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We study the dynamics of high energy heavy ion collisions through the Vlasov-Uehling-Uhlenbeck approach. Equilibration is observed, for central collisions. It is shown that the produced entropy, the pion multiplicity, flow angle, and transverse momentum distributions saturate at the moment of maximum compression and temperature. The effects of the nuclear equation of state and the Pauli principle are investigated. For the flow angle distribution there is a 20 deg reduction of the peak flow angle due to the Pauli principle. A stiff equation of state results in a 10–20 deg increase over the soft equation of state at all energies. The transverse momentum at projectile rapidity exhibits a peak structure as a function of impact parameter b. A 40% difference between soft and hard equation of state is observed for the peak impact parameter, i.e., for intermediate multiplicities.
The final states of central Ca + Ca and Nb + Nb collisions at 400 and 1050 MeV/nucleon and at 400 and 650 MeV/nucleon, respectively, are studied with two independently developed statistical models, namely the classical microcanonical model and the quantum-statistical grand canonical model. It is shown that these models are in agreement with each other for these systems. Furthermore, it is demonstrated that there is essentially a one-to-one relationship between the observed relative abundances of the light fragments p, d, t, 3He, and α and the entropy per nucleon, for breakup temperatures greater than 30 MeV. Entropy values of 3.5–4 are deduced from high-multiplicity selected fragment yield data.
We demonstrate that momentum-dependent nuclear interactions (MDI) have a large effect on the dynamics and on the observables of high-energy heavy-ion collisions: A soft potential with MDI suppresses pion and kaon yields much more strongly than a local hard potential and results in transverse momenta intermediate between soft and hard local potentials. The collective-flow angles and the deuteron-to-proton ratios are rather insensitive to the MDI. Only simultaneous measurements of these observables can give clues on the nuclear equation of state at densities of interest for supernova collapse and neutron-star stability.
The recent attempts to extract the temperature in the late stage of medium energy (20–60 MeV/nucleon) heavy ion collisions from the yields of γ- and particle-instable fragments are discussed. The quantum statistical model is employed to demonstrate that feeding from instable states distorts the yields used for the temperature determination severely. Some particle instable fragments are only moderately affected by feeding. These selected species can still be useful for determining the temperature. The breakup temperatures of the fragment conglomerate extracted with this method are T≃4–8 MeV, much smaller than the corresponding slope factors, which indicate T∼15 MeV.
We study effects of the mean field in hot compressed nuclear matter in the context of the Vlasov Uehling-Uhlenbeck theory. The expansion of a spherical distribution at different temperatures is studied along with collisions of Nb+Nb and Au+Au at lab energies from 50 to 1050 MeV/nucleon. In both the expansion and the actual heavy ion collision simulation, a transition behavior is seen only at the lowest temperature (T<10 MeV) or bombarding energy (E=50 MeV/nucleon), where the attractive part of the mean field is able to bind the expanding matter. At the lowest energy one thus sees the formation of a central residue, whereas at higher bombarding energies there is complete disintegration of the centrally colliding nuclei. The spectrum of emitted nucleons is found to be much hotter than the kinetic energy spectrum of the central emitting region. The extracted temperature slope parameters are in agreement with recent data.
In the present paper we develop the essential theoretical tools for the treatment of the dynamics of High Energy Heavy Ion Collisions. We study the influence of the nuclear equation of state and discuss the new phenomena connected with phase transitions in nuclear matter (pion condensation). Furthermore we investigate the possibility of a transition from nuclear to quark matter in High Energy Heavy Ion Collisions. In this context we discuss exotic phenomena like strongly bound pionic states, limiting temperatures, and exotic nuclei.
Streamer chamber data for collisions of Ar + KCl and Ar + BaI2 at 1.2 GeV/nucleon are compared with microscopic model predictions based on the Vlasov-Uehling-Uhlenbeck equation, for various density-dependent nuclear equations of state. Multiplicity distributions and inclusive rapidity and transverse momentum spectra are in good agreement. Rapidity spectra show evidence of being useful in determining whether the model uses the correct cross sections for binary collisions in the nuclear medium, and whether momentum-dependent interactions are correctly incorporated. Sideward flow results do not favor the same nuclear stiffness parameter at all multiplicities.
We demonstrate that strangeness separates in the Gibbs-phase coexistence between a baryon-rich quark-gluon plasma and hadron matter, even at T=0. For finite temperatures this is due to the associated production of kaons (containing s¯ quarks) in the hadron phase while s quarks remain in the deconfined phase. The s-s¯ separation results in a strong enhancement of the s-quark abundance in the quark phase. This mechanism is further supported by cooling and net strangeness enrichment due to the prefreezeout evaporation of pions and K+, K0, which carry away entropy and anti- strangeness from the system. Metastable droplets (i.e., stable as far as weak interactions are not regarded) of strange-quark matter (‘‘strangelets’’) can thus be formed during the phase transition. Such cool, compact, long-lived clusters could be experimentally observed by their unusually small Z/A ratio (≤0.1–0.3). Even if the strange-quark-matter phase is not stable under strong interactions, it should be observable by the delayed correlated emission of several hyperons. This would serve as a unique signature for the transient formation of a quark-gluon plasma.
We have calculated the D-meson spectral density at finite temperature within a self-consistent coupled-channel approach that generates dynamically the Lambda_c (2593) resonance. We find a small mass shift for the D-meson in this hot and dense medium while the spectral density develops a sizeable width. The reduced attraction felt by the D-meson in hot and dense matter together with the large width observed have important consequences for the D-meson production in the future CBM experiment at FAIR.
The production of Large Extra Dimension (LXD) Black Holes (BHs), with a new, fundamental mass scale of M_f = 1 TeV, has been predicted to occur at the Large Hadron Collider, LHC, with the formidable rate of 10^8 per year in p-p collisions at full energy, 14 TeV, and at full luminosity. We show that such LXD-BH formation will be experimentally observable at the LHC by the complete disappearance of all very high p_t (> 500 GeV) back-to-back correlated Di-Jets of total mass M > M_f = 1 TeV. We suggest to complement this clear cut-off signal at M > 2*500 GeV in the di-jet-correlation function by detecting the subsequent, Hawking-decay products of the LXD-BHs, namely either multiple high energy (> 100 GeV) SM Mono-Jets (i.e. away-side jet missing), sprayed off the evaporating BHs isentropically into all directions or the thermalization of the multiple overlapping Hawking-radiation in a eckler-Kapusta-Plasma. Microcanonical quantum statistical calculations of the Hawking evaporation process for these LXD-BHs show that cold black hole remnants (BHRs) of Mass sim M_f remain leftover as the ashes of these spectacular Di-Jet-suppressed events. Strong Di-Jet suppression is also expected with Heavy Ion beams at the LHC, due to Quark-Gluon-Plasma induced jet attenuation at medium to low jet energies, p_t < 200 GeV. The (Mono-)Jets in these events can be used to trigger for Tsunami-emission of secondary compressed QCD-matter at well defined Mach-angles, both at the trigger side and at the awayside (missing) jet. The Machshock-angles allow for a direct measurement of both the equation of state EoS and the speed of sound c_s via supersonic bang in the "big bang" matter. We discuss the importance of the underlying strong collective flow - the gluon storm - of the QCD- matter for the formation and evolution of these Machshock cones. We predict a significant deformation of Mach shocks from the gluon storm in central Au+Au collisions at RHIC and LHC energies, as compared to the case of weakly coupled jets propagating through a static medium. A possible complete stopping of pt > 50 GeV jets at the LHC in 2-3 fm yields nonlinear high density Mach shocks in he quark gluon plasma, which can be studied in the complex emission and disintegration pattern of the possibly supercooled matter. We report on first full 3-dimensional fluid dynamical studies of the strong effects of a first order phase transition on the evolution and the Tsunami-like Mach shock emission of the QCD matter.
The rapidity dependence of the single- and double- neutron to proton ratios of nucleon emission from isospin-asymmetric but mass-symmetric reactions Zr+Ru and Ru+Zr at energy range 100 ~ 800 A MeV and impact parameter range 0 ~ 8 fm is investigated. The reaction system with isospin-asymmetry and mass-symmetry has the advantage of simultaneously showing up the dependence on the symmetry energy and the degree of the isospin equilibrium. We find that the beam energy- and the impact parameter dependence of the slope parameter of the double neutron to proton ratio (F_D) as function of rapidity are quite sensitive to the density dependence of symmetry energy, especially at energies E_b ~ 400 A MeV and reduced impact parameters around 0.5. Here the symmetry energy effect on the F_D is enhanced, as compared to the single neutron to proton ratio. The degree of the equilibrium with respect to isospin (isospin mixing) in terms of the F_D is addressed and its dependence on the symmetry energy is also discussed.
We investigate the onset of multifragmentation employing an improved version of the N-body ‘‘quantum’’ molecular-dynamics approach. We study in detail the reaction 18O+197Au at 84 MeV/nucleon and find good agreement between the calculated results and the data for the double-differential proton cross section, the mass yield, the multiplicity, the kinetic energy of the fragments, and even for the kinematic correlations between intermediate mass fragments (IMF’s), which have been measured in this experiment for the first time. We observe a strong correlation between the impact parameter and both the size of the target remnant as well as the average proton multiplicity. Hence both observables can be used to determine the impact parameter experimentally. The IMF’s come from the most central collisions. The calculations confirm the experimental result that they are not emitted from an equilibrated system. Although the inclusive energy spectra look thermal, we cannot identify an impact parameter-independent isotropically emitting source. Even in central collisions global equilibrium is not observed. We find that multifragment emission at this bombarding energy is caused by a process very similar to that proposed in the macroscopic cold multifragmentation model. Thus it has a different origin than at beam energies around 1 GeV/nucleon, although the mass yield has an almost identical slope.
We investigate the hydrodynamical flow of nuclear matter in a conical-shock-wave scenario of a central, asymmetric heavy-ion collision. This work is motivated by a suggestion of Chapline and Granik that the creation of a deconfined phase of quarks and gluons behind the shock will appreciably increase the deflection angle of the matter flow. We employ several hadron matter equations of state recently suggested to solve the conical-shock-wave problem and compare the results with a calculation using the bag equation of state. We find that large differences in the deflection angle obtained in the rest frame of the shock vanish in the laboratory system. However, a signature for the deconfinement transition may be the transverse momentum of the matter flow, which is up to a factor of 2 larger for the quark-gluon plasma. Thus, an excitation function of the mean transverse momentum would show an increase at a certain bombarding energy, signaling the onset of the deconfinement transition.
We study the transition from fusion-fission phenomena at about 20 MeV/nucleon multifragmentation at 100–200 MeV/nucleon in the reaction 16O+80Br employing the quantum molecular dynamics model. The time evolution of the density and mass distribution, the charged-particle multiplicity, and spectra as well as angular distributions of light particles are investigated. The results exhibit the transition of the disassembly mechanism, but no sharp change is found. The results are in good agreement with recently measured 4-Pi data.
Inclusive neutron spectra were measured at 0°, 4°, 8°, 15°, 30°, and 42° from Nb-Nb and Au-Au collisions at 800 MeV/nucleon. A peak that originates from neutron evaporation from the projectile appears in the spectra at angles out to 8°. The shapes and magnitudes of the spectra are compared with those calculated from models of nucleus-nucleus collisions. The differential cross sections for Au-Au collisions are about four times those for Nb-Nb collisions. The predictions of the Vlasov-Uehling-Uhlenbeck (VUU) and QMD theories agree with the angular distributions of the differential cross sections except at small angles; the VUU prediction overestimates the angular distributions from a few degrees to about 20°, whereas the QMD prediction underestimates the angular distributions below 8°. The Firestreak model overestimates the angular distribution for Nb-Nb collisions and underestimates it for Au-Au collisions. Also, the VUU and QMD models agree with the measured double-differential cross sections in more angular and energy regions than the Firestreak and intranuclear cascade models; however, none of the models can account for the peaks at small angles (θ≤15°).
Within a relativistic mean-field theory (RMFT) experimental data on the single-particle spectra of lambda hypernuclei are well reproduced. It is shown that the coupling constants cannot be fixed unambiguously from the single-particle spectra. The stability and structure of multi-lambda hypernuclei is explored on the basis of the RMFT using the coupling constants as determined from the observed single lambda hypernuclear levels. It is predicted that multistrange nuclei exhibit an enhanced interaction radius, which further increases in the case of finite temperatures. We suggest that multi-lambda hypernuclei could be produced in high-energy heavy ions and observed in secondary noncharge-changing reactions. The equation of state of lambda matter and the possibility of pure lambda droplets are also discussed.
Shock discontinuities around the confinement-deconfinement transition in baryon-rich dense matter
(1989)
Nuclear transport models are important tools for interpretation of many heavy-ion experiments and are essential in efforts to probe the nuclear equation of state. In order to fulfill these roles, the model predictions should at least agree with observed single-particle-inclusive momentum spectra; however, this agreement has recently been questioned. The present work compares the Vlasov-Uehling-Uhlenbeck model to data for mass-symmetric systems ranging from 12C+12C to 139La+139La, and we find good agreement within experimental uncertainties at 0.4A and 0.8A GeV. For currently available data, these uncertainties are too large to permit effective nucleon-nucleon scattering cross sections in the nuclear medium to be extracted at a useful level of precision.
Nuclear transport models including density- and momentum-dependent mean-field effects are compared to intranuclear-cascade models and tested on recent data on inclusive p-like cross sections for 800A-MeV La+La. We find a remarkable agreement between most model calculations but a systematic disagreement with the measured yield at 20°, possibly indicating a need for modification of nuclear transport properties at high densities.
The quantum molecular dynamic method is used to study multifragmentation and fragment flow and their dependence on in-medium cross sections, momentum dependent interactions, and the nuclear equation of state, for collisions of 197Au+197Au and 93Nb+93Nb in the bombarding energy regime from 100 to 800A MeV. Time and impact parameter dependence of the fragment formation and their implications for the conjectured liquid-vapor phase transition are investigated. We find that the inclusive fragment mass distribution is independent of the equation of state and exhibits a power-law behavior Y(A)∼A-τ with an exponent τ≊-2.3. True multifragmentation events are found in central collisions for energies Elab∼30–200 MeV/nucleon. The associated light fragment (d,t,α) to proton ratios increase with the multiplicity of charged particles and decrease with energy, in agreement with recent experiments. The calculated absolute charged particle multiplicities, the multiplicities of intermediate mass (A>4) fragments, and their respective rapidity distributions do compare well with recent 4π data, but are quite insensitive to the equation of state. On the other hand, these quantities depend sensitively on the nucleon-nucleon scattering cross section, and can be used to determine σ experimentally. The transverse momentum flow of the complex fragments increases with the stiffness of the equation of state. Reduced (in-medium) n-n scattering cross sections reduce the fragment flow. Momentum dependent interactions increase the fragment flow. It is shown that the measured fragment flow at 200A MeV can be reproduced in the model. We find that also the increase of the px/A values with the fragment mass is in agreement with experiments. The calculated fragment flow is too small as compared to the plastic ball data, if a soft equation of state with in-medium corrections (momentum dependent interactions plus reduced cross sections) is employed. An alternative, most intriguing resolution of the puzzle about the stiffness of the equation of state could be an increase of the scattering cross sections due to precritical scattering in the vicinity of a phase transition.
The statistical model is used to illustrate the consequences of a successive binary decay mechanism as the initial nuclear excitation is pushed towards the limits of stability. The partition of the excitation energy between light and heavy fragments is explicitly calculated, as are the consequences of the decay of the primary light fragments to particle-bound residual nuclei which would be observed experimentally. The test nucleus 100 44 Ru is considered at initial excitations of 100, 200, 400, and 800 MeV. Exit channels of n, p, and α; and 100 clusters of 3 ≤ Z ≤ 20 ≤ 4, 6 ≤ A ≤ 48 are considered from all nuclides in the deexcitation cascade. The total primary and final cluster yields are shown versus Z and initial excitation. The primary versus final yields are also shown individually for 12C, 26Mg, and 48Ca. We show how multifragmentation yields will change with the excitation energy due to a successive binary decay mechanism. Measurements that may be prone to misinterpretation are discussed, as are those that should be representative of initial nucleus excitation.
Distillation and survival of strange quark matter droplets in ultrarelativistic heavy ion collisions
(1991)
Recently it has been suggested that rather cold droplets of absolutely stable or metastable strange-quark matter may be distilled in heavy-ion collisions during the phase transition from a baryon-rich quark-gluon plasma (QGP) to hadron matter. Here we present a model describing the hadronization of the QGP through particle emission, which is based solely on thermodynamical arguments. Pions and K+’s and K0’s carry away entropy and antistrangeness from the system, thus facilitating the cooling process and the strangelet formation. Our results are supported by revised more sophisticated rate calculations. Two rather unexpected results are obtained when this model is applied to the investigation of strangelet production. The strangeness separation mechanism and the formation process works well even for higher initial entropies per baryon, tantamount to higher bombarding energies. The surviving strangelets have a rather high strangeness content, fs∼1.2–2 [i.e., Z/A∼(-0.1)–(-0.5)]. Hence droplets of strange-quark matter with a baryon number of ∼10–30 and with a negative charge may be produced. They may serve as a unique signature for the transient formation of a quark-gluon plasma in heavy-ion collisions.
Relativistic heavy ion collisions constitute a prolific source of hyperons: tens of hyperons per event are predicted at energies E≥10 GeV/nucleon, providing a scenario for the formation of metastable exotic multihypernuclear objects. They may exhibit exceptional properties: bound neutral (e.g., 4M2Λ2n, 10M2Λ8n, pure Λ droplets, 8Λ) and even negatively charged composites objects with positive baryon number (e.g., 4M2Σ-2n, 6M2Λ2Ξ-2n) could be formed in rare events. Such negative nuclei can easily be identified in a magnetic spectrometer. They could be considerably more abundant than antinuclei of the same A. We use the relativistic meson-baryon field theory—which gives an excellent description of normal nuclear and single-Λ hypernuclear properties—to calculate the rich spectrum of such exotic objects, their stability, and their structure. We also find solutions for a large variety of bound short-lived nuclei (e.g., 8M2Λ,2Σ-2p2n), which may decay strongly via formation of cascade (Ξ) particles. Multi-Ξ hypernuclei are also evaluated. A variety of potential candidates for such metastable exotic nuclei is presented. It turns out that the properties of such exotic multihypernuclear objects reveal quite similar features as the strangelet proposed as a unique signature for quark-gluon plasma formation in heavy ion collisions.
We present a new type of flow analysis, based on a particle-pair correlation function, in which there is no need for an event-by-event determination of the reaction plane. Consequently, the need to correct for dispersion in an estimated reaction plane does not arise. Our method also offers the option to avoid any influence from particle misidentification. Using this method, streamer chamber data for collisions of Ar+KCl and Ar+BaI2 at 1.2 GeV/nucleon are compared with predictions of a nuclear transport model.
A quasiclassical Pauli potential is used to simulate the Fermi motion of nucleons in a molecular dynamical simulation of heavy ion collisions. The thermostatic properties of a Fermi gas with and without interactions are presented. The inclusion of this Pauli potential into the quantum molecular dynamics (QMD) approach yields a model with well defined fermionic ground states, which is therefore also able to give the excitation energies of the emitted fragments. The deexcitation mechanisms (particle evaporation and multifragmentation) of the new model are investigated. The dynamics of the QMD with Pauli potential is tested by a wide range of comparisons of calculated and experimental double-differential cross sections for inclusive p-induced reactions at incident energies of 80 to 160 MeV. Results at 256 and 800 MeV incident proton energy are presented as predictions for completed experiments which are as yet unpublished.
Stopping power and thermalization in relativistic heavy ion collisions is investigated employing the quantum molecular dynamics approach. For heavy systems stopping of the incoming nuclei is predicted, independent of the energy. The influence of the quantum effects and their increasing importance at low energies, is demonstrated by inspection of the mean free path of the nucleons and the n-n collision number. Classical models, which neglect these effects, overestimate the stopping and the thermalization as well as the collective flow and squeeze out. The sensitivity of the transverse and longitudinal momentum transfer to the in-medium cross section and to the pressure is investigated.
Experimental results are presented on the charge, velocity, and angular distributions of intermediate mass fragments (IMFs) for the reaction Fe+Au at bombarding energies of 50 and 100 MeV/nucleon. Results are compared to the quantum molecular dynamics (QMD) model and a modified QMD which includes a Pauli potential and follows the subsequent statistical decay of excited reaction products. The more complete model gives a good representation of the data and suggests that the major source of IMFs at large angles is due to multifragmentation of the target residue.
We present a RQMD calculation of antiproton yields and their momentum distribution in Ne + NaF collisions at 2 GeV/u. The antiprotons can be produced below threshold due to multi-step excitations for which meson-baryon interactions play a considerable role. In this system the annihilation probability for an initially produced antiproton is predicted to be about 65%.
Strange hadronic matter
(1993)
In an extended mean field theory, we find a large class of bound multistrange objects, formed from combinations of {p,n,Λ,Ξ0,Ξ-} baryons, which are stable against strong decay. We predict a maximal binding energy per baryon of EB/A≊-21 MeV, strangeness per baryon fs≊1.2, charge per baryon fq≊-0.1 to 0, and baryon density 2.5–3 times that of ordinary nuclei. For A≥6, we obtain stable combinations involving only {Λ,Ξ0,Ξ-} hyperons.
Strong correlations between baryon stopping in the projectile rapidity hemisphere and target excitation have been found in the light-ion-induced reactions at the BNL Alternating Gradient Synchrotron (AGS) (E814 group). Results in the framework of the relativistic molecular dynamics approach (RQMD) describe recent E814 data quite well. We discuss the RQMD results together with proton and pion data from the E802 group near midrapidity. They have raised the question of whether partial transparency could be seen in these experiments. The RQMD results indicate strong transverse baryon flow in central Si+Au collisions after the projectile has been stopped in the target.
We present a calculation of antiproton yields in Si+Al and Si+Au collisions at 14.5A GeV in the framework of the relativistic quantum molecular dynamics approach (RQMD). Multistep processes lead to the formation of high-mass flux tubes. Their decay dominates the initial antibaryon yield. However, the subsequent annihilation in the surrounding baryon-rich matter suppresses the antiproton yield considerably: Two-thirds of all antibaryons are annihilated even for the light Si+Al system. Comparisons with preliminary data of the E802 experiment support this analysis.
Accurate impact parameter determination in a heavy-ion collision is crucial for almost all further analysis. We investigate the capabilities of an artificial neural network in that respect. First results show that the neural network is capable of improving the accuracy of the impact parameter determination based on observables such as the flow angle, the average directed inplane transverse momentum and the difference between transverse and longitudinal momenta. However, further investigations are necessary to discover the full potential of the neural network approach.
Azimuthal correlations of pions are studied with the quantum molecular dynamics model. Pions are preferentially emitted perpendicular to the reaction plane. Our analysis shows that this anisotropy is dominated by pion absorption on the spectator matter in the reaction plane. Pions emitted perpendicular to the reaction plane undergo less rescattering than those emitted in the reaction plane and might therefore be more sensitive to the early hot and dense reaction phase.
We study dilepton production from a quark-gluon plasma of given energy density at finite quark chemical potential μ and find that the dilepton production rate is a strongly decreasing function of μ. Therefore, the signal to background ratio of dileptons from a plasma created in a heavy-ion collision may decrease significantly.
Viscous hydrodynamic calculations of high energy heavy-ion collisions (Nb-Nb and Au-Au) from 200 to 800 MeV/nucleon are presented. The resulting baryon rapidity distributions, the in-plane transverse momentum transfer (bounce-off), and the azimuthal dependence of the midrapidity particles (off-plane squeeze out) compare well with Plastic Ball data. We find that the considered observables are sensitive both to the nuclear equation of state and to the nuclear shear viscosity η. Transverse momentum distributions indicate a high shear viscosity (η≊60 MeV/fm2 c) in the compression zone, in agreement with nuclear matter estimates. The bulk viscosity ζ influences only the entropy production during the expansion stage; collective observables like flow and dN/dY do not depend strongly on ζ. The recently observed off-plane (φ=90°) squeeze-out, which is found in the triple-differential rapidity distribution, exhibits the strongest sensitivity to the nuclear equation of state. It is demonstrated that for very central collisions, b=1 fm, the squeeze-out is visible even in the double-differential cross section. This is experimentally accessible by studying azimuthally symmetric events, as confirmed recently by data of the European 4π detector collaboration at Gesellchaft für Schwerionforschung Darmstadt.
If density isomers exist they can be detected by measuring the excitation function of subthreshold kaon production. When the system reaches the density where the density isomer has influence on the equation of state (which depends on the beam energy and on the optical potential), we observe a jump in the cross section of the kaons whereas other observables change little. Above threshold Λ¯’s or p¯’s may be used to continue the search. This is the result of microscopic Boltzman-Uehling-Uhlenbeck calculations.
This thesis presents a model for the dynamical description of deconfined quark matter created in ultra-relativistic heavy ion collisions, treating quarks and antiquarks as classical point particles subject to a colour-dependent, Cornell-type potential interaction. The model provides a dynamical handle for hadronization via the recombination of quarks and antiquarks in colour neutral clusters. Gluons are not included explicitly in the model,but are described in an effective manner by the means of the potential interaction. The model includes four different quark flavours (up, down, strange and charm) and uses current masses for the quarks. The dynamical evolution of a system of colour charges subject to the Hamiltonian equations of motion of the model yields the formation of colour neutral clusters of quarks and antiquarks, which are subject only to a small remaining interaction, the strong interquark potential notwithstanding. These clusters can be mapped onto hadrons and hadronic resonances. Thus, the model allows a dynamical description of quarks degrees of freedom in heavy ion collisions, including a recombination scheme for hadronization. The thermal properties of the model turn pout to be very satisfying. The model shows a transition from a confining phase to a deconfined phase with rising temperature, going hand in hand with a softest point in the equation of state and a rise of energy density and pressure to the Stefan-Boltzmann limit of a gas of quarks and antiquarks. Moreover, the potential interaction is screened in the deconfined phase. For the dynamical description of ultra-relativistic heavy ion collision, the qMD model is coupled to UrQMD as a generator for its initial conditions. In this way, a fully dynamical description of the expansion and hadronization of the fireball created in such collisions can be achieved. Non-equilibrium aspects of the expansion dynamics and hadronization by recombination of quarks and antiquarks are discussed in detail, and a comparison with experimental data of collisions at the CERN-SPS is presented. The big advantage of the qMD model is the possibility to study cluster formation, including exotic clusters, and fluctuations in a dynamical manner. As an example, event-by-event fluctuations in electric charge are studied. Such fluctuations have been proposed as a clear criterion to distinguish a deconfined system from a hadrons gas. However, experimental data show hadron gas fluctuation measures even at RHIC, where deconfinement is taken for granted. We will see how the dynamics of quark recombination washes out the quark-gluon plasma signal in the fluctuation criterion. Moreover, we will discuss briefly the problem of entropy at recombination. In a second application, the formation of exotic hadronic clusters, larger than usual mesons and baryons, is studied. Such clusters could provide new measures for the thermalization and homogenization of a deconfined gas of colour charges. Moreover, number estimates for exotic clusters from recombination are considerably lower than corresponding predictions from thermal models, providing a clear difference between statistical hadronization and hadronization via quark recombination. A detailed analysis is provided for pentaquark candidates such as the Theta-Plus. It turns out that the distribution of exotic states over strangeness, isospin, and spin could provide a sensitive measure for thermalization and decorrelation in the deconfined quark phase, if it could be measured.
We demonstrate the occurrence of canonical suppression associated with the conservation of an U(1)-charge in current transport models. For this study a pion gas is simulated within two different transport approaches by incorporating inelastic and volume-limited collisions pi pi leftrightarrow K bar-K for the production of kaon pairs. Both descriptions can dynamically account for the suppression in the yields of rare strange particles in a limited box, being in full accordance with a canonical statistical description.
The transverse momentum dependence of the anisotropic flow v_2 for pi, K, nucleon, Lambda, Xi and Omega is studied for Au+Au collisions at sqrt s_NN = 200 GeV within two independent string-hadron transport approaches (RQMD and UrQMD). Although both models reach only 60% of the absolute magnitude of the measured v_2, they both predict the particle type dependence of v_2, as observed by the RHIC experiments: v_2 exhibits a hadron-mass hierarchy (HMH) in the low p_T region and a number-of-constituent-quark (NCQ) dependence in the intermediate p_T region. The failure of the hadronic models to reproduce the absolute magnitude of the observed v_2 indicates that transport calculations of heavy ion collisions at RHIC must incorporate interactions among quarks and gluons in the early, hot and dense phase. The presence of an NCQ scaling in the string-hadron model results suggests that the particle-type dependencies observed in heavy-ion collisions at intermediate p_T are related to the hadronic cross sections in vacuum rather than to the hadronization process itself, as suggested by quark recombination models.
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.
Elliptic flow analysis at RHIC with the Lee-Yang Zeroes method in a relativistic transport approach
(2006)
The Lee-Yang zeroes method is applied to study elliptic flow (v_2) in Au+Au collisions at sqrt s =200 A GeV, with the UrQMD model. In this transport approach, the true event plane is known and both the nonflow effects and event-by-event v_2 fluctuations exist. Although the low resolutions prohibit the application of the method for most central and peripheral collisions, the integral and differential elliptic flow from the Lee-Yang zeroes method agrees with the exact v_2 values very well for semi-central collisions.
We propose to measure correlations of heavy-flavor hadrons to address the status of thermalization at the partonic stage of light quarks and gluons in high-energy nuclear collisions, shown on the example of azimuthal correlations of D-Dbar pairs. We show that hadronic interactions at the late stage can not disturb these correlations significantly. Thus, a decrease or the complete absence of these initial correlations indicates frequent interactions of heavy-flavor quarks in the partonic stage. Therefore, early thermalization of light quarks is likely to be reached. PACS numbers: 25.75.-q
In this paper we derive a formula for the energy loss due to elastic N to N particle scattering in models with extra dimensions that are compactified on a radius R. In contrast to a previous derivation we also calculate additional terms that are suppressed by factors of frequency over compactification radius. In the limit of a large compactification radius R those terms vanish and the standard result for the non compactified case is recovered.
The pion source as seen through HBT correlations at RHIC energies is investigated within the UrQMD approach. We find that the calculated transverse momentum, centrality, and system size dependence of the Pratt-HBT radii R_L and R_S are reasonably well in line with experimental data. The predicted R_O values in central heavy ion collisions are larger as compared to experimental data. The corresponding quantity sqrt R_O^2-R_S^2 of the pion emission source is somewhat larger than experimental estimates.
Gravitational radiation from ultra high energy cosmic rays in models with large extra dimensions
(2006)
The effects of classical gravitational radiation in models with large extra dimensions are investigated for ultra high energy cosmic rays (CRs). The cross sections are implemented into a simulation package (SENECA) for high energy hadron induced CR air showers. We predict that gravitational radiation from quasi-elastic scattering could be observed at incident CR energies above 10^9 GeV for a setting with more than two extra dimensions. It is further shown that this gravitational energy loss can alter the energy reconstruction for CR energies E_CR > 5 10^9 GeV.
No black holes at IceCube
(2006)
This work is dedicated to the investigation of nuclear matter at non-zero temperatures within an effective hadronic model based on the Walecka model. It includes fermions as well as a vector omega meson and a scalar sigma meson where for the latter a quartic self-interaction has been considered. The coupling constants have been adapted to the saturation properties of infinite nuclear matter. A set of self-consistent Schwinger-Dyson equations has been set up for all included particles within the Cornwall-Jackiw-Tomboulis formalism. This has been expanded to non-zero temperatures via the imaginary time formalism. Beside tree-level two different stages of approximations have been considered: the Hartree approximation which takes into account the double-bubble diagram for the scalar meson, and an improved approximation where in addition two-particle irreducible sunset diagrams for all fields were included. In the Hartree-approximation the Schwinger-Dyson equations can be solved by quasi-particle ansaetze, while in the improved approximation spectral functions with non-zero widths have to be introduced. The Schwinger-Dyson equations are solved by the fully dressed propagators. Comparing the two levels of approximation shows the influence of finite widths on the temperature dependence of the particle properties. The consideration of finite widths in fact has a significant influence on the transition from a phase of heavy nucleons to a transition of light nucleons, observed in the Walecka-model. The temperature dependence is weakend when finte widths are taken into account.
In order to investigate the role of neuronal synchronization in perceptual grouping, a new method was developed to record selectively from multiple cortical sites of known functional specificity as determined by optical imaging of intrinsic signals. To this end, a matrix of closely spaced guide tubes was developed in cooperation with a company providing the essential manufacturing technique RMPD® (Rapid Micro Product Development). The matrix was embedded into a framework of hard and software that allowed for the mapping of each guide tube onto the cortical site an electrode would be led to if inserted into that guide tube. With these developments, it was possible to determine the functional layout of the cortex by optical imaging and subsequently perform targeted recordings with multiple electrodes in parallel. The method was tested for its accuracy and found to target the electrodes with a precision of 100 µm to the desired cortical locations. Using the developed technique, neuronal activity was recorded from area 18 of anesthetized cats. For stimulation, Gabor-patches in different geometrical configurations were placed over the recorded receptive fields merging into visual objects appropriate for testing the hypothesis of feature binding by synchrony. Synchronization strength was measured by the height of the cross-correlation centre peaks. All pairwise synchronizations were summarized in a correlation index which determined the mean difference of the correlation strengths between conditions in which recording sites should or should not fire in synchrony according to the binding hypothesis. The correlation index deviated significantly from zero for several of these configurations, further supporting the hypothesis that synchronization plays an important role in the process of perceptual grouping. Furthermore, direct evidence was found for the independence of the synchronization strength from the neuronal firing rate and for neurons that change dynamically the ensemble they participate in. In parallel to the experimental approach, mechanisms of oscillatory long range synchronization were studied by network simulations. To this end, a biologically plausible model was implemented using pyramidal and basket cells with Hodgkin-Huxley like conductances. Several columns were built from these cells and intra- and inter-columnar connections were mimicked from physiological data. When activated by independent Poisson spike trains, the columns showed oscillatory activity in the gamma frequency range. Correlation analysis revealed the tendency to locally synchronize the oscillations among the columns, but a rapid phase transition occurred with increasing cortical distance. This finding suggests that the present view of the inter-columnar connectivity does not fully explain oscillatory long range synchronization and predicts that other processes such as top-down influences are necessary for long range synchronization phenomena.
Das HADES-Experiment (High Acceptance DiElectron Spectrometer) am SIS der GSI wurde zur Messung der e+e- - Paare dileptonischer Zerfälle der leichten Vektormesonen im Energiebereich von 1 - 2 AGeV entwickelt. Im Rahmen dieser Arbeit wurden die Eigenschaften des Spurverfolgungssystems de HADES-Spektrometers untersucht. Das Spurverfolgungssystem besteht aus vier Ebenen mit Vieldrahtdriftkammern (Mini Drift Chambers (MDCs)) niedriger Massenbelegung (low-mass), die aus je 6 Auslesedrahtebenen bestehen. Eine der Hauptanforderungen an das Spurverfolgungssystem ist eine Ortsauflösung von 100 µm (hauptsächlich in y-Richtung), die benötigt wird, um die geforderte Massenauflösung von 1 % im Bereich der w-Masse zu erzielen. Gleichzeitig muss die Nachweiseffizienz für schwach ionisierende Elektronen/Positronen hoch sein. Die primäre Messgröße von Driftkammern ist die Driftzeit der entlang einer Teilchenspur generierten Elektronen der Primärionisation zum Auslesedraht. Um die gemessene Driftzeit in eine Ortskoordinate umrechnen zu können, ist eine genaue Kenntnis der Ort-Zeit-Korrelation der Driftzellen nötig. Es wurden detaillierte Simulationen der He/i - Butan Zählgasmischung mit GARFIELD, MAGBOLTZ und HEED vorgenommen. Dabei wurden Gastemperatur, Gasdruck, sowie die Kontamination des Zählgases mit O2 und H20 und die Konzentration des Löschgases variiert und die Auswirkung auf die Driftgeschwindigkeit der Elektronen und damit auf Ort-Zeit-Korrelation der Driftzellen studiert Des Weiteren wurden die Auswirkung der Höhe der Diskriminatorschwelle der Ausleseelektronik und der Einfluss des magnetischen Feldes auf die Driftzeitmessung untersucht. Ein zweidimensionales Modell der Driftzellen, das die Abhängigkeit der Ort-Zeit-Korrelation vom Einfallswinkel des Teilchens in die Driftzelle berücksichtigt, wurde in die Spurrekonstruktionssoftware integriert. Das realistische Ansprechverhalten der Driftkammern wurde in die GEANT-Simulation des HADES-Experimentes implementiert. In der vorliegenden Arbeit wird das Ansprechverhalten der inneren Driftkammern anhand von C + C Daten analysiert, die bei einer Einschussenergie von 2 AGeV im November 2001 gemessen wurden. Es wurde eine neue Methode entwickelt, die aus der Breite des am Auslesedraht influenzierten Signals (time above threshold) eine dem Energieverlust eines Teilchens korrelierte Größe bestimmt, die sich zur Identifikation von Teilchen eignet. Die vorgestellte Methode der Energieverlustmessung besitzt eine Auflösung von etwa 10 % für minimal ionisierende Teilchen und etwa 7, 2 % für stark ionisierenden Teilchen. Die Ortsauflösung der Driftzellen betrug 128 - 154 µm für minimal ionisierende Teilchen und 84 - 116µm für stark ionisierende Teilchen. Für minimal ionisierende Teilchen wurde die Ortsauflösung der Driftkammern in x- und y-Richtung zu x = 181 - 195µm und y = 87 - 104 µm bestimmt. Für stark ionisierende Teilchen wird eine Ortsauflösung von x = 119 - 148 µm und y = 57 - 79 µm erreicht. Eine Teilchenspur wird redundant in den 6 Drahtebenen einer Driftkammer nachgewiesen. Die Nachweiseffizienz der Drahtebenen einer Driftkammer lag für minimal ionisierende Teilchen bei 90 - 96 % und für stark ionisierende Teilchen bei 94 - 98 %. Es konnte somit gezeigt werden, dass die Driftkammern des HADES-Experiment über die geforderte Ortsauflösung und Nachweiseffizienz für e+|e- verfügen und aufgrund der Messung des Energieverlustes in den Driftkammern zur Teilchenidentifikation und Reduktion des Untergrundes beitragen können.
We introduce a smooth mapping of some discrete space-time symmetries into quasi-continuous ones. Such transformations are related with q-deformations of the dilations of the Euclidean space and with the non-commutative space. We work out two examples of Hamiltonian invariance under such symmetries. The Schrodinger equation for a free particle is investigated in such a non-commutative plane and a connection with anyonic statistics is found. PACS: 03.65.Fd, 11.30.Er
Results from various theoretical approaches and ideas presented at this exciting meeting (summary talk at the 5th International Conference on Physics and Astrophysics of Quark Gluon Plasma (ICPAQGP - 2005)) are reviewed. I also point towards future directions, in particular hydrodynamic behaviour induced by jets traveling through the quark-gluon plasma, which might be worth looking at in more detail.
Im Rahmen der vorliegenden Arbeit wurde ein Spracherkennungssystem realisiert, das sowohl phonembasierte als auch wortbasierte Modelle zur sprecherunabhängigen Schlüsselworterkennung im Kontext fließender Sprache verwenden kann. Das System erlaubt dabei die Wahl zwischen zwei grundlegend verschiedenen Verfahren: Entweder kann die Bewertung von Äußerungen durch Schlüsselwortmodelle mit gewählten Schwellenwerten verglichen werden, wobei eine Schwellenwertüberschreitung die Erkennung eines Schlüsselwortes signalisiert, oder es werden beliebige Phonemfolgen als Füllmodelle verwendet, die mit den Schlüsselwortmodellen konkurrieren. Der Schlüsselworterkenner kann sowohl zur 1-Schlüsselwort- Erkennung, bei der vorausgesetzt wird, dass sich in jeder Äußerung exakt ein Schlüsselwort befindet, als auch zur n-Schlüsselwort-Erkennung verwendet werden, bei der sich eine beliebige Anzahl Schlüsselwörter in jeder Äußerung befinden kann. Durch eine effiziente Implementation wurde die Fähigkeit zur Echtzeitverarbeitung auf verfügbaren Arbeitsplatzrechnern erreicht.....
Der Ursprung der Masse bekannter Teilchen und der Einschlu der Quarks in Hadronen ist einer der grundlegendsten Fragestellungen der modernen Physik. Die Kenntnis des Verhaltens von Kernmaterie unter extremen Bedingungen ist unabdingbar zum Verstandnis der Evolution des Universums und zur Theoriebildung von stellaren Objekten wie Neutronensternen und schwarzen Löchern. Einen experimentellen Zugang zur Untersuchung dieser Problematik stellt die Erzeugung heier und dichter Kernmaterie in ultrarelativistischen Schwerionenkollisionen dar. Hierzu untersucht das NA49 Experiment seit Herbst 1994 am 208-Pb-Strahl des CERN-SPS Pb+Pb Kollisionen bei 158 GeV pro Nukleon. Ein Schwerpunkt des Forschungsprogrammes liegt in der Untersuchung des Zustandes der Materie in der frühen Phase der Reaktion. Nach gegenwartem Stand der Theorie wird bei genugent hoher Energiedichte der Einschlu der Quarks in Hadronen aufgebrochen und ein Zustand der Materie erzeugt, in welchen die eektiven Freiheitsgrade von Hadronen und Hadronen-Resonanzen in die von Quarks und Gluonen übergehen - das sogenannte Quark-Gluon-Plasma (QGP). Die Honung ist nun, da sich die Formation eines solchen QGP im hadronischen Endzustand wiederspiegelt. Es wird erwartet, da die Seltsamkeitsproduktion in einem QGP sich in ihrer Rate und ihren Gleichgewichtswerten von der in einem hadronischen Feuerball-Szenario unterscheidet und sich somit als Signatur fur die Erzeugung eines GQP eignet. Von besonderen Interesse ist hier die Produktion von Hyperonen. Schwerpunkt dieser Arbeit ist die Untersuchung der Produktion von doppelt seltsamen geladenen -Hyperonen in zentralen Pb+Pb Kollisionen. Zu diesem Zweck wurden 58000 zentrale Pb+Pb Ereignisse der im Herbst 1995 aufgezeichneten Reaktionen untersucht. Die Analyse der Daten wurde auschlielich mit der zweiten Spurendriftkammer (VTPC2) durchgeführt. Zur Rekonstruktion der -Hyperonen muten Verfahren entwickelt werden, um die typischen Zerfalls-Topologien der doppelt seltsamen Hyperonen aus der Vielzahl von ca. 700 in der Vertex-TPC gemessenen geladenen Teilchenspuren herauszulösen. Aus den in der kombinatorischen Analyse rekonstruierten 720 und 138 + - Hyperonen konnten Spektren des Transversalimpulses und Rapiditatsverteilungen ermittelt werden. Die gewonnene Phasenraum-Akzeptanz fur die in der VTPC2 gemessenen und + - Hyperonen beträgt ....
Jet physics in ALICE
(2005)
This work aims at the performance of the ALICE detector for the measurement of high-energy jets at mid-pseudo-rapidity in ultra-relativistic nucleus-nucleus collisions at LHC and their potential for the characterization of the partonic matter created in these collisions. In our approach, jets at high energy with E_{T}>50 GeV are reconstructed with a cone jet finder, as typically done for jet measurements in hadronic collisions. Within the ALICE framework we study its capabilities of measuring high-energy jets and quantify obtainable rates and the quality of reconstruction, both, in proton-proton and in lead-lead collisions at LHC conditions. In particular, we address whether modification of the jet fragmentation in the charged-particle sector can be detected within the high particle-multiplicity environment of the central lead-lead collisions. We comparatively treat these topics in view of an EMCAL proposed to complete the central ALICE tracking detectors. The main activities concerning the thesis are the following: a) Determination of the potential for exclusive jet measurements in ALICE. b) Determination of jet rates that can be acquired with the ALICE setup. c) Development of a parton-energy loss model. d) Simulation and study of the energy-loss effect on jet properties.
Im Rahmen dieser Arbeit wurde der Aufbruchsmechanismus des Projektilspektators im relativistischen Energiebereich untersucht. Es zeigte sich dabei, daß die in vorherigen Experimenten beobachtete Targetunabhängigkeit der Fragmentproduktion bei 600 AMeV sich als universelle Eigenschaft des Zerfalls von angeregter und expandierter Kernmaterie erweist. Die Untersuchung von Ladungskorrelationen zeigte ebenfalls weder eine Energie- noch Projektilabhängigkeit im Rahmen der experimentellen Auflösung. Diese Ergebnisse sind im wesentlichen auch zu höheren und niedrigeren Energien von anderen Experimenten bestätigt worden. Mit diesem experimentellen Befund kann eindeutig der Beweis für die Existenz einer Multi-Fragmentproduktion bei relativistischen Energien gegeben werden. Im Rahmen von Modellen können die beobachteten Ladungsobservablen mit einem statistisch dominierten Zerfall erklärt werden. Die sich daran anschließende Frage nach dem Aufbruchsmechanismus und dessen Eigenschaften wurde weiterführend mit Ausrichtung auf kinematische und thermodynamische Eigenschaften des Systems untersucht. Dabei ergab sich, daß die kinematischen Observablen der Projektilquelle einen thermisch äquilibrierten Zustand widerspiegeln, unabhängig vom Stoßparameter und der Einschußenergie. Die hierbei beobachtete Emission von leichten Teilchen, die nicht eindeutig einer intermediären oder Projektilquelle zugeordnet werden konnten, ist hierbei Hinweis auf Nicht-Gleichgewichtsanteile, die in der frühen Phase der Reaktion gebildet werden. Mit der Untersuchung von kollektiven Eigenschaften des zerfallenden Systems wurde versucht, einen quantitativen Einblick in die Reaktionskinematik und den damit zusammenhängenden Energietransfer in den Projektilspektator zu erhalten. Diese Analysen ergaben, daß es bei gleichem Stoßparameter eine starke Abhängigkeit des "Bounce Off" von der Targetmasse gibt, während zu höheren Energien, beim gleichen System, nur ein kleiner Effekt zu höheren Impulsüberträgen (5-10 MeV/c) beobachtet wird. Die Energiebilanz des Systems und die hieraus extrahierten Anregungsenergien zeigten zum ersten Mal in experimentellen Daten ohne Zuhilfenahme von theoretischen Modellen, daß für die stark asymmetrischen Systeme nicht der gleiche Zusammenhang zwischen Anregungsenergie und Z bounce; erhalten wird wie bei den symmetrischen Systemen. Dies zeigt sich bei den asymmetrischen Systemen durch eine Saturation der Anregungsenergie mit kleiner werdendem Z bounce, im Gegensatz zu den symmetrischen Systemen, die einen weiteren Anstieg zeigen. Die absoluten Werte der maximalen Anregungsenergie von <E0/A0> ~ 21-23 MeV bei halbzentralen Reaktionen von 197 Au + 197 Au bei 800 AMeV und <E0/A0> ~27 MeV bei 238 U + 238 U 1000 AMeV sind verschieden bei gleichem Z bound. Es stellt sich jedoch heraus, daß mit Ausnahme der stark asymmetrischen Systeme die Anregungsenergie pro herausgeschlagenem Nukleon (<E Knock/A>) in Abhängigkeit von der prozentualen Größe des Prefragments zu peripheren Reaktionen monoton und energieunabhängig steigt.Werden die experimentell bestimmten Anregungsenergien verglichen mit denen aus theoretischen Modellen, so sind diese immer deutlich geringer. Im statistischen Modell von Botvina und Mitarbeitern, das von D´esesquelles mit unseren Daten verglichen wurde [D´ese 96] [D´ese 95], ergaben sich maximale Anregungsenergien von <E0/A0> ~ 7-8 MeV in zentralen Reaktionen. Ein Vergleich mit QMD + SMM ergibt, daß für die asymmetrischen Systeme (197AU + 12C)mit einer Anregungsenergien von maximal <E0/A0> ~ 8-9 MeV eine Beschreibung der Daten möglich ist. Für die symmetrischen Systeme zeigt sich eine zunehmende Diskrepanz mit zunehmender Targetmasse zwischen den experimentellen und theoretischen Anregungsenergien. Die Ladungsobservablen der Daten werden von der verwendeten QMD + SMM-Rechnung und der QMD (SACA)-Rechnung gut wiedergegeben. Durch Anpassung von Rechnungen mit dem Quantenstatischen Modell [Hahn 88b] (QSM) an die experimentellen Daten ergaben sich Aufbruchsdichten bei zentralen Reaktionen von rho/rho 0 ~ 0.3 bis 0.4, diese sind konsistent mit dem Aufbruch eines äquilibrierten und expandierten Systems. Die aus QSM erhaltenen Temperaturen des Quellsystems in Abhängigkeit von der Anregungsenergie geben im wesentlichen den von Pochodzalla und Mitarbeitern beobachteten Verlauf der kalorischen Kurve wieder. Die Frage, ob dieser Verlauf einen Phasenübergang von flüssig zu gasförmig darstellt, ist anhand dieser Methode nicht zu entscheiden. Die Ergebnisse der Ladungsobservablen in Verbindung mit den kollektiven Eigenschaften zeigen, daß die Anregungsenergie, die zum Erreichen des Maximums der M Fragmentproduktion ( <M IMF> ~ 4.4) nötig ist <E0/A0> ~ 11 MeV, einen geringeren absoluten Wert hat als der Bereich des möglichen Phasenübergangs <E0/A0> ~17 MeV. Im Gegensatz dazu stellt sich das Maximum der mittleren IMF -Produktion energie-, target- und projektilunabhängig bei <E0/A0> ~11 MeV ein. Mit diesemVergleich wird deutlich, daß zur näheren Untersuchung des Phasenübergangs von Kernmaterie nicht die in der Anregungsenergie saturierenden asymmetrischen Projektil-Target Kombinationen benutzt werden können. Die physikalische Fragestellung einer neuen Generation von Experimenten mit dem ALADIN-Detektor müßte in der Quantifizierung des Phasenübergangs und seiner dynamischen Observablen liegen. Dabei ist Beantwortung der Frage nach der zeitlichen Entwicklung der Fragmentproduktion über Korrelationen der Fragmente im Bereich des Phasenübergangs im Vergleich zum Maximum der universellen Kurve sowie die ereignisweise Bestimmung von dynamischen Observablen anzustreben.
In the present work, the Heidelberg electron beam ion trap (EBIT) at the Max-Planck-Institute für Kernphysik (MPIK) has been used to produce, trap highly charged argon ions and study their magnetic dipole (M1) forbidden transitions. These transitions are of relativistic origin and, hence, provide unique possibilities to perform precise studies of relativistic effects in many electron systems. In this way, the transitions energies of the 1s22s22p for the 2P3/2 - 2P1/2 transition in Ar13+ and the 1s22s2p for the 3P1 - 3P2 transition in Ar14+, for 36Ar and 40Ar isotopes were compared. The observed isotopic effect has confirmed the relativistic nuclear recoil effect corrections due to the finite nuclear mass in a recent calculation made by Tupitsyn [TSC03], in which major inconsistencies of earlier theoretical methods have been corrected for the first time. The finite mass, or recoil effect, composed of the normal mass shift (NMS), and the specific mass shift (SMS) were corrected for relativistic contributions, RNMS and RSMS. The present experimental results have shown that the recoil effects on the Breit level are indeed very important, as well as the effects of the correlated relativistic dynamics in a many electron ion.
This a review of the present status of heavy-ion collisions at intermediate energies. The main goal of heavy-ion physics in this energy regime is to shed some light on the nuclear equation of state (EOS), hence we present the basic concept of the EOS in nuclear matter as well as of nuclear shock waves which provide the key mechanism for the compression of nuclear matter. The main part of this article is devoted to the models currently used for describing heavy-ion reactions theoretically and to the observables useful for extracting information about the EOS from experiments. A detailed discussion of the flow effects with a broad comparison with the avaible data is presented. The many-body aspects of such reactions are investigated via the multifragmentation break up of excited nuclear systems and a comparison of model calculations with the most recent multifragmentation experiments is presented.
In the framework of the relativistic quantum dynamics approach we investigate antiproton observables in Au-Au collisions at 10.7A GeV. The rapidity dependence of the in-plane directed transverse momentum p(y) of p's shows the opposite sigh of the nucleon flow, which has indeed recently been discovered at 10.7A GeV by the E877 group. The "antiflow" of p's is also predicted at 2A GeV and at 160 A GeV and appears at all energies also for pi's and K's. These predicted p anticorrelations are a direct proof of strong p annihilation in massive heavy ion reactions.
The quantum statistical model (QSM) is used to calculate nuclear fragment distributions in chemical equilibrium. Several observable isotopic effects are predicted for intermediate energy heavy ion collisions. It is demonstrated that particle ratios for different systemsdo not depend on the breakup density-the only free parameter in our model.The importance of entropy measurements is discussed. Specific particle ratios for the system Au-Au are predicted, which can be used to determine the chemical potentials of the hot midrapidity fragment source in nearly central heavy ion collisions. Pacs-Nr. 25.70 Pq
The Monte Carlo parton string model for multiparticle production in hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions at high energies is described. An adequate choice of the parameters in the model gives the possibility of recovering the main results of the dual parton model, with the advantage of treating both hadron and nuclear interactions on the same footing, reducing them to interactions between partons. Also the possibility of considering both soft and hard parton interactions is introduced.
The properties of pions from the hot and dense reaction stage of relativistic heavy ion collisions are investigated with the quantum molecular dynamics model. Pions originating from this reaction stage stem from resonance decay with enhanced mass. They carry high transverse momenta. The calculation shows a direct correlation between high pt pions, early freeze-out times and high freeze-out densities.
Dilepton spectra for p+p and p+d reactions at 4.9GeV are calculated. We consider electromagnetic bremsstrahlung also in inelastic reactions. N* and Delta* decay present the major contributions to the pho and omega meson yields.Pion annihilation yields only 1.5% of all pho's in p+d. The pho mass spectrum is strongly distorted due to phase space effects, populating dominantly dilepton masses below 770MeV.
We calculate thermal photon and neutral pion spectra in ultrarelativistic heavy-ion collisions in the framework of three-fluid hydrodynamics. Both spectra are quite sensitive to the equation of state used. In particular, within our model, recent data for S + Au at 200 AGeV can only be understood if a scenario with a phase transition (possibly to a quark-gluon plasma) is assumed. Results for Au+Au at 11 AGeV and Pb + Pb at 160 AGeV are also presented.
We predict the formation of highly dense baryon-rich resonance matter in Au+Au collisions at AGS energies. The final pion yields show observable signs for resonance matter. The Delta1232 resonance is predicted to be the dominant source for pions of small transverse momenta. Rescattering e ects consecutive excitation and deexcitation of Delta's lead to a long apparent life- time (> 10 fm/c) and rather large volumina (several 100 fm3) of the Delta-matter state. Heavier baryon resonances prove to be crucial for reaction dynamics and particle production at AGS.
Strong mean meson fields, which are known to exist in normal nuclei, experience a violent deformation in the course of a heavy-ion collision at relativistic energies. This may give rise to a new collective mechanism of the particle production, not reducible to the superposition of elementary nucleon-nucleon collisions.
We investigate the sensivity of pionic bounce-off and squeeze-out on the density and momentum dependence of the real part of the nucleon optical potential. For the in-plane pion bounce-off we find a strong sensivity on both the density and momentum dependence whereas the out-of-plane pion squeeze-out shows a strong sensivity only towards the momentum dependence but little sensivity towards the density dependence.
We demonstrate the importance of the Bose-statistical effects for pion production in relativistic heavy-ion collisions. The evolution of the pion phase-space density in central collisions of ultrarelativistic nuclei is studied in a simple kinetic model taking into account the effect of Bose-simulated pion production by the NN collisions in a dense cloud of mesons.
Triple differential cross sections of pions in heavy ion collisions at 1 GeV/nucl. are studied with the IQMD model. After discussing general properties of resonance and pion production we focus on azimuthal correlations: At projectile- and target-rapidities we observe an anticorrelation in the in-plane transverse momentum between pions and protons. At c.m.-rapidity, however, we find that high pt pions are being preferentially emitted perpendicular to the event-plane. We investigate the causes of those correlations and their sensitivity on the density and momentum dependence of the real and imaginary part of the nucleon and pion optical potential.
The rapidity distribution of thermal photons produced in Pb+Pb collisions at CERN-SPS energies is calculated within scaling and three- fluid hydrodynamics. It is shown that these scenarios lead to very different rapidity spectra. A measurement of the rapidity dependence of photon radiation can give cleaner insight into the reaction dynamics than pion spectra, especially into the rapidity dependence of the temperature.
Spectra of various particle species have been calculated with the Quantum Molecular Dynamics (QMD) model for very central collisions of Au+Au. They are compatible with the idea of a fully stopped thermal source which exhibits a transversal expansion besides the thermal distribution of an ideal gas. How- ever, the microscopic analyses of the local flow velocities and temperatures indicate much lower temperatures at densities associated with the freeze-out. The results express the overall impossibility of a model-independent determi- nation of nuclear temperatures from heavy ion spectral data, also at other energies (e.g. CERN) or for other species (i.e. pions, kaons, hyperons)
In the framework of RQMD we investigate antiproton observables in massive heavy ion collisions at AGS energies and compare to preliminary results of the E878 collaboration. We focus here on the considerable influence of the real part of an antinucleon nucleus optical potential on the ¯p momentum spectra. Pacs-numbers: 14.20 Dh, 25.70.-z
In the framework of the relativistic quantum molecular dynamics approach (RQMD) we investigate antideuteron (d) observables in Au+Au collisions at 10.7 AGeV. The impact parameter dependence of the formation ratios d/p2 and d/p2 is calculated. In central collisions, the antideuteron formation ratio is predicted to be two orders of magnitude lower than the deuteron formation ratio. The d yield in central Au+Au collisions is one order of magnitude lower than in Si+Al collisions. In semicentral collisions di erent configuration space distributions of p s and d s lead to a large squeeze out e ect for antideuterons, which is not predicted for the p s.
Different numerical approaches and algorithms arising in the context of modelling of cellular tissue evolution are discussed in this thesis. Being suited in particular to off-lattice agent-based models, the numerical tool of three-dimensional weighted kinetic and dynamic Delaunay triangulations is introduced and discussed for its applicability to adjacency detection. As there exists no implementation of a code that incorporates all necessary features for tissue modelling, algorithms for incremental insertion or deletion of points in Delaunay triangulations and the restoration of the Delaunay property for triangulations of moving point sets are introduced. In addition, the numerical solution of reaction-diffusion equations and their connection to agent-based cell tissue simulations is discussed. In order to demonstrate the applicability of the numerical algorithms, biological problems are studied for different model systems: For multicellular tumour spheroids, the weighted Delaunay triangulation provides a great advantage for adjacency detection, but due to the large cell numbers the model used for the cell-cell interaction has to be simplified to allow for a numerical solution. The agent-based model reproduces macroscopic experimental signatures, but some parameters cannot be fixed with the data available. A much simpler, but in key properties analogous, continuum model based on reaction-diffusion equations is likewise capable of reproducing the experimental data. Both modelling approaches make differing predictions on non-quantified experimental signatures. In the case of the epidermis, a smaller system is considered which enables a more complete treatment of the equations of motion. In particular, a control mechanism of cell proliferation is analysed. Simple assumptions suffice to explain the flow equilibrium observed in the epidermis. In addition, the effect of adhesion on the survival chances of cancerous cells is studied. For some regions in parameter space, stochastic effects may completely alter the outcome. The findings stress the need of establishing a defined experimental model to fix the unknown model parameters and to rule out further models.
We calculate the evolution of quark-gluon-plasma droplets during the hadronization in a thermodynamical model. It is speculated that cooling as well as strangeness enrichment allow for the formation of strangelets even at very high initial entropy per baryon S/Ainit H 500 and low initial baryon numbers of Ainit B H 30. It is shown that the droplet with vanishing initial chemical potential of strange quarks and a very moderate chemical potential of up/down quarks immediately charges up with strangeness. Baryon densi- ties of H 2 0 and strange chemical potentials of µs > 350 MeV are reached if strangelets are stable. The importance of net baryon and net strangeness fluctuations for the possible strangelet formation at RHIC and LHC is em- phasized. Pacs-Classif.: 25.15.tr, 12.38.Mh, 24.85.tp
The extension of the Periodic System into hitherto unexplored domains - anti- matter and hypermatter - is discussed. Starting from an analysis of hyperon and single hypernuclear properties we investigate the structure of multi-hyperon objects (MEMOs) using an extended relativistic meson field theory. These are contrasted with multi-strange quark states (strangelets). Their production mechanism is stud- ied for relativistic collisions of heavy ions from present day experiments at AGS and SPS to future opportunities at RHIC and LHC. It is pointed out that abso- lutely stable hypermatter is unlikely to be produced in heavy ion collisions. New attention should be focused on short lived metastable hyperclusters ( / 10 10s) and on intensity interferometry of multi-strange-baryon correlations.
We demonstrate that the creation of strange matter is conceivable in the midrapidity region of heavy ion collisions at Brookhaven RHIC and CERN LHC. A finite net-baryon density, abundant (anti)strangeness production, as well as strong net-baryon and net-strangeness fluctuations, provide suitable initial conditions for the formation of strangelets or metastable exotic multistrange ( baryonic) objects. Even at very high initial entropy per baryon SyAinit ¯ 500 and low initial baryon numbers of Ainit B ¯ 30 a quark-gluon-plasma droplet can immediately charge up with strangeness and accumulate net-baryon number. PACS numbers: 25.75.Dw, 12.38.Mh, 24.85.+
Abstract: An accurate impact parameter determination in a heavy ion collision is crucial for almost all further analysis. The capabilities of an artificial neural network are investigated to that respect. A novel input generation for the network is proposed, namely the transverse and longitudinal momentum distribution of all outgoing (or actually detectable) particles. The neural network approach yields an improvement in performance of a factor of two as compared to classical techniques. To achieve this improvement simple network architectures and a 5 × 5 input grid in (pt, pz) space are suffcient.
We want to draw the attention to the dynamics of a (finite) hadronizing quark matter drop. Strange and antistrange quarks do not hadronize at the same time for a baryon-rich system1. Both the hadronic and the quark matter phases enter the strange sector fs 6= 0 of the phase diagram almost immediately, which has up to now been neglected in almost all calculations of the time evolution of the system. Therefore it seems questionable, whether final particle yields reflect the actual thermodynamic properties of the system at a certain stage of the evolution. We put special interest on the possible formation of exotic states, namely strangelets (multistrange quark clusters). They may exist as (meta-)stable exotic isomers of nuclear matter 2. It was speculated that strange matter might exist also as metastable exotic multi-strange (baryonic) objects (MEMO s 3). The possible creation in heavy ion collisions of long-lived remnants of the quark-gluon-plasma, cooled and charged up with strangeness by the emission of pions and kaons, was proposed in 1,4,5. Strangelets can serve as signatures for the creation of a quark gluon plasma. Currently, both at the BNL-AGS and at the CERN-SPS experiments are carried out to search for MEMO s and strangelets, e. g. by the E864, E878 and the NA52 collaborations9,
The microscopic phasespace approach URQMD is used to investigate the stopping power and particle production in heavy systems at SPS and RHIC energies. We find no gap in the baryon rapidity distribution even at RHIC. For CERN energies URQMD shows a pile up of baryons and a supression of multi-nucleon clusters at midrapidity.
The stopping behaviour of baryons in massive heavy ion collisions ( s k 10AGeV) is investigated within di erent microscopic models. At SPS-energies the predictions range from full stopping to virtually total transparency. Experimental data are indicating strong stopping. The initial baryo-chemical potentials and temperatures at collider energies and their impact on the formation probability of strange baryon clusters and strangelets are discussed.
Nuclear clusters as a probe for expansion flow in heavy ion reactions at 10-A/GeV - 15-A/GeV.
(1996)
A phase space coalescence description based on the Wigner-function method for cluster formation in relativistic nucleus-nucleus collisions is presented. The momentum distributions of nuclear clusters d,t and He are predicted for central Au(11.6AGeV)Au and Si(14.6AGeV)Si reactions in the framework of the RQMD transport approach. Transverse expansion leads to a strong shoulderarm shape and di erent inverse slope parameters in the transverse spectra of nuclear clusters deviating markedly from thermal distributions. A clear bounce-o event shape is seen: the averaged transverse flow velocities in the reaction plane are for clusters larger than for protons. The cluster yields particularly at low pt at midrapidities and the in-plane (anti)flow of clusters and pions change if suitably strong baryon potential interactions are included. This allows to study the transient pressure at high density via the event shape analysis of nucleons, nucleon clusters and other hadrons.
We investigate the properties of di erent modifications to the linear -model (including a dilaton field associated with broken scale invariance) at finite baryon density and nonzero temperature T. The explicit breaking of chiral symmetry and the way the vector meson mass is generated are significant for the appearance of a phase of nearly vanishing nucleon mass besides the solution describing normal nuclear matter. The elimination of the abnormal solution prohibits the onset of a chiral phase transition but allows to lower the compressibility to a reasonable range. The repulsive contributions from the vector mesons are responsible for the wide range of stability of the normal phase in the (µ, T)-plane. The abnormal solution becomes not only energet- ically preferable to the normal state at high temperature or density, but also mechanically stable due to the inclusion of dilatons. PACS number:12.39.F
We discuss the properties of two distinct forms of hypothetical strange matter, small lumps of strange quark matter (strangelets) and of hyperon matter (metastable exotic multihypernuclear objects: MEMOs), with special empha- sis on their relevance for present and future heavy ion experiments. The masses of small strangelets up to AB = 40 are calculated using the MIT bag model with shell mode filling for various bag parameters. The strangelets are checked for possible strong and weak hadronic decays, also taking into account multiple hadron decays. It is found that strangelets which are stable against strong decay are most likely highly negative charged, contrary to previous findings. Strangelets can be stable against weak hadronic decay but their masses and charges are still rather high. This has serious impact on the present high sensitivity searches in heavy ion experiments at the AGS and CERN facilities. On the other hand, highly charged MEMOs are predicted on the basis of an extended relativistic mean field model. Those objects could be detected in future experiments searching for short lived, rare composites. It is demonstrated that future experiments can be sensitive to a much wider variety of strangelets.
According to the Walecka mean field theory of nuclear interaction the collective mutual deceleration of the colliding nuclei gives rise to the bremsstrahlung of real and virtual ! mesons. It is shown that decays of these mesons may give a noticeable contribution to the observed yields of the baryon antibaryon pairs, dileptons and pions. Excitation functions and rapidity distributions of particles produced by this mechanism are calculated under some simplifying assumptions about the space time variation of meson fields in nuclear collisions. The calculated multiplicities of coherently produced particles grow fast with the bombarding energy, reaching a saturation above the RHIC bombarding energy. In the case of central Au+Au collisions the bremsstrahlung mechanism becomes comparable with particle production in incoherent hadron hadron collisions above the AGS energies. The rapidity spectra of antibaryons and pions exhibit a characteristic two hump structure which is a consequence of incomplete projectile target stopping at the initial stage of the reaction. The predicted distribution of e+e pairs has a strong peak at invariant masses Me+e < 0.5 GeV.
Measured hadron yields from relativistic nuclear collisions can be equally well understood in two physically distinct models, namely a static thermal hadronic source versus a time-dependent, non-equilibrium hadronization off a quark gluon plasma droplet. Due to the time-dependent particle evaporation off the hadronic surface in the latter approach the hadron ratios change (by factors of / 5) in time. The overall particle yields then reflect time averages over the actual thermodynamic properties of the system at a certain stage of evolution.
We study the time scale for pressure equilibration in heavy ion collisions at AGS energies within the three-fluid hydrodynamical model and a microscopic cascade model (UrQMD). We find that kinetic equilibrium is reached in both models after a time of 5 fm/c (center-of-mass time). Thus, observables which are sensitive to the early stage of the reaction differ considerably from the expectations within the instant thermalization scenario (one-fluid hydrodynamical model).
Basic problems of the semiclassical microscopic modelling of strongly interacting systems are discussed within the framework of Quantum Molecular Dynamics (QMD). This model allows to study the influence of several types of nucleonic interactions on a large variety of observables and phenomena occur- ring in heavy ion collisions at relativistic energies. It is shown that the same predictions can be obtained with several numerically completely di erent and independently written programs as far as the same model parameters are employed and the same basic approximations are made. Many observ- ables are robust against variations of the details of the model assumptions used. Some of the physical results, however, depend also on rather technical parameters like the preparation of the initial configuration in phase space. This crucial problem is connected with the description of the ground state of single nuclei, which di ers among the various approaches. An outlook to an improved molecular dynamics scheme for heavy ion collisions is given.
Abstract: We study transverse expansion and directed flow in Au(11AGeV)Au reactions within a multi-fluid dynamical model. Although we do not employ an equation of state (EoS) with a first order phase transition, we find a slow increase of the transverse velocities of the nucleons with time. A similar behaviour can be observed for the directed nucleon flow. This is due to non-equilibrium e ects which also lead to less and slower conversion of longitudinal into transverse momentum. We also show that the proton rapidity distribution at CERN energies, as calculated within this model, agrees well with the preliminary NA44-data.