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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.
We discuss the possibility of producing a new kind of nuclear system by putting a few antibaryons inside ordinary nuclei. The structure of such systems is calculated within the relativistic mean field model assuming that the nucleon and antinucleon potentials are related by the G parity transformation. The presence of antinucleons leads to decreasing vector potential and increasing scalar potential for the nucleons. As a result, a strongly bound system of high density is formed. Due to the significant reduction of the available phase space the annihilation probability might be strongly suppressed in such systems.
To describe ultrarelativistic heavy-ion collisions we construct a three-fluid hydrodynamical model. In contrast to one-fluid hydrodynamics, it accounts for the finite stopping power of nuclear matter, i.e. for nonequilibrium e ects in the early stage of the reaction. Within this model, we study baryon dynamics in the BNL-AGS energy range. For the system Au+Au we find that kinetic equilibrium between projectile and target nucleons is established only after a time teq CM H 5 fm/c C 2RAu/³CM. Observables which are sensitive to the early stage of the collision (like e.g. nucleon flow) therefore di er considerably from those calculated in the one-fluid model.
We discuss the early evolution of ultrarelativistic heavy-ion collisions within a multi- fluid dynamical model. In particular, we show that due to the finite mean-free path of the particles compression shock waves are smeared out considerably as compared to the one-fluid limit. Also, the maximal energy density of the baryons is much lower. We discuss the time scale of kinetic equilibration of the baryons in the central region and its relevance for directed flow. Finally, thermal emission of direct photons from the fluid of produced particles is calculated within the three-fluid model and two other simple expansion models. It is shown that the transverse momentum and rapidity spectra of photons give clue to the cooling law and the early rapidity distribution of the photon source.
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.
Noneequilibrium models (three-fluid hydrodynamics and UrQMD) use to discuss the uniqueness of often proposed experimental signatures for quark matter formation in relativistic heavy ion collisions. It is demonstrated that these two models - although they do treat the most interesting early phase of the collisions quite differently(thermalizing QGP vs. coherent color fields with virtual particles) - both yields a reasonable agreement with a large variety of the available heavy ion data.
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).
Entropy production in the compression stage of heavy ion collisions is discussed within three distinct macroscopic models (i.e. generalized RHTA, geometrical overlap model and three-fluid hydrodynamics). We find that within these models \sim 80% or more of the experimentally observed final-state entropy is created in the early stage. It is thus likely followed by a nearly isentropic expansion. We employ an equation of state with a first-order phase transition. For low net baryon density, the entropy density exhibits a jump at the phase boundary. However, the excitation function of the specific entropy per net baryon, S/A, does not reflect this jump. This is due to the fact that for final states (of the compression) in the mixed phase, the baryon density \rho_B increases with \sqrt{s}, but not the temperature T. Calculations within the three-fluid model show that a large fraction of the entropy is produced by nuclear shockwaves in the projectile and target. With increasing beam energy, this fraction of S/A decreases. At \sqrt{s}=20 AGeV it is on the order of the entropy of the newly produced particles around midrapidity. Hadron ratios are calculated for the entropy values produced initially at beam energies from 2 to 200 AGeV.
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.
Impact parameter dependencies in Pb(160 AGeV)+Pb reactions : hydrodynamical vs. cascade calculations
(1999)
We investigate the impact parameter dependence of the specific entropy S/A in relativistic heavy ion collisions. Especially the anti-Lambda/anti-proton ratio is found to be a useful tool to distinguish between chemical equilibrium assumptions assumed in hydrodynamics (here: the 3-fluid model) and the chemical non-equilibrium scenario like in microscopic models as the UrQMD model.
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.
Nonequilibrium models (three-fluid hydrodynamics, UrQMD, and quark molecular dynamics) are used to discuss the uniqueness of often proposed experimental signatures for quark matter formation in relativistic heavy ion collisions from the SPS via RHIC to LHC. It is demonstrated that these models - although they do treat the most interesting early phase of the collisions quite differently (thermalizing QGP vs. coherent color fields with virtual particles) -- all yield a reasonable agreement with a large variety of the available heavy ion data. Hadron/hyperon yields, including J/Psi meson production/suppression, strange matter formation, dileptons, and directed flow (bounce-off and squeeze-out) are investigated. Observations of interesting phenomena in dense matter are reported. However, we emphasize the need for systematic future measurements to search for simultaneous irregularities in the excitation functions of several observables in order to come close to pinning the properties of hot, dense QCD matter from data. The role of future experiments with the STAR and ALICE detectors is pointed out.
Report-no: UFTP-492/1999 Journal-ref: Phys.Rev. C61 (2000) 024909 We investigate flow in semi-peripheral nuclear collisions at AGS and SPS energies within macroscopic as well as microscopic transport models. The hot and dense zone assumes the shape of an ellipsoid which is tilted by an angle Theta with respect to the beam axis. If matter is close to the softest point of the equation of state, this ellipsoid expands predominantly orthogonal to the direction given by Theta. This antiflow component is responsible for the previously predicted reduction of the directed transverse momentum around the softest point of the equation of state.
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.
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.
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.
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.
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.
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.
Studying Walecka's mean-field theory we find that one can reproduce the observed binding energy and density of nuclear matter within experimental precision in an area characterized by a line in the coupling-constant plane. A part of this line defines systems which exhibit a phase transition around Tc~200 MeV for zero baryon density. The rest corresponds to such systems where the phase transition is absent; in that case a peak appears in the specific heat around T~200 MeV. We interpret these results as indicating that the hadron phase of nuclear matter alone indicates the occurrence of an abrupt change in the bulk properties around ρV~0 and T~200 MeV.
Kinetic energy flow in Nb(400 A MeV) + Nb: evidence for hydrodynamic compression of nuclear matter
(1984)
A kinetic-energy—flow analysis of multiplicity-selected collisions of 93Nb(Elab=400A MeV)+93Nb is performed on the basis of the nuclear fluid dynamical model. The effects of finite particle numbers on the flow tensor are explicitly taken into account. Strong sidewards peaks are predicted in dN/dcosθF, the distribution of event by event flow angles. This is in qualitative agreement with recent data from the "Plastic Ball" electronic detection system. Cascade simulations fail to reproduce the data.
We analyze the phase structure of the nonlinear mean-field meson theory of baryonic matter (nucleons plus delta resonances). Depending on the choice of the coupling constants, we find three physically distinct phase transitions in this theory: a nucleonic liquid-gas transition in the low temperature, Tc<20 MeV, low density, ρ≃0.5ρ0, regime, a high-temperature (T≃150 MeV) finite density transition from a gas of massive hadrons to a nearly massless baryon, antibaryon plasma, and, third, a strong phase transition from the nucleonic fluid to a resonance-dominated ‘‘delta-matter’’ isomer at ρ>2ρ0 and Tc<50 MeV. All three phase transitions are of first order. It is shown that the occurrence of these different phase transitions depends critically on the coupling constants. Since the production of pions also depends strongly on the coupling constants, it is seen that the equation of state cannot be derived unambiguously from pion data.
The influence of fluctuations of the shape degree of freedom in collisions of deformed nuclei with energies between 0.8 and 2.1 GeV/nucleon is analyzed on the basis of an intranuclear cascade simulation for the strongly deformed systems 46Ti+ 46Ti and 166Er+ 166Er. While there is a considerable sensitivity of the global event variables to the orientation for polarized beams and targets, this dependence disappears in the average over all orientations for impact parameter selected and integrated events. The dependence of the nuclear stopping and thermalization on the size of the system under consideration and on the bombarding energy is also investigated.
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.
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.
With the use of the cranking formula, the coordinate-dependent mass parameters of the kinetic-energy operator in fission processes and heavy-ion collisions are calculated in the two-center oscillator model. It is shown that the reduced mass and also the classical moment of inertia are obtained for large separations of the fragments. For small separations, however, the mass parameter for the motion of the centers of mass of the fragments is larger than the reduced mass by an order of magnitude.
We study the extrapolation of nuclear shell structure to the region of superheavy nuclei in self-consistent mean-field models—the Skyrme-Hartree-Fock approach and the relativistic mean-field model—using a large number of parametrizations which give similar results for stable nuclei but differ in detail. Results obtained with the folded-Yukawa potential which is widely used in macroscopic-macroscopic models are shown for comparison. We focus on differences in the isospin dependence of the spin-orbit interaction and the effective mass between the models and their influence on single-particle spectra. The predictive power of the mean-field models concerning single-particle spectra is discussed for the examples of 208Pb and the spin-orbit splittings of selected neutron and proton levels in 16O, 132Sn, and 208Pb. While all relativistic models give a reasonable description of spin-orbit splittings, all Skyrme interactions show a wrong trend with mass number. The spin-orbit splitting of heavy nuclei might be overestimated by 40%–80%, which exposes a fundamental deficiency of the current nonrelativistic models. In most cases the occurrence of spherical shell closures is found to be nucleon-number dependent. Spherical doubly magic superheavy nuclei are found at 184298114, 172292120, or 184310126 depending on the parametrization. The Z=114 proton shell closure, which is related to a large spin-orbit splitting of proton 2f states, is predicted only by forces which by far overestimate the proton spin-orbit splitting in 208Pb. The Z=120 and N=172 shell closures predicted by the relativistic models and some Skyrme interactions are found to be related to a central depression of the nuclear density distribution. This effect cannot appear in macroscopic-microscopic models or semiclassical approaches like the extended Thomas-Fermi-Strutinski integral approach which have a limited freedom for the density distribution only. In summary, our findings give a strong argument for 172292120 to be the next spherical doubly magic superheavy nucleus.
the development of the mass asymmetry vibrations in the final stages of the fission process is studied with an approximate treatment of the coupling to relative motion. A parametrized friction is introduced and its effects are studied. Numerical results are presented for 236U, together with estimates for the kinetic energy of the fragments. RADIOACTIVITY, FISSION 236U; calculated mass distribution, kinetic energy distribution. Collective dynamics, shell correction method, cranking model.
With the mass asymmetry described by the dynamical collective fragmentation coordinate ξ, and with use of the asymmetric two-center shell model, the fission mass distributions for 226Ra, 236U, and 258Fm (which are typical representatives for triple-, double-, and single-humped distributions) are explained.
The properties of symmetric nuclear matter are investigated in the nonlinear relativistic mean field theory of nuclear matter. We consider the constraints imposed by four nuclear ground state properties on the coupling constants and on the equation of state at zero and at finite temperature. We find that the compression constant K(ρ0) as well as the temperature is irrelevant for the stiffness of the equation of state for m*(ρ0)≤0.7. The main point is that the relativistic mean field theory exhibits acausal and unphysical behavior for compressibilities below K(ρ0)=200 MeV. Every set of coupling constants with a negative quartic coupling constant c is unstable against small quantum fluctuations.
We study a relativistic model of the nucleus consisting of nucleons coupled to mesonic degrees of freedom via an effective Lagrangian whose parameters are determined by a fit to selected nuclear ground-state data. We find that the model allows a very good description of nuclear ground-state properties. Because of the relativistic nature of the model, the spin properties are uniquely fixed. We discuss variations of the parametrization and of the data which suggest that the present fit has exhausted the limits of the mean-field approximation, and discuss extensions which go beyond the mean field.
Different collective deformation coordinates for neutrons and protons are introduced to allow for both stretching and γ transitions consistent with experiments. The rotational actinide nuclei 234-238U and 232Th are successfully analyzed in this model. NUCLEAR STRUCTURE 232Th, 234-238U calculated B (E2) values, collective model.
The nucleons taking part in heavy ion reaction are considered as a three-component fluid. The first and second components correspond to the nucleons of the target and the projectile, while the thermalized nucleons produced in the course of the collision belong to the third component. Making use of the Boltzmann equation, hydrodynamical equations are derived. An equation of state for anisotropic nuclear matter obtained from a field theoretical model in mean field approximation is applied in a one dimensional version of the three-component fluid model. The speed of thermalization is analyzed and compared to the results of cascade and kinetic models. NUCLEAR REACTIONS Relativistic heavy-ion reactions, hydrodynamic description.
The time dependent Hartree-Fock approximation is used to study the dynamical formation of long-lived superheavy nuclear complexes. The effects of long-range Coulomb polarization are treated in terms of a classical quadrupole polarization model. Our calculations show the existence of "resonantlike" structures over a narrow range of bombarding energies near the Coulomb barrier. Calculations of 238U + 238U are presented and the consequences of these results for supercritical positron emission are discussed. NUCLEAR REACTIONS 238U + 238U collisions as a function of bombarding energy, in the time-dependent Hartree-Fock approximation. Superheavy molecules and strongly damped collisions.
Proton spectra have been calculated for the reaction 12C(85 MeV/nucleon) + 197Au using a three-dimensional hydrodynamical model with viscosity and thermal conductivity and final thermal breakup. The theoretical results are compared to recent data. It is shown that the predicted flow effects are not observable as a result of the impact parameter averaging inherent in the inclusive proton spectra. In contrast, angular distributions of medium mass nuclei (A>3) in nearly central collisions can provide signatures for flow effects.
The fluid dynamical model is used to study the reactions 20Ne+238U and 40Ar+40Ca at Elab=390 MeV/nucleon. The calculated double differential cross sections d²ð/dΩdE exhibit sidewards maxima in agreement with recent experimental data. The azimuthal dependence of the triple differential distributions, to be obtained from an event-by-event analysis of 4π; exclusive experiments, can yield deeper insight into the collision process: Jets of nuclear matter are predicted with a strongly impact-parameter-dependent thrust angle θjet(b). NUCLEAR REACTIONS Ar+Ca, Ne+U, Elab=393 MeV/nucleon, fluid dynamics with thermal breakup, double differential cross sections, azimuthal dependence of triple differential cross sections, event-by-event thrust analysis of 4π exclusive experiments.
We investigate the structure of the potential energy surfaces of the superheavy nuclei 158258Fm100, 156264Hs108, 166278112, 184298114, and 172292120 within the framework of self-consistent nuclear models, i.e., the Skyrme-Hartree-Fock approach and the relativistic mean-field model. We compare results obtained with one representative parametrization of each model which is successful in describing superheavy nuclei. We find systematic changes as compared to the potential energy surfaces of heavy nuclei in the uranium region: there is no sufficiently stable fission isomer any more, the importance of triaxial configurations to lower the first barrier fades away, and asymmetric fission paths compete down to rather small deformation. Comparing the two models, it turns out that the relativistic mean-field model gives generally smaller fission barriers.
We present an analysis of high energy heavy ion collisions at intermediate impact parameters, using a two-dimensional fluid-dynamical model including shear and bulk viscosity, heat conduction, a realistic treatment of the nuclear binding, and an analysis of the final thermal emission of free nucleons. We find large collective momentum transfer to projectile and target residues (the highly inelastic bounce-off effect) and explosion of the hot compressed shock zones formed during the impact. As the calculated azimuthal dependence of energy spectra and angular distributions of emitted nucleons depends strongly on the coefficients of viscosity and thermal conductivity, future exclusive measurements may allow for an experimental determination of these transport coefficients. The importance of 4π measurements with full azimuthal information is pointed out.
Angular and energy distributions of fragments emitted from fast nucleus-nucleus collisions (Ne--> U at 250, 400, and 800 MeV/N) are calculated with use of nuclear fluid dynamics. A characteristic dependence of the energy spectra and angular distributions on the impact parameter is predicted. The preferential sideward emission of reaction fragments observed in the calculation for nearly central collisions seems to be supported by recent experimental data.