and lambda) as well as on the ratio R_out/R_side.
We present calculations of two-pion and two-kaon correlation functions in relativistic heavy ion collisions from a relativistic transport model that includes explicitly a first-order phase transition from a thermalized quark-gluon plasma to a hadron gas. We compare the obtained correlation radii with recent data from RHIC. The predicted R_side radii agree with data while the R_out and R_long radii are overestimated. We also address the impact of in-medium modifications, for example, a broadening of the rho-meson, on the correlation radii. In particular, the longitudinal correlation radius R_long is reduced, improving the comparison to data.
We calculate the Gaussian radius parameters of the pion-emitting source in high energy heavy ion collisions, assuming a first order phase transition from a thermalized Quark-Gluon-Plasma (QGP) to a gas of hadrons. Such a model leads to a very long-lived dissipative hadronic rescattering phase which dominates the properties of the two-pion correlation functions. The radii are found to depend only weakly on the thermalization time tau i, the critical temperature T c (and thus the latent heat), and the specific entropy of the QGP. The dissipative hadronic stage enforces large variations of the pion emission times around the mean. Therefore, the model calculations suggest a rapid increase of R out/R side as a function of K T if a thermalized QGP were formed.
Directed and elliptic flow
(1999)
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.
The centrality dependence of (multi-)strange hadron abundances is studied for Pb(158 AGeV)Pb reactions and compared to p(158 GeV)Pb collisions. The microscopic transport model UrQMD is used for this analysis. The predicted Lambda/pi-, Xi-/pi- and Omega-/pi- ratios are enhanced due to rescattering in central Pb-Pb collisions as compared to peripheral Pb-Pb or p-Pb collisions. A reduction of the constituent quark masses to the current quark masses m_s \sim 230 MeV, m_q \sim 10 MeV, as motivated by chiral symmetry restoration, enhances the hyperon yields to the experimentally observed high values. Similar results are obtained by an ad hoc overall increase of the color electric field strength (effective string tension of kappa=3 GeV/fm). The enhancement depends strongly on the kinematical cuts. The maximum enhancement is predicted around midrapidity. For Lambda's, strangeness suppression is predicted at projectile/target rapidity. For Omega's, the predicted enhancement can be as large as one order of magnitude. Comparisons of Pb-Pb data to proton induced asymmetric (p-A) collisions are hampered due to the predicted strong asymmetry in the various rapidity distributions of the different (strange) particle species. In p-Pb collisions, strangeness is locally (in rapidity) not conserved. The present comparison to the data of the WA97 and NA49 collaborations clearly supports the suggestion that conventional (free) hadronic scenarios are unable to describe the observed high (anti-)hyperon yields in central collisions. The doubling of the strangeness to nonstrange suppression factor, gamma_s \approx 0.65, might be interpreted as a signal of a phase of nearly massless particles.
Abschließend sollen hier die wichtigsten, neuen Ergebnisse herausgestellt und ein Ausblick auf mögliche zukünftige Studien gegeben werden. In dieser Arbeit wurden vorwiegend Schwerionenkollisionen bei Einschußenergien zwischen ungefähr 40 MeV/Nukleon und 400 MeV/Nukleon mit dem Quantenmolekulardynamik-Modell untersucht. Ein Schwerpunkt war hierbei die Beschreibung der Umkehr des kollektiven, transversalen Seitwärtsflusses in der Reaktionsebene. Der negative Seitwärtsfluß, der bei niedrigen Energien der Größenordnung kleiner als 100 MeV/Nukleon durch die attraktiven Wechselwirkungen verursacht wird, verschwindet bei Steigerung der Einschußenergie bei der Balance-Energie E-bal. einsetzt. Oberhalb dieser dominieren die repulsiven Wechselwirkungen, so daß positiver transversaler Fluß einsetzt. Sowohl die negativen Flußwinkel als auch der Übergang hin zu positiven Flußwinkeln konnte fur eine große Anzahl verschiedener Energien und Stoßparameter mit unterschiedlichen Zustandsgleichungen für die Systeme 40-20-Ca + 40-20-Ca und 197-79 Au + 197-79 Au mit dem Quantenmolekulardynamik-Modell beschrieben werden. Ziel muß es bleiben, die verschiedenen, grundlegenden physikalischenWechselwirkungen eindeutig und unabhängig voneinander zu bestimmen. Ein erfolgversprechender Weg sind die hier vorgestellten Methoden und die Hinweise zur ad quaten Interpretation experimenteller Ergebnisse. Die Abhängigkeit der Balance-Energien von der Masse des betrachteten Systems ist sehr sensitiv auf den Nukleon-Nukleon Wirkungsquerschnitt im Medium. Hier wurde systematisch gezeigt, daß die Balance-Energien stark vom Stoßparameter abhängen. Die Zunahme der Balance-Energie mit dem Stoßparameter ist ungefähr linear. Für das System Ca+Ca kann sich die Balance-Energie beim Übergang von zentraleren zu mittleren Stoßparametern mehr als verdoppeln. Daher ist für die Interpretation der gemessenen Balance-Energien in bezug auf eine Modifikation des nukleo- nischen Wirkungsquerschnitts im Medium oder der Zustandsgleichung eine genaue Kenntnis des Stoßparameters von größter Wichtigkeit. Vorläufige experimentelle Analysen scheinen die vorhergesagte Stoßparameterabhängigkeit sehr gut zu bestätigen [Wes 95]. Weiterhin hat sich herauskristallisiert, daß bei der Berücksichtigung impulsabhängiger Wechselwirkungen die Balance-Energien bei größeren Stoßparametern signifikant kleiner sind als für den Fall der Nichtberücksichtung. Daher konnten experimentelle Bestimmungen der Balance- Energien bei größeren Stoßparametern signifikante Hinweise auf die tatsächliche Bedeutung der impulsabhängigen Wechselwirkungen in diesem Energiebereich geben. Es wurde gezeigt, daß für schwere Systeme wie Au+Au die langreichweitige internukleare Coulomb-Wechselwirkung vor dem Kontakt der Kerne im Energiebereich der Balance-Energien nicht vernachlässigt werden darf. Die hervorgerufene Repulsion bewirkt eine Drehung des Systems. Während in diesem gedrehten System dynamischer negativer Fluß beobachtbar ist, ist er es nicht im Laborsystem. Die im gedrehten Kontaktbezugssystem bestimmten Balance- Energien fur Au+Au sind erwartungsgemäß kleiner als für Ca+Ca und nehmen mit wachsendem Stoßparameter zu. Ein neuartiger Zwei-Komponenten-Fluß konnte in semiperipheren Kollisionen von Ca+Ca be- schrieben und analysiert werden. Dabei wird in einem Ereignis in verschiedenen Rapiditätsbereichen gleichzeitig positiver und negativer transversaler Fluß möglich. Die wenig komprimierte Spektatorenmaterie, die vermehrt aus schwereren Fragmenten besteht, zeigt negativen Fluß bei großen Rapiditäten, wohingegen dieKompressionszone in Form von einzelnen Nukleonen positiven transversalen Fluß zeigt. Aufgrund der großen Sensitivität gegenüber den Systemparametern und der Zustandsgleichung lohnt es sich, diesen Effekt experimentell zu untersuchen. Beim Studium azimuthaler Verteilungen wurde deutlich, daß auch in den Balance-Punkten noch kollektiver Fluß in Form von azimuthaler Asymmetrie vorliegt. Im Gegensatz zur bekannten hochenergetischen Bevorzugung der Emissionswinkel senkrecht zur Reaktionsebene für Teilchen aus der Wechselwirkungszone wurde hier die bei kleineren Energien preferentielle Emission in die Reaktionsebene aufgezeigt. Diese nimmt mit der Teilchenmasse und dem Stoßparameter zu. Das systematische Studium der Anregungsfunktion dieser azimuthalen Asymmetrie könnte durch die Übergangsenergien, die durch den Wechsel von der preferentiellen Emission in die Reaktionsebene zu der Bevorzugung der Winkel senkrecht zur Reaktionsebene definiert sind, wertvolle, ergänzende Information zu den Balance-Energien liefern.
Invited talk at the 7th International Conference on Strangeness in Quark Matter, SQM 2003, Atlantic Beach, North Carolina, USA, 12-17 Mar, 2003. 11 pages, 12 figures. Journal-ref: J.Phys. G30 (2004) S139-S150. We review recent developments in the field of microscopic transport model calculations for ultrarelativistic heavy ion collisions. In particular, we focus on the strangeness production, for example, the phi-meson and its role as a messenger of the early phase of the system evolution. Moreover, we discuss the important e ects of the (soft) field properties on the multiparticle system. We outline some current problems of the models as well as possible solutions to them
Invited talk at the XXXIII International Symposium on Multiparticle Dynamics, Krakow, Poland, 5-11 Sept, 2003. 5 pages, 1 figure Journal-ref: Acta Phys.Polon. B35 (2004) 23-28. We review the recent developments on microscopic transport calculations for two-particle correlations at low relative momenta in ultrarelativistic heavy ion collisions at RHIC.
Invited talk at the International Workshop XXX on Gross Properties of Nuclei and Nuclear Excitations - Ultrarelativistic Heavy-Ion Collisions, Jan. 13-19, 2002, Hirschegg, Austria. Report-no: LBNL-49674. We discuss predictions for the pion and kaon interferometry measurements in relativistic heavy ion collisions at SPS and RHIC energies. In particular, we confront relativistic transport model calculations that include explicitly a first-order phase transition from a thermalized quark-gluon plasma to a hadron gas with recent data from the RHIC experiments. We critically examine the "HBT-puzzle" both from the theoretical as well as from the experimental point of view. Alternative scenarios are briefly explained.
Noneequilibrium models (three-fluid hydrodynamics and UrQMD) use to discuss the uniqueness of often proposed experimental signatures for quark matter formation in relativistic heavy ion collisions. It is demonstrated that these two models - although they do treat the most interesting early phase of the collisions quite differently(thermalizing QGP vs. coherent color fields with virtual particles) - both yields a reasonable agreement with a large variety of the available heavy ion data.
Nonequilibrium models (three-fluid hydrodynamics, UrQMD, and quark molecular dynamics) are used to discuss the uniqueness of often proposed experimental signatures for quark matter formation in relativistic heavy ion collisions from the SPS via RHIC to LHC. It is demonstrated that these models - although they do treat the most interesting early phase of the collisions quite differently (thermalizing QGP vs. coherent color fields with virtual particles) -- all yield a reasonable agreement with a large variety of the available heavy ion data. Hadron/hyperon yields, including J/Psi meson production/suppression, strange matter formation, dileptons, and directed flow (bounce-off and squeeze-out) are investigated. Observations of interesting phenomena in dense matter are reported. However, 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. The role of future experiments with the STAR and ALICE detectors is pointed out.
Probing the density dependence of the symmetry potential in intermediate energy heavy ion collisions
(2005)
Based on the ultrarelativistic quantum molecular dynamics (UrQMD) model, the effects of the density-dependent symmetry potential for baryons and of the Coulomb potential for produced mesons are investigated for neutron-rich heavy ion collisions at intermediate energies. The calculated results of the Delta-/Delta++ and pi -/pi + production ratios show a clear beam-energy dependence on the density-dependent symmetry potential, which is stronger for the pi -/pi + ratio close to the pion production threshold. The Coulomb potential of the mesons changes the transverse momentum distribution of the pi -/pi + ratio significantly, though it alters only slightly the pi- and pi+ total yields. The pi- yields, especially at midrapidity or at low transverse momenta and the p-/pi+ ratios at low transverse momenta, are shown to be sensitive probes of the density-dependent symmetry potential in dense nuclear matter. The effect of the density-dependent symmetry potential on the production of both, K0 and K+ mesons, is also investigated.
The influence of the isospin-independent, isospin- and momentum-dependent equation of state (EoS), as well as the Coulomb interaction on the pion production in intermediate energy heavy ion collisions (HICs) is studied for both isospin-symmetric and neutron-rich systems. The Coulomb interaction plays an important role in the reaction dynamics, and strongly influences the rapidity and transverse momentum distributions of charged pions. It even leads to the pi- pi+ ratio deviating slightly from unity for isospin-symmetric systems. The Coulomb interaction between mesons and baryons is also crucial for reproducing the proper pion flow since it changes the behavior of the directed and the elliptic flow components of pions visibly. The EoS can be better investigated in neutron-rich system if multiple probes are measured simultaneously. For example, the rapidity and the transverse momentum distributions of the charged pions, the pi- pi+ ratio, the various pion flow components, as well as the difference of pi+-pi- flows. A new sensitive observable is proposed to probe the symmetry potential energy at high densities, namely the transverse momentum distribution of the elliptic flow difference [Delta v_2^pi+ - pi-(p_t rm c.m.].
We investigate the sensitivity of several observables to the density dependence of the symmetry potential within the microscopic transport model UrQMD (ultrarelativistic quantum molecular dynamics model). The same systems are used to probe the symmetry potential at both low and high densities. The influence of the symmetry potentials on the yields of pi-, pi+, the pi-/pi+ ratio, the n/p ratio of free nucleons and the t/3He ratio are studied for neutron-rich heavy ion collisions (208Pb+208Pb, 132Sn+124Sn, 96Zr+96Zr) at E_b=0.4A GeV. We find that these multiple probes provides comprehensive information on the density dependence of the symmetry potential.
Several observables of unbound nucleons which are to some extent sensitive to the medium modifications of nucleon-nucleon elastic cross sections in neutron-rich intermediate energy heavy ion collisions are investigated. The splitting effect of neutron and proton effective masses on cross sections is discussed. It is found that the transverse flow as a function of rapidity, the Q_zz as a function of momentum, and the ratio of halfwidths of the transverse to that of longitudinal rapidity distribution R_t/l are very sensitive to the medium modifications of the cross sections. The transverse momentum distribution of correlation functions of two-nucleons does not yield information on the in-medium cross section.
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.
Dilepton spectra are calculated within the microscopic transport model UrQMD and compared to data from the CERES experiment. The invariant mass spectra in the region between 300 MeV and 600 MeV depend strongly on the mass dependence of the rho meson decay width which is not sufficiently determined by the Vector Meson Dominance model. A consistent explanation of both the recent Pb+Au data and the proton induced data can be given without additional medium effects.