Horst Stöcker

High energy heavy ion collisions—probing the equation of state of highly excited hardronic matter

Abstract We review the recent progress in extracting the equation of state of hot dense hadronic matter from relativistic heavy ion collisions. At first a discussion of the bulk properties of infinite nuclear matter is presented. Next the theoretical approaches are developed which describe the complicated dynamics and non-equilibrium features in actual high energy nucleus-nucleus collisions: Nuclear fluid dynamics, the intranuclear cascade model, classical equation of motion simulations, the Vlasov Uehling-Uhlenbeck theory and the time dependent Dirac equation with meson field dynamics are exhibited. The recent experimental confirmation of the early hydrodynamic predictions on nuclear shock compression establishes the key mechanism for creating high nuclear density and temperatures in the laboratory, and thus the key mechanism for investigating the nuclear equation of state. Evidence for a suprisingly stiff nuclear equation of state is presented from a comparison of the distinct theoretical predictions to recent high multiplicity selected 4π data on fragment formation, pion production and collective sidewards flow. We also discuss the possible creation of a deconfined quark gluon plasma at future ultra-relativistic heavy ion facilities.

Longitudinal momentum transfer and the nucleon's mean free path in medium energy heavy ion collisions - TDHF versus Vlasov-Uehling-Uhlenbeck theory

Abstract Two pure mean field theories, the classical Vlasov- and the quantal TDHF-approach, are used to study 85 MeV/N 12 C induced reactions with targets from 12 C to 197 Au. Both theories predict nearly identical results: the nuclei slip through each other; for C+C about 85% of the longitudinal momentum is conserved in the surviving fragments. Inclusion of two body collisions via an Uehling-Uhlenbeck collision integral yields - in sharp contrast to results at lower energies - two clearly distinct components: only 20% of the initial momentum resides in the slipped-through fragments, which retain only 40% of the nucleons. The remaining 60% of the nucleons undergo one or more n-n scatterings and form a mid-rapidity source. These nucleons decelerate rapidly with a time constant t = 12.5 fm/ c , corresponding to a deceleration length of x = 2.5 fm. The number of slipped-through nucleons decreases even further when heavier target nuclei are studied: for C+Au collisions, 97% of the projectile nucleons undergo at least one collision, transferring 80% of the total longitudinal momentum to the target-like fragment. The number of emitted uncollided projectile nucleons falls off exponentially with the thickness of the target nucleus, yielding a mean free path of the nucleon of λ = 2.6 fm.

Prospects of intermediate energy nuclear collisions

Abstract We focus on central nuclear collisions--“multifragmentation events”--in the energy range 20–400 MeV/n. They seem well suited to study bulk properties of nuclear matter at moderate entropies. Various ways of extracting information on the produced entropy are discussed. We emphasize the importance of medium mass fragment production for this goal. The consequences of a first order liquid-vapor phase transition at low densities ϱ ϱ 0 are pointed out--the release of latent heat results in an increase of the entropy at energies E LAB ≲ 200 MeV/n. It is pointed out that a minimum in the mass distribution is indicative of the onset of condensation. Such a minimum has indeed been observed in multifragmentation events. The medium energy reactions also provide an enhanced sensitivity to the stiffness of the nuclear equation of state at high densities ϱ > ϱ 0 . This is discovered in a 4π exclusive energy flow analysis performed on the basis of the nuclear fluid dynamical model. A strong bombarding energy dependence of the flow effects is predicted, which is not found in cascade simulations. The flow analysis can also be used to reveal the presence of a high density abnormal state via a characteristic change of the flow pattern at a critical bombarding energy.

Stopping power, equilibration, and collective flow in the reactions Ar + Pb and Nb + Nb: A Theoretical analysis

Abstract The approach to local kinetic equilibrium in relativistic heavy ion collisions is studied by following the time evolution of the Wigner function for Ar (770 MeV/N)+Pb in configuration and momentum space using the Vlasov-Uehling-Uhlenbeck theory. Rapid equilibrium of the participant region is observed within 10 fm/ c . Total stopping of the projectile occurs at small impact parameters. For intermediate impact parameters, the theory predicts simultaneously the bounce-off effect of the projectile fragments and the sidewards flow of the participant matter. The latter can be displayed via a large angle peak in the flow angle, θ f , distributions, while the bounce-off is most easily observed via a pronounced peak in the rapidity dependence of the transverse momentum transfer p x ( y ). A drastic dependence of p x and θ f on impact parameter and bombarding energy is predicted for Ar + Pb and Nb + Nb. Recent data support our analysis.

Circumstantial evidence for a stiff nuclear equation of state

Abstract We discuss the recent attempts to extract the nuclear equation of state from event-by-event data on high energy heavy ion collisions via the Vlasov-Uehling-Uhlenbeck theory. In this approach, the time evolution of the Wigner function is followed in configuration and momentum space. Rapid stopping of the projectile occurs at small impact parameters. For intermediate impact parameters, the theory predicts simultaneously the bounce-off effect of the projectile fragments and the sidewards flow of the participant matter. The latter can be displayed via a peak in the distribution of the flow angle Op at large values of Op, while the bounce-off is most easily observed via a pronounced maximum of the transverse momentum transfer p x (y) at the projectile rapidity. A drastic dependence of p x and Op on the mass of the colliding system, impact parameter, and bombarding energy is predicted. Recent data are used to extract an equation of state. The resulting EOS is consistently the same and in quantitative agreement with results obtained from pion multiplicities via various methods.

Temperatures in heavy-ion collisions from pion multiplicities

Abstract A thermodynamically consistent treatment of the nuclear interaction is employed to study the dependence of pion production on the nuclear equation of state in heavy-ion collisions. Massive baryon resonances, heavy mesons and the Bose condensation of pions are incorporated into a macrocanonical relativistic quantum-statistical treatment of the highly excited system. The measured pion multiplicities, which vary over eight orders of magnitude in the bombarding energy range from 30 MeV/nucleon to 4 GeV/nucleon, are reproduced within a simple one-dimensional fluiddynamical model if it is assumed that nuclear matter is rather incompressible. The pion yields are in this model directly related to the compression energy, which amounts to one-half of the total center-of-mass energy at all BEVALAC energies. The maximum compression derived is uncertain by about 10% and 30% at E lab = 0.4 and 1.8 GeV / nucleon , respectively. The temperatures of the system in the moment of the chemical freeze-out of the pion/delta degree of freedom are determined from the measured pion yields and range from 10 MeV to 100 MeV. An extrapolation to CERN/BNL energies, i.e. E lab > 10 GeV / nucleon , yields T = 150–200 MeV . A strong energy dependence of the cross sections and the slopes of hard γs is predicted by this model. The calculated photon yields are in surprising agreement with the data on γ- production at intermediate energies.

Deconfinement in the baryon rich region

Abstract The dynamics of deconfinement and hadronization at high chemical potentials, i.e. in baryon rich matter, are discussed. Quark gluon plasma formation in the fragmentation regions is characterized by low temperatures. Condensation discontinuities are predicted which result in substantial entropy production during hadronization in the fragmentation regions, by far exceeding the entropy expected if deconfinement would not occur. This excess entropy may be useful for plasma diagnostics, since it is directly related to the coupling strength and nonperturbative effects in the deconfined phase. Energy densities of 1 – 2 GeV/fm3 are obtained in stopping collisions of heavy nuclei at bombarding energies Elab = 5–10 GeV/n.

Theory of relativistic heavy ion collisions

Abstract The current status of heavy ion physics from medium energies to the quark gluon plasma is discussed in the light of several theoretical approaches. Relativistic mean field theory is discussed. The nuclear equation of state at high density and temperature is investigated in a nuclear fluid dynamic model: nuclear matter is considered as a relativistic interacting Bose and Fermi gas of π and η mesons, photons, and nucleonic resonances. At the microscopic level, the approach to local kinetic equilibrium in relativistic heavy ion collisions is studied by following the time evolution of the Wigner function in configuration and momentum space using the Vlasov-Uehling-Uhlenbeck theory. This theoretical approach includes the nuclear mean field, two body collisions, particle production, relativistic kinematics, and the Pauli principle. A Newtonian Force Model, TDHF, the Vlasov equation, the IntraNuclear Cascade model, macroscopic Nuclear Fluid Dynamics, and a simple shock model are studied as reference cases. In the VUU theory, rapid equilibration of the participant region is observed within time spans on the order of 10 fm/c. Total stopping of the projectile occurs at small impact parameters: a sidesplash of nuclear matter is predicted due to the interplay of the nuclear compressional energy and collisions. These theoretical approaches are compared to the experimental data. The pion yields, single particle spectra, and kinetic energy flow angular distributions are found to be sensitive to the nuclear compressibility and the Pauli principle: preliminary evidence for a surprisingly stiff nuclear equation of state is presented. Nuclear fragmentation or complex particle production is studied in a quantum statistical model that includes the isotopes up to Ne and also by applying a six dimensional coalescence model to the VUU final state.

Fragment yields and phase coexistence in nuclear collisions

Abstract It is shown that the apparent power-law behavior of the fragment yields obtained in high-energy proton-nucleus and nucleus-nucleus collisions can be understood in terms of the coexistence of liquid and vapor phases of nuclear matter. The fragment yields are computed by calculating the disassembly of the liquid and vapor sources microanonically. Good agreement with data is obtained for a wide range of breakup densities.

Irradiation symmetry of heavy ion driven inertial confinement fusion (ICF) targets

The symmetry of heavy ion driven inertial confinement fusion targets is investigated with a two-dimensional Eulerian hydrodynamic code. The importance of the beam geometry is studied. The HIBALL design in its present form seems to inhibit a spherical implosion of the target. It is shown that the beam angle in the HIBALL geometry should be about 35 degrees.