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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.
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.
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.
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.
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.
The equilibration of hot and dense nuclear matter produced in the central region in central Au+Au collisions at square root s = 200A GeV is studied within the microscopic transport model UrQMD. The pressure here becomes isotropic at t approx 5 fm/c. Within the next 15 fm/c the expansion of the matter proceeds almost isentropically with the entropy per baryon ratio S/A approx 150. During this period the equation of state in the (P, epsilon)-plane has a very simple form, P = 0.15 epsilon. Comparison with the statistical model (SM) of an ideal hadron gas reveals that the time of approx 20 fm/c may be too short to attain the fully equilibrated state. Particularly, the fractions of resonances are overpopulated in contrast to the SM values. The creation of such a long-lived resonance-rich state slows down the relaxation to chemical equilibrium and can be detected experimentally.
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.
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.
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.
Abstract: Local thermal and chemical equilibration is studied for central AqA collisions at 10.7 160 AGeV in the Ultrarelativis- . tic Quantum Molecular Dynamics model UrQMD . The UrQMD model exhibits strong deviations from local equilibrium at the high density hadron string phase formed during the early stage of the collision. Equilibration of the hadron resonance matter is established in the central cell of volume Vs125 fm3 at later stages, tG10 fmrc, of the resulting quasi-isentropic expansion. The thermodynamical functions in the cell and their time evolution are presented. Deviations of the UrQMD quasi-equilibrium state from the statistical mechanics equilibrium are found. They increase with energy per baryon and lead to a strong enhancement of the pion number density as compared to statistical mechanics estimates at SPS energies. PACS: 25.75.-q; 24.10.Lx; 24.10.Pa; 64.30.qt
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.