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Institute
- Physik (75) (remove)
New data with a minimum bias trigger for 158 GeV/nucleon Pb + Pb have been analyzed. Directed and elliptic flow as a function of rapidity of the particles and centrality of the collision are presented. The centrality dependence of the ratio of elliptic flow to the initial space elliptic anisotropy is compared to models.
Irreversibility, steady state, and nonequilibrium physics in relativistic heavy ion collisions
(1999)
Heavy ion collisions at ultrarelativistic energies offer the opportunity to study the irreversibility of multiparticle processes. Together with the many-body decays of resonances, the multiparticle processes cause the system to evolve according to Prigogine s steady states rather than towards statistical equilibrium. These results are general and can be easily checked by any microscopic string-, transport-, or cascade model for heavy ion collisions. The absence of pure equilibrium states sheds light on the di culties of thermal models in describing the yields and spectra of hadrons, especially mesons, in heavy ion collisions at bombarding energies above 10 GeV/nucleon. PACS numbers: 25.75.-q, 05.70.Ln, 24.10.Lx
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.
We introduce a transport approach which combines partonic and hadronic degrees of freedom on an equal footing and discuss the resulting reaction dynamics. The initial parton dynamics is modeled in the framework of the parton cascade model, hadronization is performed via a cluster hadronization model and configuration space coalescence, and the hadronic phase is described by a microscopic hadronic transport approach. The resulting reaction dynamics indicates a strong influence of hadronic rescattering on the space-time pattern of hadronic freeze-out and on the shape of transverse mass spectra. Freeze-out times and transverse radii increase by factors of 2 3 depending on the hadron species.
Relativistic hadron-hadron collisions in the ultra-relativistic quantum molecular dynamics model
(1999)
Hadron-hadron collisions at high energies are investigated in the Ultra- relativistic-Quantum-Molecular-Dynamics approach. This microscopic trans- port model describes the phenomenology of hadronic interactions at low and intermediate energies ( s < 5 GeV) in terms of interactions between known hadrons and their resonances. At higher energies, s > 5 GeV, the excitation of color strings and their subsequent fragmentation into hadrons dominates the multiple production of particles in the UrQMD model. The model shows a fair overall agreement with a large body of experimental h-h data over a wide range of h-h center-of-mass energies. Hadronic reaction data with higher precision would be useful to support the use of the UrQMD model for relativistic heavy ion collisions.
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.
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
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.
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.
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.
To fulfil the requirements of ESS on beam transmission and emittance growth a detailed knowledge of the physics of beam formation as well as the interaction of the H- with the residual gas is substantial. Space charge compensated beam transport using solenoids for ion optics is in favour for the Low Energy Beam Transport (LEBT) between ion source and the first RFQ. Space charge compensation reduces the electrical self fields and beam radii and therefore emittance growth due to aberrations and redistribution. Transport of H- near the ion source is negatively influenced by the dipole fields required for beam extraction and e--dumping and the high gas pressure. The destruction of the rotational symmetry together with the space charge forces causes emittance growth and particle losses within the extraction system. High residual gas pressure near the extractor together with the high cross section for stripping will influence the transmission as well as space charge compensation. Therefore a detailed knowledge of the interaction of the residual gas with the beam and the influence of the external fields on the distribution of the compensation particles is necessary to reduce particle losses and emittance growth. Preliminary experiments using positive hydrogen ions for reference already show the influence of dipole fields on beam emittance. First measurements with H- confirm these results. Additional information on the interactions of the residual gas with the beam ions have been gained from the measurements using the momentum and energy analyser.
A LEBT system consisting of an ion source, two solenoids, and a diagnostic section has been set up to investigate the space charge compensation process due to residual gas ionization [1] and to study experimentally the rise of compensation. To gain the radial beam potential distribution time resolved measurements of the residual gas ion energy distribution were carried out using a Hughes Rojanski analyzer [2,3]. To measure the radial density profile of the ion beam a CCD-camera performed time resolved measurements, which allow an estimation the rise time of compensation. Further the dynamic effect of the space charge compensation on the beam transport was shown. A numerical simulation under assumption of selfconsistent states [4] of the beam plasma has been used to determine plasma parameters such as the radial density profile and the temperature of the electrons. The acquired data show that the theoretical estimated rise time of space charge compensation neglecting electron losses is shorter than the build up time determined experimentally. An interpretation of the achieved results is given.
The hypothesis of statistical production of J/psi mesons at hadronization is formulated and checked against experimental data. It explains in the natural way the observed scaling behavior of the J/psi to pion ratio at the CERN SPS energies. Using the multiplicities of J/psi and eta mesons the hadronization temperature T_H = 175 MeV is found, which agrees with the previous estimates of the temperature parameter based on the analysis of the hadron yield systematics.
The experimental results on the pion, strangeness and J/psi production in high energy nuclear collisions are discussed. The anomalous energy dependence of pion and strangeness production is consistent with the hypothesis that a transition to a deconfined phase takes place between the top AGS (15 AGeV) and the SPS (200 AGeV) energies. The J/psi production systematics at the SPS can be understood assuming that the J/psi mesons are created at hadronization according to the available hadronic phase space. This new interpretation of the J/psi data allows one to establish a coherent picture of high energy nuclear collisions based on the statistical approaches of the collision early stage and hadronization. Surprisingly, the statistical model of strong interactions is successful even in the region reserved up to now for pQCD based models.
Im NA49-Experiment wird der hadronische Endzustand von Kern und Protonen induzierten Reaktionen gemessen, um die Eigenschaften von Kernmaterie unter extremen Bedingungen zu untersuchen. Dabei stellt die Flugzeitmessung ein wichtiges Instrument zur Teilchenidentifizierung dar. Der von Yu.N. Pestov 1971 erstmal vorgestellte und nach ihm benannte Pestov-Zähler ist ein gasgefüllter Parallelplatten-Zähler, der im Funken/Überschlag-Modus betrieben wird. Die Besonderheit dieses Zählers ist die Lokalisierung der Entladung, die durch eine Anode aus halbleitendem Glas mit einem hohen spezifischen Widerstand und ein Zählgas mit großer Photonen-Absorption erreicht wird. In der Protonenstrahlzeit 1997 wurde der PesTOF-Detektor (Pestov Time Of Flight) bestehend aus zwölf einzelnen Zählern, erstmals im Vertex-1 Magneten des NA49-Experimentes eingesetzt. Neben der guten Zeitauflösung sind die Unempfindlichkeit gegenüber dem magnetischen Feld und die gute Ortsauflösung die auch bei großen Spurdichten ein korrektes Zuordnen der Treffer ermöglicht, die Voraussetzungen für diesen Einsatz. Der kinematische Akzeptanzbereich für die Identifikation von Pionen liegt bei Rapiditäten von y ~ 2-5 - 3 und Tranzversalimpulsen von pt <= 500 MeV/c. Der Akzeptanzbereich der Kaonen liegt bei einer Rapidität von y ~ 2 und Tranzversalimpulsen von pt <= 500 MeV/c. Der Detektor konnte über den gesamten Zeitraum stabil und zuverlässig betrieben werden. Die gemessene gaußförmige Zeitauflösung beträgt 78 ps, wobei die Hochspannung die 1.5fache Schwellenspannung betrug. Neben dem gaußförmigen Anteil der Zeitauflösung zeigt der Detektor jedoch auch einen asymmetrischen nicht gaußförmigen Anteil ("Tail"). Aufgrund einer verzögerten Funkenentwicklung im Zähler liegen etwa 12.6% der Signale außerhalb der gaußförmigen Verteilung bzw. sind etwa 4% der Signale um mehr als 500 ps verspätet. Neuere Untersuchungen mit anderen Zählgasen und Zählergeometrien haben gezeigt, dass der Anteil der verzögerten Signale in Zukunft deutlich reduziert werden kann. Der Verlauf der gemessenen pt und mt-Verteilungen der identifizierten Kaonen und Pionen kann durch Simulationen mit dem VENUS-Modell reproduziert werden. Mit der möglichen Verbesserung der Zeitauflösung und dem geplanten Ausbau des PesTOF-Detektors mit bis zu 80 einzelnen Zählern wird der Impuls- und Akzeptanzbereich, in dem Teilchen identifiziert werden können, deutlich vergrößert werden. Die Messungen dieser Arbeit geben einen Ausblick darauf dass es in Zukunft möglich sein wird, relevante physikalische Größen mit dem PesTOF-Detektor im NA49-Experiment zu messen. Insbesondere in nicht symmetrischen Stoßsystemen ist der Einsatz von Flugzeitdetektoren in dem rückwärtigen kinematischen Bereich der Reaktion interessant. Mit den in dieser Arbeit gefundenen positiven Eigenschaften und den sich abzeichnenden Modifikationen am Zählgas und Zähler ist der Pestov-Zähler ein interessanter Detektor für zukünftige Experimente.
Im Rahmen dieser Arbeit wurde erstmals die Realisierung eines (e,3e)- Experimentes an Helium mittels der Cold Target Recoil Ion Momentum Spectroscopy (COLTRIMS) behandelt. Dabei ging es hauptsächlich um den Aufbau, die Entwicklung, Test und die Durchführung des Experiments. Dazu wurde ein neues Kammersystem am Atomphysikkanal der Frankfurter EZR mit zweistufigem Ultraschallgasjet aufgebaut, an dem in Zukunft noch weitere COLTRIMS- Experimente stattfinden werden. In dieser Arbeit wurde eine Dreifach-Koinzidenz zwischen dem gestreuten Projektilelektron, dem einfach- oder zweifach geladenem Rückstoßion und dem langsamen Elektron verwirklicht. Sie stellt das wesentliche Ergebnis der vorliegenden Arbeit dar. Koinzident zum Streuwinkel und Energieverlust des Projektilelektrons wurden hierbei Flugzeiten und Auftrefforte rte von He1 - bzw. He2 - Ionen und von einem der ionisierten Elektronen gemessen. Anhand der durchgeführten umfangreichen Eichmessungen unter Hinzuziehung von Impuls- und Energieerhaltungssätzen lassen sich somit sämtliche Impulse der Teilchen errechnen. Somit gewinnt man Informationen über den Ionisationsprozeß. Desweiteren lassen sich multidifferentielle Wirkungsquerschnitte bestimmen, die sich mit theoretischen Modellen vergleichen lassen. Die Rückstoßionenimpulsverteilungen und die Flugzeitspektren für das He2 -Ion demonstrieren die Signifikaz der erreichten Statistik, trotz der geringen Koinzidenzrate von 17 h-1. Die Meßdaten wurden einer groben Auswertung unterzogen. Die entgültige Analyse, Ergebnisdeutung, Interpretation und Vergleich mit der Theorie fand in dieser Arbeit nicht statt. Die Projektilenergie lag bei allen Messungen bei 550 eV. Der Elektronenstrahl wurde, entgegen der vorherrschenden Meinung, mit einem Blendensystem auskollimiert. Im nächsten Schritt sollen statt mit nur einem mit zwei oder mehreren Schlitzblenden nacheinander der Elektronenstrahl auskollimiert werden, so daß die am vorderen Schlitz gestreuten Elektronen in den nachfolgenden ausgeblendet werden können. Somit verringert man die problematische Untergrundrate auf dem Elektronendetektor. Für weitere Untersuchungen werden momentan neue Spektrometerkonzepte entwickelt. Bei der Konzeption des neuen Spektrometers wird der Abstand zwischen Targetzone und Elektronendetektor größer gewählt. Dies verringert zwar den Nachweisraumwinkel für die Elektronen, aber man erreicht dadurch eine Verringerung der Untergrundselektronen. Der Verringerung des Nachweisraumwinkels kann man entgegenwirken, indem man einen großen MCP- Detektor mit 80 mm Durchmesser einsetzt. Der Eintrittsbereich des Projektilstrahls in das Rückstoßionenimpulsspektrometer sollte großzügig gewählt werden, da auf diese Art und Weise verhindert werden kann, daß der Elektronenstrahl die Potentialringe in Eintrittsbereich streift und wohlmöglich unerwünschte Sekundärelektronen erzeugt, die im Extraktionsfeld des Spektrometers auf den Elektronendetektor hin beschleunigt werden und ebenfalls für Untergrund sorgen. Eine Pulsung der Elektronenkanone über die Wehneltspannung vorzunehmen und den Puls als Start oder Trigger für die Datenaufnahme einzusetzen ist nur dann sinnvoll, wenn die Flugzeit der Elektronen um mindestens eine Größenordnung größer ist als die erreichbare Pulslänge. Nach Auskunft unserer Elektronik liegen die erreichbaren Pulslängen bei etwa 5 ns. Aufgrund der notwendigen Stabilität sowohl in der Elektronik als auch in der Kühlung des Kaltkopfes ist eine insgesamt kürzere Meßzeit erstrebenswert.
We investigate various properties of neutron star matter within an e ective chiral SU(3)L × SU(3)R model. The predictions of this model are compared with a Walecka-type model. It is demonstrated that the importance of hy- peron degrees are strongly depending on the interaction used, even if the equation of state near saturation density is nearly the same in both models. While the Walecka-type model predicts a strange star core with strangeness fraction fS 4/3, the chiral model allows only for fS 1/3 and predicts that 0, + and 0 will not exist in star, in contrast to the Walecka-type model. PACS: 26.60+c, 21.65+f, 24.10Jv
A microscopic model of deconfined matter based on color interactions between semi-classical quarks is studied. A hadronization mechanism is imposed to examine the properties and the disassembly of a thermalized quark plasma and to investigate the possible existence of a phase transition from quark matter to hadron matter.
UrQMD at RHIC energies
(1999)
Im Rahmen der vorliegenden Arbeit wurde eine Apparatur zur Messung von Fotoströmen in Halbleitermaterialien aufgebaut und charakterisiert. Der Fotostrommeßplatz gestattet es, mit spektral hoher Auflösung Fotostromspektren mit sehr gutem Signal-zu-Rausch-Verhältnis aufzunehmen, wobei die Möglichkeit besteht, die Proben bei tiefen Temperaturen einem äußeren Magnetfeld bis 9T auszusetzen. Mit Hilfe einer elektrischen Kontaktierung auf der Probenvorder- bzw. -rückseite kann durch Anlegen einer Spannung ein variables, homogen über den intrinsischen Bereichen der Proben abfallendes, elektrisches Feld erzeugt werden. Mit Hilfe des Meßaufbaus wurden Fotostromspektren von GaAs/Al0,3Ga0,7As-Übergittern fur verschiedene elektrische und magnetische Felder aufgenommen. Unter Variation des elektrischen Feldes ohne ein zusätzliches Magnetfeld wird deutlich die sog. Wannier-Stark-Quantisierung beobachtet. Es lassen sich die vor einiger Zeit an der RWTH Aachen an identischen Probenstrukturenvorgenommenen Untersuchungen bestätigen bzw. reproduzieren. Die magnetfeldfreien Messungen dienen ferner der genauen Bestimmung des über dem Übergitter abfallenden elektrischen Feldes in Abhängigkeit von der an der Probe angeliegenden Vorspannung. Die Feldbestimmung erfordert dabei aufgrund des Einflusses der Coulomb-Wechselwirkung der Ladungstrager auf den Verlauf der Ubergange in Abhängigkeit vom elektrischen Feld eine gewisse Vorsicht. Messungen ohne Magnetfeld sind außerdem bei der Zuordnung der Übergange in den mit Magnetfeld gemessenen Fotostromspektren äußerst hilfreich. Im Rahmen dieser Arbeit wurden erstmals Fotostrommessungen an Halbleiterübergittern im magnetischen Feld durchgeführt, wobei der gleichzeitige Einfluß eines elektrischen und eines magnetischen Feldes untersucht wurde. Dazu wurde bei elektrischen Feldstärken im Wannier-Stark- sowie im Minibandbereich das äußere Magnetfeld bis 9T variiert. Im Magnetfeld zeigt sich eine deutliche Landau-Quantisierung. Die zu den Landau-Niveaus gehorenden exzitonischen Zustände der Wannier-Stark-Übergänge schieben mit steigendem Magnetfeld zu höheren Energien. In den gemessenen Spektren läßt sich eine Vielzahl von Übergangen ausmachen, die zu einem großen Teil den einzelnen Leichtloch- bzw. Schwerloch-Übergangen zugeordnet werden können. Modellrechnungen zeigen, daß man zu jedem Wannier-Stark-Übergang einen eigenen exzitonischen Landau-Facher erwarten kann, worauf es in den Messungen ebenfalls Hinweise gibt. Eine zweifelsfreie Identifikation von mutmaßlich im Magnetfeld drehimpulsaufgespaltenen Niveaus kann erst geleistet werden, wenn weitere Messungen bei definierter Polarisation des Anregungslichtes vorliegen. Aus den aufgenommenen Fotostromspektren der Übergitterproben lassen sich für spätere zeitaufgelöste Untersuchungen einige interessante Energiebereiche fur mögliche Anregungen von Quanteninterferenz-Phänomenen ableiten. Die aus den Spektren ermittelten Linienbreiten der Wannier-Stark-Übergange von 3-4 meV garantieren eine ausreichende Schmalbandigkeit für die Anregung von Bloch-Oszillationen. Die Linienbreiten sind, bis auf wenige Ausnahmen, unabhängig vom Magnetfeld, so daß keine signifikante Magnetfeldabhängigkeit der beispielsweise für Vier-Wellen-Misch-Experimente relevanten Dephasierungszeiten der Interband-Polarisation zu erwarten ist. Die Ergebnisse lassen allerdings keine Ruckschlüsse auf die Magnetfeldabhängigkeit von Intraband-Polarisationen zu.
In der vorliegenden Arbeit werden Stöße zwischen Alpha-Teilchen und Li-ähnlichen Ionen sowie Stöße zwischen vollständig ionisierten Projektilionen und dem Li-ähnlichen Ion N4+ untersucht. Hierzu wird die zeitabhängige Schrödinger-Gleichung unter Verwendung einer effektiven Einteilchenbeschreibung im Rahmen der nichtpertubativen Basis Generator Methode (BGM) gelöst.
Das Ziel der Untersuchung von ultra-relativistischen Schwerionenkollisionen ist die Suche nach dem Quark Gluon Plasma (QGP), einem Zustand hochdichter stark wechselwirkender Materie in dem der Einschluss von Quarks und Gluonen in Hadronen aufgehoben ist. Die bisher gewonnenen experimentellen Hinweise deuten daraufhin,daß in Schwerionenkollisionen bei den derzeit höchsten zur Verfügung stehenden Energien von 158 GeV/Nukleon in Pb+Pb Reaktionen am CERN-SPS die Rahmenbedingungen für einen Phasenübergang von hadronischer Materie zu einer partonischen Phaseerfüllt sind. Die exakte Phasenstruktur stark wechselwirkender Materie hingegen ist derzeit noch nicht vollständig verstanden. Da inklusive hadronische Observablen und "penetrierende Proben" nicht direkt sensitiv auf die Existenz und Natur des Phasenübergangs sind, wurde die Analyse von Einzelereignis-"event-by-event"-Fluktuationenvorgeschlagen. Das Fluktuationsverhalten von Einzelereignis-Observablen sollte direkt sensitiv auf die Natur des zu beobachtenden Phasenübergangssein. In dieser Arbeit wurden Fluktuationen in der "chemischen" Zusammensetzung der Teilchenquelle untersucht und erste Ergebnisse werden präsentiert.
Freeze out of particles across three dimensional space-time hypersurface is discussed in a simple kinetic model. The final momentum distribution of emitted particles, for freeze out surfaces with space-like normal, shows a non-exponential transverse momentum spectrum. The slope parameter of the pt distribution increases with increasing pt, in agreement with recently measured SPS pion and h spectra.
The modification of the width of the rho meson due to in-medium decays and collisions is evaluated. In high temperature and/or high density hadronic matter, the collision width is much larger than the one-loop decay width. The large width of the meson in matter seems to be consistent with some current interpretations of the e+e mass spectra measured at the CERN/SPS.
In continuum and fluid dynamical models, particles, which leave the system and reach the detectors, can be taken into account via freeze-out (FO) or final break-up schemes, where the frozen out particles are formed on a 3-dimensional hypersurface in space-time. Such FO descriptions are important ingredients of evaluations of two-particle correlation data, transverse-, longitudinal-, radial- and cylindrical- flow analyses, transverse momentum and transverse mass spectra and many other observables. The FO on a hypersurface is a discontinuity, where the pre FO equilibrated and interacting matter abruptly changes to non-interacting particles, showing an ideal gas type of behavior.
Introduction: Until now it is not possible to determine the equation of state (EOS) of hadronic matter from QCD. One succesfully applied alternative way to describe the hadronic world at high densities and temperatures are effective models like the RMF-models [1], where the relevant degrees of freedom are baryons and mesons instead of quarks and gluons. Since approximate chiral symmetry is an essential feature of QCD, it should be a useful concept for building and restricting e ective models. It has been shown [2,3] that effective sigma-omega models including SU(2) chiral symmetry are able to obtain a reasonable description of nuclear matter and finite nuclei. Recently [4] we have shown that an extended SU(3) × SU(3) chiral sigma-omega model is able to describe nuclear matter ground state properties, vacuum properties and finite nuclei satisfactorily. This model includes the lowest SU(3) multiplets of the baryons (octet and decuplet[5]), the spin-0 and the spin-1 mesons as the relevant degrees of freedom. Here we will discuss the predictions of this model for dense, hot, and strange hadronic matter.
The modification of the width of rho mesons due to in-medium decays and collisions is evaluated. The decay width is calculated from the imaginary part of the one-loop selfenergy at finite temperature. The collision width is related to the cross sections of the rho + pion and the rho + nucleon reactions. A calculation based on an e ective Lagrangian shows the importance of including the direct pho pi - > pho pi scattering which is dominated by the a1 exchange. A large broadening of the spectral function is found, accompanied by a strength suppression at the pole. http://www.arxiv.org/abs/nucl-th/9812059
We calculate the shadowing of sea quarks and gluons and show that the shadowing of gluons is not simply given by the sea quark shadowing, especially at small x. The calculations are done in the lab frame approach by using the generalized vector meson dominance model. Here the virtual photon turns into a hadronic fluctuation long before the nucleus. The subsequent coherent interaction with more than one nucleon in the nucleus leads to the depletion sigma(gamma*A )< A*sigma(gamma * N) known as shadowing. A comparison of the shadowing of quarks to E665 data for 40Ca and 207Pb shows good agreement.
We derive the relativistic quantum transport equation for the pion distribution function based on an effective Lagrangian of the QHD-II model. The closed-time-path Green s function technique and the semiclassical, quasiparticle, and Born approximations are employed in the derivation. Both the mean field and collision term are derived from the same Lagrangian and presented analytically. The dynamical equation for the pions is consistent with that for the nucleons and Delta's which we developed before. Thus, we obtain a relativistic transport model which describes the hadronic matter with N,Delta, and pi degrees of freedom simultaneously. Within this approach, we investigate the medium effects on the pion dispersion relation as well as the pion absorption and pion production channels in cold nuclear matter. In contrast to the results of the nonrelativistic model, the pion dispersion relation becomes harder at low momenta and softer at high momenta as compared to the free one, which is mainly caused by the relativistic kinetics. The theoretically predicted free piN->Delta cross section is in agreement with the experimental data. Medium effects on the piN->Delta cross section and momentum-dependent Delta-decay width are shown to be substantial. PACS-numbers: 24.10.Jv, 13.75.Cs, 21.65.1f, 25.75.2q
Hot hypernuclear matter is investigated in an explicit SU(3) quark model based on a mean field description of nonoverlapping baryon bags bound by the self-consistent exchange of scalar sigma, zeta and vector omega,phi mesons. The sigma, omega mean fields are assumed to couple to the u, d-quarks while the zeta ,phi mean fields are coupled to the s-quark. The coupling constants of the mean fields with the quarks are assumed to satisfy SU(6) symmetry. The calculations take into account the medium dependence of the bag parameter on the scalar fields sigma, zeta. We consider only the octet baryons N,Lambda,Sigma, Xi in hypernuclear matter. An ideal gas of the strange mesons K and K is introduced to keep zero net strangeness density. Our results for symmetric hypernuclear matter show that a phase transition takes place at a critical temperature around 180 MeV in which the scalar mean fields sigma, zeta take nonzero values at zero baryon density. Furthermore, the bag contants of the baryons decrease significantly at and above this critical temperature indicating the onset of quark deconfinement. The present results imply that the onset of quark deconfinement in SU(3) hypernuclear matter is much stronger than in SU(2) nuclear matter. PACS:21.65.+f, 24.85.+p, 12.39Ba
We study the effects of strict conservation laws and the problem of negative contributions to final momentum distribution during the freeze out through 3-dimensional hypersurfaces with space-like normal. We study some suggested solutions for this problem, and demonstrate it on one example. PACS: 24.10.Nz, 25.75.-q
A new chiral SU(3) Lagrangian is proposed to describe the properties of kaons and antikaons in the nuclear medium, the ground state of dense matter and the kaon-nuclear interactions consistently. The saturation properties of nuclear matter are reproduced as well as the results of the Dirac-Brückner theory. After taking into account the coupling between the omega meson and the kaon, we obtain similar results for the e ective kaon and antikaon energies as calculated in the one-boson-exchange model while in our model the parameters of the kaon-nuclear interactions are constrained by the SU(3) chiral symmetry. PACS number(s): 14.40.Aq, 12.39.Fe, 21.30.Fe
We investigate in stable strange hadronic matter (SHM) the modifica- tion of the masses of the scalar (sigma,sigma') and the vector (omega,phi) mesons. The baryon ground state is treated in the relativistic Hartree approximation in the nonlinear sigma-omega and linear sigma'- phi model. In stable SHM, the masses of all the mesons reveal considerable reduction due to large vacuum polarization contribution from the hyperons and small density dependent effects caused by larger binding. PACS: 21.65+f, 24.10Jv
We calculate the initial non-equilibrium conditions from perturbative QCD (pQCD) within Glauber multiple scattering theory for s = 200 AGeV and s = 5.5 ATeV. At the soon available collider energies one will particularly test the small x region of the parton distributions entering the cross sections. Therefore shadowing effects, previously more or less unimportant, will lead to new e ects on variables such as particle multiplicities dN/dy, transverse energy production d T /dy, and the initial temperature Ti. In this paper we will have a closer look on the effects of shadowing by employing di erent parametrizations for the shadowing effect for valence quarks, sea quarks and gluons. Since the cross sections at midrapidity are dominated by processes involving gluons the amount of their depletion is particularly important. We will therefore have a closer look on the results for dN/dy, d ¯E T /dy, and Ti by using two different gluon shadowing ratios, di ering strongly in size. As a matter of fact, the calculated quantities di er significantly.
We investigate the hadronic cooling of a quark droplet within a microscopic model. The color flux tube approach is used to describe the hadronization of the quark phase. The model reproduces experimental particle ratios equally well compared to a static thermal hadronic source. Furthermore, the dynamics of the decomposition of a quark-gluon plasma is investigated and time dependent particle ratios are found.
We investigate event-by-event fluctuations for ensembles with non-fixed multiplicity. Moments of event observable distributions, like total energy distribution, total transverse momentum distribution, etc, are shown to be related to the multi-body correlations present in the system. For classical systems, these moments reduce in the absence of any correlations to the mo- ments of particle inclusive momentum distribution. As a consequence, a zero value for the recently introduced Phi-variable is shown to indicate the van- ishing of two-body correlations from one part, and of correlations between multiplicity and momentum distributions from the other part. It is often misunderstood as a measure of the degree of equilibration in the system.
Kinetic freeze out models
(1999)
Freeze out of particles across a space-time hypersurface is discussed in kinetic models. The calculation of final momentum distribution of emitted particles is described for freeze out surfaces, with spacelike normals. The resulting non-equilibrium distribution does not resemble, the previously proposed, cut Jüttner distribution, and shows non-exponential pt-spectra similar to the ones observed in experiments. PACS: 24.10.Nz, 25.75.-q
We develop a relativistic model to describe the bound states of positive energy and negative energy in finite nuclei at the same time. Instead of searching for the negative-energy solution of the nucleon s Dirac equation, we solve the Dirac equations for the nucleon and the anti-nucleon simultaneously. The single-particle energies of negative-energy nucleons are obtained through changing the sign of the single-particle energies of positive-energy anti-nucleons. The contributions of the Dirac sea to the source terms of the meson fields are evaluated by means of the derivative expansion up to the leading derivative order for the one-meson loop and one-nucleon loop. After refitting the parameters of the model to the properties of spherical nuclei, the results of positive-energy sector are similar to that calculated within the commonly used relativistic mean field theory under the no-sea approximation. However, the bound levels of negative-energy nucleons vary drastically when the vacuum contributions are taken into account. It implies that the negative-energy spectra deserve a sensitive probe to the e ective interactions in addition to the positive-energy spectra.
We develop a relativistic model to describe the bound states of positive energy and negative energy in finite nuclei at the same time. Instead of searching for the negative-energy solution of the nucleon's Dirac equation, we solve the Dirac equations for the nucleon and the anti-nucleon simultaneously. The single-particle energies of negative-energy nucleons are obtained through changing the sign of the single-particle energies of positive-energy anti-nucleons. The contributions of the Dirac sea to the source terms of the meson fields are evaluated by means of the derivative expansion up to the leading derivative order for the one-meson loop and one-nucleon loop. After refitting the parameters of the model to the properties of spherical nuclei, the results of positive-energy sector are similar to that calculated within the commonly used relativistic mean field theory under the no-sea approximation. However, the bound levels of negative-energy nucleons vary drastically when the vacuum contributions are taken into account. It implies that the negative-energy spectra deserve a sensitive probe to the effective interactions in addition to the positive-energy spectra.
The effects of internal quark structure of baryons on the composition and structure of neutron star matter with hyperons are investigated in the quark- meson coupling (QMC) model. The QMC model is based on mean-field description of nonoverlapping spherical bags bound by self-consistent exchange of scalar and vector mesons. The predictions of this model are compared with quantum hadrodynamic (QHD) model calibrated to reproduce identical nuclear matter saturation properties. By employing a density dependent bag constant through direct coupling to the scalar field, the QMC model is found to exhibit identical properties as QHD near saturation density. Furthermore, this modified QMC model provides well-behaved and continuous solutions at high densities relevant to the core of neutron stars. Two additional strange mesons are introduced which couple only to the strange quark in the QMC model and to the hyperons in the QHD model. The constitution and structure of stars with hyperons in the QMC and QHD models reveal interesting di erences. This suggests the importance of quark structure e ects in the baryons at high densities. PACS number(s): 26.60.+c, 21.65.+f, 12.39.Ba, 24.85.+p
A selection of recent data referring to Pb+Pb collisions at the SPS CERN energy of 158 GeV per nucleon is presented which might describe the state of highly excited strongly interacting matter both above and below the deconfinement to hadronization (phase) transition predicted by lattice QCD. A tentative picture emerges in which a partonic state is indeed formed in central Pb+Pb collisions which hadronizes at about T = 185 MeV, and expands its volume more than tenfold, cooling to about 120 MeV before hadronic collisions cease. We suggest further that all SPS collisions, from central S+S onward, reach that partonic phase, the maximum energy density increasing with more massive collision systems.
Hadronic yields and yield ratios observed in Pb+Pb collisions at the SPS energy of 158 GeV per nucleon are known to resemble a thermal equilibrium population at T=180 +/- 10 MeV, also observed in elementary e+ + e- to hadron data at LEP. We argue that this is the universal consequence of the QCD parton to hadron phase transition populating the maximum entropy state. This state is shown to survive the hadronic rescattering and expansion phase, freezing in right after hadronization due to the very rapid longitudinal and transverse expansion that is inferred from Bose-Einstein pion correlation analysis of central Pb+Pb collisions.
The two-proton correlation function at midrapidity from Pb+Pb central collisions at 158 AGeV has been measured by the NA49 experiment. The results are compared to model predictions from static thermal Gaussian proton source distributions and transport models RQMD and VENUS. An effective proton source size is determined by minimizing CHI-square/ndf between the correlation functions of the data and those calculated for the Gaussian sources, yielding 3.85 +-0.15(stat.) +0.60-0.25(syst.) fm. Both the RQMD and the VENUS model are consistent with the data within the error in the correlation peak region.
We present first data on event-by-event fluctuations in the average transverse momentum of charged particles produced in Pb+Pb collisions at the CERN SPS. This measurement provides previously unavailable information allowing sensitive tests of microscopic and thermodynamic collision models and to search for fluctuations expected to occur in the vicinity of the predicted QCD phase transition. We find that the observed variance of the event-by-event average transverse momentum is consistent with independent particle production modified by the known two-particle correlations due to quantum statistics and final state interactions and folded with the resolution of the NA49 apparatus. For two specific models of non-statistical fluctuations in transverse momentum limits are derived in terms of fluctuation amplitude. We show that a significant part of the parameter space for a model of isospin fluctuations predicted as a consequence of chiral symmetry restoration in a non-equilibrium scenario is excluded by our measurement.
Net proton and negative hadron spectra for central \PbPb collisions at 158 GeV per nucleon at the CERN SPS were measured and compared to spectra from lighter systems. Net baryon distributions were derived from those of net protons, utilizing model calculations of isospin contributions as well as data and model calculations of strange baryon distributions. Stopping (rapidity shift with respect to the beam) and mean transverse momentum \meanpt of net baryons increase with system size. The rapidity density of negative hadrons scales with the number of participant nucleons for nuclear collisions, whereas their \meanpt is independent of system size. The \meanpt dependence upon particle mass and system size is consistent with larger transverse flow velocity at midrapidity for \PbPb compared to \SS central collisions.
We argue that the measurement of open charm gives a unique opportunity to test the validity of pQCD-based and statistical models of nucleus-nucleus collisions at high energies. We show that various approaches used to estimate D-meson multiplicity in central Pb+Pb collisions at 158 A GeV give predictions which differ by more than a factor of 100. Finally we demonstrate that decisive experimental results concerning the open charm yield in A+A collisions can be obtained using data of the NA49 experiment at the CERN SPS.
Die vorliegende Diplomarbeit beschreibt den Aufbau und erste Anwendungen einer neuartigen Technik zur Manipulation von Fallenpotentialen für Bose-Einstein-Kondensate. Das Dipolpotential, das ein gegen die atomare Resonanz verstimmter Laserstrahl auf die Atome ausübt, wird hierzu genutzt. Es wurde eine Apparatur aufgebaut, mit der sehr schnelle räumliche Bewegung und gleichzeitige Intensitätsänderung von Laserstrahlen erzielt wird. Durch schnelles Scannen des Laserstrahls in x- und y-Richtung und gleichzeitige Modulation seiner Intensität werden beliebige zeitgemittelte Potentiale erzeugt. Diese Potentiale wurden sowohl als räumliche und/oder zeitliche Modifikation herkömmlicher Magnetfallenpotentiale als auch als eigenständige Fallen mit neuartiger Geometrie verwendet. Mit diesem Aufbau wurden Experimente an Bose-Einstein-Kondensaten durchgeführt, bei denen die große räumliche und zeitliche Auflösung genutzt wurden. Die Speicherung von Atomen in zeitgemittelten, rotverstimmten optischen Fallen verschiedener Geometrie wurde demonstriert und eine durch das Scannen hervorgerufene Aufheizung der Probe wurde gefunden und untersucht. Dies ist die erstmalige Speicherung von Bose- Einstein-Kondensaten in zeitgemittelten Dipolfallen, deren Gestalt im Prinzip frei wählbar ist. Außerdem wurden kollektive Anregungen eines Bose-Einstein-Kondensats in einer Magnetfalle untersucht, die durch zeitgemittelte optische Potentiale induziert wurden. Der Schwerpunkt dieser Untersuchung waren insbesondere Moden mit hohem Drehimpuls, die in rein magnetischen Fallenpotentialen zuvor nicht angeregt worden waren. Bisherige Limitation von Gleichstrommagnetfallen, in denen nur zylindersymmetrische Moden angeregt werden konnten, wurden durch die Verwendung zeitgemittelten optischen Potentialen zusätzlich zum Magnetfallenpotential umgangen. In einem dritten Experiment konnte der suprafluide Charakter eines Bose-Einstein-Kondensats studiert werden. Die kritische Geschwindigkeit für die Bewegung eines Fremdobjektes duch das Kondensat wurde erstmals gemessen. Als Fremdobjekt diente ein gegen die atomare Resonanz blauverstimmter Laserstrahl, der auf die Atome ein repulsives Potential ausübt.
In dieser Arbeit wurden Untersuchungen zur Einstellung und Analyse des Sauerstoffgehalts an YBa2Cu3O6+x-Dünnfilmen durchgeführt. Zur Analyse des Sauerstoffgehalts wurde ein optisches Verfahren angewendet. Durch Messung der Transmission un der Reflektion in einem Spektralbereich von 2000nm bis 3000nm wird mit Hilfe des im Rahmen dieser Arbeit erstellten Markov-Modells die optische Leitfähigkeit bestimmt. Aus den gewonnen Werten der optischen Leitfähigkeit kann so auf den Sauerstoffgehalt in YBa2Cu3O6+x geschlossen werden.