How to Proceed  Hot and Dense Nuclear  Compression, Expansion and the

Status and Highlights

Substantial progress has been made in the phenomenological description of the hot and dense interaction zone generated in relativistic heavy ion collisions during the last couple of years. This is based on exclusive measurements of nucleons, pions, kaons and fragments that became available with a good characterisation of the collision geometry, i.e. the magnitude and direction of the impact parameter vector.
 

Collective Motion

 

Figure: Excitation function of side flow shown in terms of the slope of the in-plane transverse momentum distribution with respect to rapidity at midrapidity. Data are from GSI, Bevalac, and AGS.

 

At the low end of the energy range discussed here pion production is not yet relevant and the overall conditions can be inferred from the final state momentum space distributions of the nucleons and light nuclei. At finite impact parameters pronounced directional emission patterns are found in the reactions: (i) a sideward deflection of the forward and backward going nucleons in the reaction plane (sideflow) and (ii) an enhanced emission perpendicular to the reaction plane at centre-of-mass angles or midrapidity (squeeze-out). Both phenomena show a strong impact parameter and system size dependence that is being exploited in order to separate the contributions from individual nucleon-nucleon scatterings, the momentum dependence of the interaction and the mean field. Especially sensitive to the interplay of those processes is the so-called balance energy, where the flow vanishes as a consequence of the transition from an attractive to a repulsive nucleon-nucleon interaction. The balance energy, located at around beam kinetic energies per nucleon of 80-100 MeV, can also be viewed as the borderline for the onset of a hydrodynamical expansion and contains important information on the nuclear compressibility and the in-medium nucleon-nucleon cross sections. From the experimental data in conjunction with modern transport theories one is lead to the conclusion that a reduction of the scattering cross section is necessary due to the surrounding medium. At slightly higher beam energies the collective effects are fully developed and most pronounced, as demonstrated in Figure . The sideward deflection extracted from the momentum distribution of nucleons projected into the reaction plane shows consistently from different experiments a broad maximum and almost plateau like behaviour up to a beam kinetic energy per nucleon of about 1 GeV. This is very much reminiscent of scaling properties of hydrodynamical calculations and supports the view that heavy ion reactions indeed lead to states that exhibit macroscopic properties of nuclear matter. The quantitative evaluation of the driving mechanism of the directed collective flow, i.e. the importance of nucleon-nucleon collisions versus the mean field, requires a systematic study of the excitation function of all flow observables and a careful comparison to transport theories. Equally important and interesting is the understanding of the onset and of the decline of the phenomenon since the disappearance of flow is indicative for a reduced pressure in the system as it is especially towards the higher energies expected for a different phase.

 

Figure: Excitation function of freeze-out temperature and transverse expansion velocity. The data (from MSU, GANIL, Bevalac, GSI, AGS and SPS) are labelled according to the mass of the nuclear overlap zone and the particle type (LP$\equiv$light particles as nucleons, pions etc. IMF$\equiv$intermediate mass fragments) used in the analysis.

 

While the total energy that is observed in the directed motion only comprises a small fraction of the available energy it was realised in the systematic study of different ejectiles from various reactions that a surprisingly large fraction of the available energy is transformed into yet another collective degree of freedom. The spectra of the observed particles can only be explained by introducing a collective expansion scheme, in which all particles originate from a common velocity field that is superimposed to the (random) thermal motion. Since a large fraction of the available energy is bound in the collective motion this has the effect to lower the portion assigned to thermal motion and thereby helps to explain the relatively high yields of light nuclei that favor low temperatures and entropies. Quantitatively, many groups have succeeded in describing the measured hadron spectra in terms of an expanding system that freezes out at a well determined fixed temperature, a concept that seems to be applicable to the highest energies where even the phase boundary to the QGP might be reached as described in the next section. A compilation of the model parameters, temperature and average transverse expansion velocity, is shown in Figure . At beam kinetic energies per nucleon below about 1 GeV and in central collisions for the heavier systems the expansion proceeds in an almost spherically symmetric fashion, while for higher incident energies and lighter mass systems larger longitudinal velocities are observed. In those cases transverse momentum spectra at midrapidity have been used to extract the average transverse expansion velocity. Initially, in the domain of hadronic matter, the temperature as well as the expansion velocity rise almost linearly with the logarithm of the incident energy leading to quite exotic conditions where up to 50% of the available energy is transformed into collective kinetic energy. Note that for the highest beam energies shown (AGS and SPS data) the temperature values are deduced from an analysis of hadron yields and the spectra using these temperature values then yield the transverse flow velocities shown. A detailed understanding of the expansion scheme is not achieved yet. That the simple picture of a sudden and common freeze-out needs to be refined is made evident by systematic differences arising from different analysis approaches (Figure ): The temperatures derived in the analysis of spectra of light nuclei (A < 20) are systematically lower and the average flow velocities are larger as compared to results obtained from light particle ($\Delta$ 4) data. The rather complete set of data available with a long lever arm in the ejectile masses is well suited to allow a more refined characterisation of the freeze-out scenario. Further studies and high statistics measurements should allow to determine the flow profile as it develops during the expansion together with the freeze-out conditions that might be very different from the static ones due to supersonic expansion with . A theory that reproduces the expansion properties is not at hand yet.
 

Particle Production

    The thermodynamic conditions implied by the analysis of the spectra of light nuclei can be tested by the yields of produced particles. Below a beam kinetic energy of 2A GeV produced mesons like pions and eta mesons originate almost exclusively from the decay of baryon resonances and can be used to determine the baryon resonance population at freeze-out. One finds that the -resonance is populated with 10 and 20% probability at 1 and 2/A GeV beam energy and estimates a probability of 30% for the high density phase at 2A GeV; this implies that one faces the formation of resonance matter and has to consider interactions among resonances. These baryon resonances become especially important for the production of heavier mesons since they serve as an energy reservoir in multiple collisions and enhance sub-threshold processes. Within the current accuracy all non-strange baryon and meson yields can be consistently accounted for both by dynamical calculations and by a thermal model including chemical equilibrium.

 

Figure: Near Threshold Meson Production Probabilities. Recent data from GSI and some older data from the Bevalac.

 

For strange mesons the situation looks quite different. Kaon (K⁺) production rates are low with respect to phase space expectations based on non-strange mesons as can be seen from Figure . The production probability per participant nucleon is represented for the various mesons versus the fraction of the incident energy that is available for the meson production. While $K^-N\rightarrow \Lambda \pi$-mesons follow the overall trend set by the pion data (solid line), kaons show a different near threshold production behaviour. The attempt to interpret their production probabilities shows a strong sensitivity to poorly known  $NN\rightarrow NK^+\Lambda$cross sections, to the -resonance population and to the equation of state. By constraining the first two points by new measurements of the elementary cross section and a consistent analysis of complete sets of pion data that are becoming available, there is a chance to isolate the effects of the equation of state. One other observation from Figure  is remarkable and deserves further attention: in heavy ion collisions, at the same energy available to a colliding nucleon pair, antikaons (K^-) are produced with comparable yields as K⁺. This is surprising, because the K^- production cross section in nucleon-nucleon collisions at comparable incident energies is reduced by an order of magnitude with respect to K⁺ production, and in addition the absorption process ( $K^-N\rightarrow \Lambda \pi$) should further suppress the K^- to K⁺ ratio. To explain the similarity of the observed yields, a different mechanism may be needed for the strange meson production: theoretically, the difference could be a signal for the partial restoration of chiral symmetry since, at densities somewhat in excess of normal nuclear matter density, K^- should experience a reduction of the mass while K⁺ masses are changed very little. At twice ground state nuclear matter density, a value that is typically reached in heavy ion collisions at SIS energies, the K^- meson might have lost already 50% of its mass. These exciting possibilities certainly demand further efforts. For example, the low momentum parts of the kaon spectra where in-medium effects are most pronounced have to be measured. In general, experiments aimed at delineating the properties of vector mesons in hadronic matter are currently of great interest as they provide the opportunity to test predictions about the partial restoration of chiral symmetry: as one approaches the phase boundary between the "normal" hadronic world and the quark gluon plasma the masses of the vector mesons should be reduced because of the disappearance of the quark condensate. Precursor phenomena are already expected at normal nuclear matter density and should be enhanced at the temperatures and densities available at the SIS accelerator. With hadronic observables the $\Lambda$-meson can be reconstructed, while for the $\rho$ and  mesons the measurement of dileptons is the mandatory choice to pursue this interesting question. The dilepton spectrometer HADES is currently being built at GSI. This detector will combine dilepton mass resolutions of the order of 1 % with a very large acceptance and hence be a unique facility for the investigation of the properties of (vector) mesons in hadronic matter, of dilepton production in pp and $\pi$p collisions, and of electromagnetic form factors of hadrons. The experiments with the Hades facility will use the relativistic heavy ion beams (including protons and deuterons) from the SIS accelerator as well secondary beams from the pion beamline which is currently under construction at GSI. First experiments are planned for late 1998. The Hades collaboration presently consists of about 100 European physicists from 14 different institutions.
 
 

Sideflow of Produced Particles

    Besides measuring the production yields of particles, some of the predictions based on the partial restoration of chiral symmetry can also be tested by the propagation properties of particles through their expanding environment. According to recent theoretical studies dropping masses are accompanied by modifications of the propagation of the particles through the nuclear medium. An example is shown in the lower part of Figure : various in-medium potentials for kaons were tested for their relevance to the finally observed sideward flow pattern. The sideflow of the nucleons offers the qualitative feature of pointing into the direction of the highest baryon density. Depending on their interaction particles can be either attracted towards this direction or repelled. Because of the associated production mechanism near threshold, the difference between $\Lambda$ and K⁺ has to arise from differences in the rescattering and/or the potentials and thus probes the propagation process.

 

Figure: Sideflow of lambdas and kaons measured at GSI in comparison to nucleons. In the lower part of the figure transport model predictions for various in-medium potentials for kaons are shown.

 

Data with enough accuracy to resolve the different theoretical assumptions start to emerge and thus open the possibility to cross check the ideas that are introduced for the understanding of the production process. Currently, within the framework of the chiral models the available K⁺ data on the production and the flow seem to be consistent by requiring the balancing action of a scalar and a vector potential. Certainly more exclusive data with stronger flow effects in heavier systems will be needed to reach final conclusions. Measurements of K^- flow will also help to clarify the situation.