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We discuss the present collective flow signals for the phase transition to quark-gluon plasma (QGP) and the collective flow as a barometer for the equation of state (EoS). A study of Mach shocks induced by fast partonic jets propagating through the QGP is given. We predict a significant deformation of Mach shocks in central Au+Au collisions at RHIC and LHC energies as compared to the case of jet propagation in a static medium. Results of a hydrodynamical study of jet energy loss are presented.
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
Homogeneous nucleation of quark gluon plasma, finite size effects and longlived metastable objects
(1998)
The general formalism of homogeneous nucleation theory is applied to study the hadronization pattern of the ultra-relativistic quark-gluon plasma (QGP) undergoing a first order phase transition. A coalescence model is proposed to describe the evolution dynamics of hadronic clusters produced in the nucle- ation process. The size distribution of the nucleated clusters is important for the description of the plasma conversion. The model is most sensitive to the initial conditions of the QGP thermalization, time evolution of the energy den- sity, and the interfacial energy of the plasma hadronic matter interface. The rapidly expanding QGP is first supercooled by about T = T Tc = 4 6%. Then it reheats again up to the critical temperature Tc. Finally it breaks up into hadronic clusters and small droplets of plasma. This fast dynamics occurs within the first 5 10 fm/c. The finite size e ects and fluctuations near the critical temperature are studied. It is shown that a drop of longitudinally expanding QGP of the transverse radius below 4.5 fm can display a long-lived metastability. However, both in the rapid and in the delayed hadronization scenario, the bulk pion yield is emitted by sources as large as 3 4.5 fm. This may be detected experimentally both by a HBT interferometry signal and by the analysis of the rapidity distributions of particles in narrow pT -intervals at small |pT | on an event-by-event basis. PACS numbers: 12.38.Mh, 24.10.Pa, 25.75.-q, 64.60.Qb
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.
Background: In this interdisciplinary project, the biological effects of heavy ions are compared to those of X-rays using tissue slice culture preparations from rodents and humans. Advantages of this biological model are the conservation of an organotypic environment and the independency from genetic immortalization strategies used to generate cell lines. Its open access allows easy treatment and observation via live-imaging microscopy. Materials and methods: Rat brains and human brain tumor tissue are cut into 300 micro m thick tissue slices. These slices are cultivated using a membrane-based culture system and kept in an incubator at 37°C until treatment. The slices are treated with X-rays at the radiation facility of the University Hospital in Frankfurt at doses of up to 40 Gy. The heavy ion irradiations were performed at the UNILAC facility at GSI with different ions of 11.4 A MeV and fluences ranging from 0.5–10 x 106 particles/cm². Using 3D-confocal microscopy, cell-death and immune cell activation of the irradiated slices are analyzed. Planning of the irradiation experiments is done with simulation programs developed at GSI and FIAS. Results: After receiving a single application of either X-rays or heavy ions, slices were kept in culture for up to 9d post irradiation. DNA damage was visualized using gamma H2AXstaining. Here, a dose-dependent increase and time-dependent decrease could clearly be observed for the X-ray irradiation. Slices irradiated with heavy ions showed less gamma H2AX-positive cells distributed evenly throughout the slice, even though particles were calculated to penetrate only 90–100 micro m into the slice. Conclusions: Single irradiations of brain tissue, even at high doses of 40 Gy, will result neither in tissue damage visible on a macroscopic level nor necrosis. This is in line with the view that the brain is highly radio-resistant. However, DNA damage can be detected very well in tissue slices using gamma H2AX-immuno staining. Thus, slice cultures are an excellent tool to study radiation-induced damage and repair mechanisms in living tissues.
A nonlinear chiral SU(3) approach including the spin 3 2 decuplet is developed to describe dense matter. The coupling constants of the baryon resonances to the scalar mesons are determined from the decuplet vacuum masses and SU(3) symmetry relations. Di erent methods of mass generation show significant differences in the properties of the spin- 3 2 particles and in the nuclear equation of state
We calculate p, ±,K± and (+ 0) rapidity distributions and compare to experimental data from SIS to SPS energies within the UrQMD and HSD transport approaches that are both based on string, quark, diquark (q, ¯q, qq, ¯q ¯q) and hadronic degrees of freedom. The two transport models do not include any explicit phase transition to a quark-gluon plasma (QGP). It is found that both approaches agree rather well with each other and with the experimental rapidity distributions for protons, s, ± and K±. In- spite of this apparent agreement both transport models fail to reproduce the maximum in the excitation function for the ratio K+/ + found experimen- tally between 11 and 40 A·GeV. A comparison to the various experimental data shows that this failure is dominantly due to an insu cient description of pion rapidity distributions rather than missing strangeness . The modest di erences in the transport model results on the other hand can be attributed to di erent implementations of string formation and frag- mentation, that are not su ciently controlled by experimental data for the elementary reactions in vacuum.
We analyze the hadronic freeze-out in ultra-relativistic heavy ion collisions at RHIC in a transport approach which combines hydrodynamics for the early, dense, deconfined stage of the reaction with a microscopic non-equilibrium model for the later hadronic stage at which the hydrodynamic equilibrium assumptions are not valid. With this ansatz we are able to self-consistently calculate the freeze-out of the system and determine space-time hypersurfaces for individual hadron species. The space-time domains of the freeze-out for several hadron species are found to be actually four-dimensional, and di er drastically for the individual hadrons species. Freeze-out radii distributions are similar in width for most hadron species, even though the is found to be emitted rather close to the phase boundary and shows the smallest freeze- out radii and times among all baryon species. The total lifetime of the system does not change by more than 10% when going from SPS to RHIC energies.
We calculate the yields of a variety of hadrons for RHIC and LHC energies assuming thermodynamical equilibration of the produced minijets, and using as input results from pQCD for the energy densities at midrapidity. In the calculation of the production of partons and of transverse energy one has to account for nuclear shadowing. By using two parametrizations for the gluon shadowing one derives energy densities di ering strongly in magnitude. In this publication we link those perturbatively calculated energy densities of partons via entropy conservation in an ideal fluid to the hadron multiplicities at chemical freeze-out.
We calculate the yields of pions, kaons, and Æ-mesons for RHIC and LHC energies assuming thermodynamical equilibration of the produced minijets, and using as input results from pQCD for the energy densities at midrapidity. In the calculation of the production of partons and of transverse energy one has to account for nuclear shadowing. By using two parametrizations for the gluon shadowing one derives energy densities differing strongly in magnitude. In this publication we link those perturbatively calculated energy densities of partons via entropy conservation in an ideal fluid to the hadron multiplicities at chemical freeze-out.
We use 4stout improved staggered lattice data at imaginary chemical potentials to calculate fugacity expansion coefficients in finite temperature QCD. We discuss the phenomenological interpretation of our results within the hadron resonance gas (HRG) model, and the hints they give us about the hadron spectrum. We also discuss features of the higher order coefficients that are not captured by the HRG. This conference contribution is based on our recent papers [1, 2].
Measured hadron yields from relativistic nuclear collisions can be equally well understood in two physically distinct models, namely a static thermal hadronic source vs. a time-dependent, nonequilibrium hadronization o a quark-gluon plasma droplet. Due to the time-dependent particle evapora- tion o the hadronic surface in the latter approach the hadron ratios change (by factors of <H 5) in time. Final particle yields reflect time averages over the actual thermodynamic properties of the system at a certain stage of the evolution. Calculated hadron, strangelet and (anti-)cluster yields as well as freeze-out times are presented for di erent systems. Due to strangeness distillation the system moves rapidly out of the T, µq plane into the µs-sector. Classif.: 25.75.Dw, 12.38.Mh, 24.85.+p
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.
Hadron and hadron cluster production in a hydrodynamical model including particle evaporation
(1997)
We discuss the evolution of the mixed phase at RHIC and SPS within boostinvariant hydrodynamics. In addition to the hydrodynamical expansion, we also consider evaporation of particles o the surface of the fluid. The back-reaction of this evaporation process on the dynamics of the fluid shortens the lifetime of the mixed phase. In our model this lifetime of the mixed phase is d 12 fm/c in Au + Au at RHIC and d 6.5 fm/c in Pb + Pb at SPS, even in the limit of vanishing transverse expansion velocity. Strong separation of strangeness occurs, especially in events (or at rapidities) with relatively high initial net baryon and strangeness number, enhancing the multiplicity of MEMOs (multiply strange nuclear clusters). If antiquarks and antibaryons reach saturation in the course of the pure QGP or mixed phase, we find that at RHIC the ratio of antideuterons to deuterons may exceed 0.3 and even 4He/4He > 0.1. In S + Au at SPS we find only N/N H 0.1. Due to fluctuations, at RHIC even negative baryon number at midrapidity is possible in individual events, so that the antibaryon and antibaryon-cluster yields exceed those of the corresponding baryons and clusters.
n this article we will focus on the appearance of the hadron-quark phase transition and the formation of strange matter in the interior region of the hypermassive neutron star and its conjunction with the spectral properties of the emitted gravitational waves (GWs). A strong hadron-quark phase transition might give rise to a mass-radius relation with a twin star shape and we will show in this article that a twin star collapse followed by a twin star oscillation is feasible. If such a twin star collapse would happen during the postmerger phase it will be imprinted in the GW-signal.
Gravitational waves from a core g-mode in supernovae as probes of the high-density equation of state
(2023)
Using relativistic supernova simulations of massive progenitor stars with a quark-hadron equation of state (EoS) and a purely hadronic EoS, we identify a distinctive feature in the gravitational-wave signal that originates from a buoyancy-driven mode (g-mode) below the proto-neutron star convection zone. The mode frequency lies in the range 200≲f≲800Hz and decreases with time. As the mode lives in the core of the proto-neutron star, its frequency and power are highly sensitive to the EoS, in particular the sound speed around twice saturation density.
Gravitational waves from a core g-mode in supernovae as probes of the high-density equation of state
(2023)
Using relativistic supernova simulations of massive progenitor stars with a quark-hadron equation of state (EoS) and a purely hadronic EoS, we identify a distinctive feature in the gravitational-wave signal that originates from a buoyancy-driven mode (g-mode) below the proto-neutron star convection zone. The mode frequency lies in the range 200≲f≲800Hz and decreases with time. As the mode lives in the core of the proto-neutron star, its frequency and power are highly sensitive to the EoS, in particular the sound speed around twice saturation density.
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 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.
The ultrarelativistic quantum molecular dynamics model (UrQMD) is used to study global observables in central reactions of Au+Au at sqrt[s]=200A GeV at the Relativistic Heavy Ion Collider (RHIC). Strong stopping governed by massive particle production is predicted if secondary interactions are taken into account. The underlying string dynamics and the early hadronic decoupling implies only small transverse expansion rates. However, rescattering with mesons is found to act as a source of pressure leading to additional flow of baryons and kaons, while cooling down pions.
Abstract Geant4 is a toolkit for simulating the passage of particles through matter. It includes a complete range of functionality including tracking, geometry, physics models and hits. The physics processes offered cover a comprehensive range, including electromagnetic, hadronic and optical processes, a large set of long-lived particles, materials and elements, over a wide energy range starting, in some cases, from 250 eV and extending in others to the TeV energy range. It has been designed and constructed to expose the physics models utilised, to handle complex geometries, and to enable its easy adaptation for optimal use in different sets of applications. The toolkit is the result of a worldwide collaboration of physicists and software engineers. It has been created exploiting software engineering and object-oriented technology and implemented in the C++ programming language. It has been used in applications in particle physics, nuclear physics, accelerator design, space engineering and medical physics. PACS: 07.05.Tp; 13; 23
The novel momentum analysis technique introduced by Danielewicz and Odyniec can be used to detect and exhibit collective flow in the light system Ar(1800 MeV/nucleon) + KCl where the usual kinetic energy flow analysis fails. The microscopic Vlasov-Uehling-Uhlenbeck theory which includes the nuclear mean field, two-body collisions, and Pauli blocking is used to study this phenomenon. The resulting transverse momentum transfers turn out to be quite sensitive to the nuclear equation of state. From a comparison with experimental data, evidence is presented for a rather stiff nuclear equation of state. The cascade model is unable to describe the data.
The non-equilibrium quantum field dynamics is usually described in the closed-time-path formalism. The initial state correlations are introduced into the generating functional by non-local source terms. We propose a functional approach to the Dyson-Schwinger equation, which treats the non-local and local source terms in the same way. In this approach, the generating functional is formulated for the connected Green functions and one-particle-irreducible vertices. The great advantages of our approach over the widely used two-particle-irreducible method are that it is much simpler and that it is easy to implement the procedure in a computer program to automatically generate the Feynman diagrams for a given process. The method is then applied to a pure gluon plasma to derive the gauge-covariant transport equation from the Dyson-Schwinger equation in the background covariant gauge. We discuss the structure of the kinetic equation and show its relationship with the classical one. We derive the gauge-covariant collision part and present an approximation in the vicinity of equilibrium. The role of the non-local source kernel in the non-equilibrium system is discussed in the context of a free scalar field. PACS numbers: 12.38.Mh, 25.75.-q, 24.85.+p, 11.15.Kc
The recent discovery of binary neutron star mergers has opened a new and exciting venue of research into hot and dense strongly interacting matter. For the first time, this elusive state of matter, described by the theory of quantum chromo dynamics, can be studied in two very different environments. On the macroscopic scale, in the collisions of neutron stars; and on the microscopic scale, in collisions of heavy ions at particle collider facilities. We will discuss the conditions that are created in these mergers and the corresponding high energy nuclear collisions. This includes the properties of quantum chromo dynamics matter, that is, the expected equation of state as well as expected chemical and thermodynamic properties of this exotic matter. To explore this matter in the laboratory, a new research prospect is available at the Facility for Antiproton and Ion Research, FAIR. The new facility is being constructed adjacent to the existing accelerator complex of the GSI Helmholtz Centre for Heavy Ion Research at Darmstadt/Germany, expanding the research goals and technical possibilities substantially. The worldwide unique accelerator and experimental facilities of FAIR will open the way for a broad spectrum of unprecedented research supplying a variety of experiments in hadron, nuclear, atomic, and plasma physics as well as biomedical and material science, which will be briefly described.
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.
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
We present a theoretical description of nuclear collisions which consists of a three-dimensional fluid-dynamical model, a chemical equilibrium breakup calculation for local light fragment (i.e., p, n, d, t, 3He, and 4He) production, and a final thermal evaporation of these particles. The light fragment cross sections and some properties of the heavy target residues are calculated for the asymmetric system Ne+U at 400 MeV/N. The results of the model calculations are compared with recent experimental data. Several observable signatures of the collective hydrodynamical processes are consistent with the present data. An event-by-event analysis of the flow patterns of the various clusters is proposed which can yield deeper insight into the collision dynamics.
The lightest supersymmetric particle, most likely the lightest neutralino, is one of the most prominent particle candidates for cold dark matter (CDM). We show that the primordial spectrum of density fluctuations in neutralino CDM has a sharp cut-off, induced by two different damping mechanisms. During the kinetic decoupling of neutralinos, non-equilibrium processes constitute viscosity effects, which damp or even absorb density perturbations in CDM. After the last scattering of neutralinos, free streaming induces neutralino flows from overdense to underdense regions of space. Both damping mechanisms together define a minimal mass scale for perturbations in neutralino CDM, before the inhomogeneities enter the non- linear epoch of structure formation. We find that the very first gravitationally bound neutralino clouds ought to have masses above 10-6M , which is six orders of magnitude above the mass of possible axion miniclusters.
Subensemble is a type of statistical ensemble which is the generalization of grand canonical and canonical ensembles. The subensemble acceptance method (SAM) provides general formulas to correct the cumulants of distributions in heavy-ion collisions for the global conservation of all QCD charges. The method is applicable for an arbitrary equation of state and sufficiently large systems, such as those created in central collisions of heavy ions. The new fluctuation measures insensitive to global conservation effects are presented. The main results are illustrated in the hadron resonance gas and van der Waals fluid frameworks.
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.
In power systems, flow allocation (FA) methods enable to allocate the usage and costs of the transmission grid to each single market participant. Based on predefined assumptions, the power flow is split into isolated generator-specific or producer-specific sub-flows. Two prominent FA methods, Marginal Participation (MP) and Equivalent Bilateral Exchanges (EBEs), build upon the linearized power flow and thus on the Power Transfer Distribution Factors (PTDFs). Despite their intuitive and computationally efficient concepts, they are restricted to networks with passive transmission elements only. As soon as a significant number of controllable transmission elements, such as high-voltage direct current (HVDC) lines, operate in the system, they lose their applicability. This work reformulates the two methods in terms of Virtual Injection Patterns (VIPs), which allows one to efficiently introduce a shift parameter q to tune contributions of net sources and net sinks in the network. In this work, major properties and differences in the methods are pointed out, and it is shown how the MP and EBE algorithms can be applied to generic meshed AC-DC electricity grids: by introducing a pseudo-impedance ω¯ , which reflects the operational state of controllable elements and allows one to extend the PTDF matrix under the assumption of knowing the current flow in the system. Basic properties from graph theory are used to solve for the pseudo-impedance in dependence of the position within the network. This directly enables, e.g., HVDC lines to be considered in the MP and EBE algorithms. The extended methods are applied to a low-carbon European network model (PyPSA-EUR) with a spatial resolution of 181 nodes and an 18% transmission expansion compared to today’s total transmission capacity volume. The allocations of MP and EBE show that countries with high wind potentials profit most from the transmission grid expansion. Based on the average usage of transmission system expansion, a method of distributing operational and capital expenditures is proposed. In addition, it is shown how injections from renewable resources strongly drive country-to-country allocations and thus cross-border electricity flows.
In this talk we discuss the effects of the hadronic rescattering on final state observables in high energy nuclear collisions. We do so by employing the UrQMD transport model for a realistic description of the hadronic decoupling process. The rescattering of hadrons modifies every hadronic bulk observable. For example apparent multiplicity of resonances is suppressed as compared to a chemical equilibrium freeze-out model. Stable and unstable particles change their momentum distribution by more than 30% through rescattering. The hadronic rescattering also leads to a substantial decorrelation of the conserved charge distributions. These findings show that it is all but trivial to conclude from the final state observables on the properties of the system at an earlier time where it may have been in or close to local equilibrium.
We estimate the feeddown contributions from decays of unstable A=4 and A=5 nuclei to the final yields of protons, deuterons, tritons, 3He, and 4He produced in relativistic heavy-ion collisions at sNN>2.4 GeV, using the statistical model. The feeddown contribution effects do not exceed 5% at LHC and top RHIC energies due to the large penalty factors involved, but are substantial at intermediate collision energies. We observe large feeddown contributions for tritons, 3He, and 4He at sNN≲10 GeV, where they may account for as much as 70% of the final yield at the lower end of the collision energies considered. Sizable (>10%) effects for deuteron yields are observed at sNN≲4 GeV. The results suggest that the excited nuclei feeddown cannot be neglected in the ongoing and future analysis of light nuclei production at intermediate collision energies, including HADES and CBM experiments at FAIR, NICA at JINR, RHIC beam energy scan and fixed-target programmes, and NA61/SHINE at CERN. We further show that the freeze-out curve in the T-μB plane itself is affected significantly by the light nuclei at high baryochemical potential.
We study the thermodynamic properties of infinite nuclear matter with the Ultrarelativistic Quantum Molecular Dynamics (URQMD), a semiclassical transport model, running in a box with periodic boundary conditions. It appears that the energy density rises faster than T4 at high temperatures of T approx. 200 - 300 MeV. This indicates an increase in the number of degrees of freedom. Moreover, We have calculated direct photon production in Pb+Pb collisions at 160 GeV/u within this model. The direct photon slope from the microscopic calculation equals that from a hydrodynamical calculation without a phase transition in the equation of state of the photon source.
The isospin and strangeness dimensions of the Equation of State are explored. RIA and the SIS200 accelerator at GSI will allow to explore these regions in compressed baryonic matter. 132 Sn + 132 Sn and 100 Sn + 100 Sn collisions as well as the excitation functions of K/pi, Lambda/pi and the centrality dependence of charmonium suppression from the UrQMD and HSD transport models are presented and compared to data. Unambiguous proof for the creation of a 'novel phase of matter' from strangeness and charm yields is not in sight.
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.
The upcoming high energy experiments at the LHC are one of the most outstanding efforts for a better understanding of nature. It is associated with great hopes in the physics community. But there is also some fear in the public, that the conjectured production of mini black holes might lead to a dangerous chain reaction. In this Letter we summarize the most straightforward arguments that are necessary to rule out such doomsday scenarios.
Entropy production in the initial compression stage of relativistic heavy-ion collisions from AGS to SPS energies is calculated within a three-fluid hydrodynamical model. The entropy per participating net baryon is found to increase smoothly and does not exhibit a jump or a plateau as in the 1-dimensional one-fluid shock model. Therefore, the excess of pions per participating net baryon in nucleus-nucleus collisions as compared to proton-proton reactions also increases smoothly with beam energy.
We estimate the energy density epsilon pile-up at mid-rapidity in central Pb+Pb collisions from 2 200 GeV/nucleon. epsilon is decomposed into hadronic and partonic contributions. A detailed analysis of the collision dynamics in the framework of a microscopic transport model shows the importance of partonic degrees of freedom and rescattering of leading (di)quarks in the early phase of the reaction for Elab 30 GeV/nucleon. In Pb+Pb collisions at 160 GeV/nucleon the energy density reaches up to 4 GeV/fm3, 95% of which are contained in partonic degrees of freedom.
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 study of hidden charm production is an important part of the heavy ion program. The standard approach to this problem [1] assumes that c¯c bound states are created only at the initial stage of the reaction and then partially destroyed at later stages due to interactions with the medium [2, 3, 4].
We investigate transverse hadron spectra from relativistic nucleus-nucleus collisions which reflect important aspects of the dynamics - such as the generation of pressure - in the hot and dense zone formed in the early phase of the reaction. Our analysis is performed within two independent transport approaches (HSD and UrQMD) that are based on quark, diquark, string and hadronic degrees of freedom. Both transport models show their reliability for elementary pp as well as light-ion (C+C, Si+Si) reactions. However, for central Au+Au (Pb+Pb) collisions at bombarding energies above ~ 5 A.GeV the measured K+- transverse mass spectra have a larger inverse slope parameter than expected from the calculation. Thus the pressure generated by hadronic interactions in the transport models above ~ 5 A.GeV is lower than observed in the experimental data. This finding shows that the additional pressure - as expected from lattice QCD calculations at finite quark chemical potential and temperature - is generated by strong partonic interactions in the early phase of central Au+Au (Pb+Pb) collisions.
The recently proposed baryon-strangeness correlation (C_BS) is studied with a string-hadronic transport model (UrQMD) for various energies from E_lab=4 AGeV to \sqrt s=200 AGeV. It is shown that rescattering among secondaries can not mimic the predicted correlation pattern expected for a Quark-Gluon-Plasma. However, we find a strong increase of the C_BS correlation function with decreasing collision energy both for pp and Au+Au/Pb+Pb reactions. For Au+Au reactions at the top RHIC energy (\sqrt s=200 AGeV), the C_BS correlation is constant for all centralities and compatible with the pp result. With increasing width of the rapidity window, C_BS follows roughly the shape of the baryon rapidity distribution. We suggest to study the energy and centrality dependence of C_BS which allow to gain information on the onset of the deconfinement transition in temperature and volume.
Intranuclear cascade calculations and fluid dynamical predictions of the kinetic energy flow are compared for collisions of 40Ca + 40Ca and 238U + 238U. The aspect ratio, R13, as obtained from the global analysis, is independent of the bombarding energy for the intranuclear cascade model. Fluid dynamics, on the other hand, predicts a dramatic increase of R13 at medium energies Elab≲200 MeV/nucleon. In fact, R13(Elab) directly reflects the incompressibility of the nuclear matter and can be used to extract the nuclear equation of stat at high densities. Distortions of the flow tensor due to few nucleon scattering are analyzed. Possible procedures to remove this background from experimental data are discussed.
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.
Equilibrium properties of infinite relativistic hadron matter are investigated using the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) model. The simulations are performed in a box with periodic boundary conditions. Equilibration times depend critically on energy and baryon densities. Energy spectra of various hadronic species are shown to be isotropic and consistent with a single temperature in equilibrium. The variation of energy density versus temperature shows a Hagedorn-like behavior with a limiting temperature of 130 +/- 10 MeV. Comparison of abundances of different particle species to ideal hadron gas model predictions show good agreement only if detailed balance is implemented for all channels. At low energy densities, high mass resonances are not relevant; however, their importance raises with increasing energy density. The relevance of these different conceptual frameworks for any interpretation of experimental data is questioned.
The equilibration of hot and dense nuclear matter produced in the central cell of central Au+Au collisions at RHIC (sqrt s = 200 A GeV) energies is studied within a microscopic transport model. The pressure in the cell becomes isotropic at t approx 5 fm/c after beginning of the collision. Within the next 15 fm/c the expansion of matter in the cell proceeds almost isentropically with the entropy per baryon ratio S/A approx 150, and the equation of state in the (P,epsilon) plane has a very simple form, P=0.15 epsilon. Comparison with the statistical model of an ideal hadron gas indicates that the time t approx 20 fm/c may be too short to reach the fully equilibrated state. Particularly, the creation of long-lived resonance-rich matter in the cell decelerates the relaxation to chemical equilibrium. This resonance-abundant state can be detected experimentally after the thermal freeze-out of particles.
A canonical partition function for the two-component excluded volume model is derived, leading to two di erent van der Waals approximations. The one is known as the Lorentz-Berthelot mixture and the other has been proposed recently. Both models are analysed in the canonical and grand canonical ensemble. In comparison with the one-component van der Waals excluded volume model the suppression of particle densities is reduced in these two-component formulations, but in two essentially di erent ways. Presently used multi-component models have no such reduction. They are shown to be not correct when used for components with di erent hard-core radii. For high temperatures the excluded volume interaction is refined by accounting for the Lorentz contraction of the spherical excluded volumes, which leads to a distinct enhancement of lighter particles. The resulting e ects on pion yield ratios are studied for AGS and SPS data.