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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.
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.
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.
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.
We investigate the effects of strong color fields and of the associated enhanced intrinsic transverse momenta on the phi-meson production in ultrarelativistic heavy ion collisions at RHIC. The observed consequences include a change of the spectral slopes, varying particle ratios, and also modified mean transverse momenta. In particular, the composition of the production processes of phi-mesons, that is, direct production vs. coalescence-like production, depends strongly on the strength of the color fields and intrinsic transverse momenta and thus represents a sensitive probe for their measurement.
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.
To be published in J. Phys. G - Proceedings of SQM 2004 : We review the results from the various hydrodynamical and transport models on the collective flow observables from AGS to RHIC energies. A critical discussion of the present status of the CERN experiments on hadron collective flow is given. We emphasize the importance of the flow excitation function from 1 to 50 A.GeV: here the hydrodynamic model has predicted the collapse of the v2-flow ~ 10 A.GeV; at 40 A.GeV it has been recently observed by the NA49 collaboration. Since hadronic rescattering models predict much larger flow than observed at this energy we interpret this observation as evidence for a first order phase transition at high baryon density r b. Moreover, the connection of the elliptic flow v2 to jet suppression is examined. It is proven experimentally that the collective flow is not faked by minijet fragmentation. Additionally, detailed transport studies show that the away-side jet suppression can only partially (< 50%) be due to hadronic rescattering. Furthermore, the change in sign of v1, v2 closer to beam rapidity is related to the occurence of a high density first order phase transition in the RHIC data at 62.5, 130 and 200 A.GeV.
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
The influence of high and low energy hadronic models on lateral distribution functions of cosmic ray air showers for Auger energies is explored. A large variety of presently used high and low energy hadron interaction models are analysed and the resulting lateral distribution functions are compared. We show that the slope depends on both the high and low energy hadronic model used. The models are confronted with available hadron-nucleus data from accelerator experiments.
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.
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.
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.
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.
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.
REVTEX, 27 pages incl. 10 figures and 3 tables; Phys. Rev. C (in press) Journal-ref: Phys.Rev. C62 (2000) 064906. We study the local equilibrium in the central V = 125 fm3 cell in heavy-ion collisions at energies from 10.7 A GeV (AGS) to 160 A GeV (SPS) calculated in the microscopic transport model. In the present paper the hadron yields and energy spectra in the cell are compared with those of infinite nuclear matter, as calculated within the same model. The agreement between the spectra in the two systems is established for times t >= 10 fm/c in the central cell. The cell results do not deviate noticeably from the infinite matter calculations with rising incident energy, in contrast to the apparent discrepancy with predictions of the statistical model (SM) of an ideal hadron gas. The entropy of this state is found to be very close to the maximum entropy, while hadron abundances and energy spectra differ significantly from those of the SM.
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.
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.
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.
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.
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.
The equilibration of hot and dense nuclear matter produced in the central cell of central Au+Au collisions at RHIC (sqrt s = 200 A GeV) energies is studied within a microscopic transport model. The pressure in the cell becomes isotropic at t approx 5 fm/c after beginning of the collision. Within the next 15 fm/c the expansion of matter in the cell proceeds almost isentropically with the entropy per baryon ratio S/A approx 150, and the equation of state in the (P,epsilon) plane has a very simple form, P=0.15 epsilon. Comparison with the statistical model of an ideal hadron gas indicates that the time t approx 20 fm/c may be too short to reach the fully equilibrated state. Particularly, the creation of long-lived resonance-rich matter in the cell decelerates the relaxation to chemical equilibrium. This resonance-abundant state can be detected experimentally after the thermal freeze-out of particles.
The yields of strange particles are calculated with the UrQMD model for p,Pb(158 AGeV)Pb collisions and compared to experimental data. The yields are enhanced in central collisions if compared to proton induced or peripheral Pb+Pb collisions. The enhancement is due to secondary interactions. Nevertheless, only a reduction of the quark masses or equivalently an increase of the string tension provides an adequate description of the large observed enhancement factors (WA97 and NA49). Furthermore, the yields of unstable strange resonances as the Lambda star(1520) resonance or the phi meson are considerably affected by hadronic rescattering of the decay products.
Enhanced antiproton production in Pb(160 AGeV)+Pb reactions: evidence for quark gluon matter?
(2000)
The centrality dependence of the antiproton per participant ratio is studied in Pb(160 AGeV)+Pb reactions. Antiproton production in collisions of heavy nuclei at the CERN/SPS seems considerably enhanced as compared to conventional hadronic physics, given by the antiproton production rates in pp and antiproton annihilation in p p reactions. This enhancement is consistent with the observation of strong in-medium effects in other hadronic observables and may be an indication of partial restoration of chiral symmetry.
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.
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.
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.
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.
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 SENECA model, a new hybrid approach to air shower simulations, is presented. It combines the use of efficient cascade equations in the energy range where a shower can be treated as one-dimensional, with a traditional Monte Carlo method which traces individual particles. This allows one to reproduce natural fluctuations of individual showers as well as the lateral spread of low energy particles. The model is quite efficient in computation time. As an application of the new approach, the influence of the low energy hadronic models on shower properties for AUGER energies is studied. We conclude that these models have a significant impact on the tails of lateral distribution functions, and deserve therefore more attention.
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.