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The systematics of statistical model parameters extracted from heavy-ion collisions at lower energies are exploited to extrapolate in the LHC regime. Predictions of various particle ratios are presented and particle production in central Pb-Pb collisions at LHC is discussed in the context of the statistical model. The sensitivity of several ratios on the temperature and the baryon chemical potential is studied in detail, and some of them, which are particularly appropriate to determine the chemical freeze-out point experimentally, are indicated. The impact of feed-down contributions from resonances, especially to light hadrons, is illustrated.

In astrophysics as well as in hadron physics, progress has recently been made on the determination of the hadronic equation of state (EoS) of compressed matter. The results are contradictory, however. Simulations of heavy-ion reactions are now sufficiently robust to predict the stiffness of the EoS from (i) the energy dependence of the ratio of K+from Au + Au and C + C collisions and (ii) the centrality dependence of the K+multiplicities. The data are best described with a compressibility coefficient at normal nuclear matter density ? of around 200 MeV, a value which is usually called 'soft'. The recent observation of a neutron star with a mass of twice the solar mass is only compatible with theoretical predictions if the EoS is stiff. We review the present situation.

The recently discovered sharp peak in the excitation function of the K+/?+ratio around 30 AGeV in relativistic heavy-ion collisions is discussed in the framework of the statistical model. In this model, the freeze-out of an ideal hadron gas changes from a situation where baryons dominate to one with mainly mesons. This transition occurs at a temperature T= 140 MeV and a baryon chemical potential ?B= 410 MeV corresponding to an energy of . The calculated maximum in the K+/?+ratio is, however, much less pronounced than that observed by the NA49 Collaboration. The smooth increase of the K?/??ratio with incident energy and the shape of the excitation functions of the ?/?+, ??/?+and ??/?+ratios all exhibiting maxima at different incident energies is consistent with the presently available experimental data. The measured K+/?+ratio exceeds the calculated one just at the incident energy when the freeze-out condition is changing. We speculate that at this point freeze-out might occur in a modified way. We discuss a scenario of an early freeze-out which indeed increases the K+/?+ratio while most other particle ratios remain essentially unchanged. Such an early freeze-out is supported by results from HBT studies.

The status of the energy dependence of the chemical freeze-out temperature and chemical potential obtained in heavy-ion collisions is presented. Recent proposals for chemical freeze-out conditions are compared.

The production of K⁺ and of K⁻ mesons in heavy-ion collisions at beam energies of 1 to 2 A GeV has systematically been investigated with the kaon spectrometer KaoS. The ratio of the K⁺ production excitation function for Au+Au and for C+C reactions increases with decreasing beam energy, which is expected for a soft nuclear equation-of-state. A comprehensive study of the K⁺ and of the K⁻ emission as a function of the size of the collision system, of the collision centrality, of the kaon energy, and of the polar emission angle has been performed. The K⁻/K⁺ ratio is found to be nearly constant as a function of the collision centrality and can be explained by the dominance of strangeness exchange. On the other hand, the spectral slopes and the polar emission patterns are different for K⁻ and for K⁺. Furthermore the azimuthal distribution of the particle emission has been investigated. K⁺ mesons and pions are emitted preferentially perpendicular to the reaction plane as well in Au+Au as in Ni+Ni collisions. In contrast for K⁻ mesons in Ni+Ni reactions an in-plane flow was observed for the first time at these incident energies.

The production and the propagation of K⁺- and of K⁻-mesons in heavy-ion collisions at beam energies of 1 to 2 A GeV have systematically been investigated with the Kaon Spectrometer (KaoS) at the SIS at the GSI. The ratio of the K⁺-production excitation function for Au+Au and for C+C reactions increases with decreasing beam energy, which is expected for a soft nuclear equation-of-state. At 1.5 A GeV a comprehensive study of the K⁺- and of the K⁻-emission as a function of the size of the collision system, of the collision centrality, of the kaon energy, and of the polar emission angle has been performed. The K⁻/K⁺ ratio is found to be nearly constant as a function of the collision centrality. The spectral slopes and the polar emission patterns are different for K⁻ and K⁺. These observations indicate that K⁺-mesons decouple earlier from the reaction zone than K⁻-mesons.

Abstract: A review of meson emission in heavy-ion collisions at incident energies from SIS up to collider energies is presented. A statistical model assuming chemical equilibrium and local strangeness conservation (i.e. strangeness conservation per collision) explains most of the observed features, e.g. the different centrality dependences of pions and kaons. Furthermore, the independence of theK + toK - ratio on the number of participating nucleons observed between SIS and relativistic heavy-ion collider (RHIC) is consistent with this model. The observed maximum in theK +/π+ excitation function is also seen in the ratio of strange to non-strange particle production. The appearance of this maximum around 30 A.GeV is due to the energy dependence of the chemical freeze-out parametersT and μB.

The production and propagation of kaons and antikaons in relativistic heavy-ion collisions have been systematically investigated with the Kaon spectrometer at SIS/GSI. Experimental results on the K⁺ and K⁻ yield and on the azimuthal emission pattern of K⁺ mesons are presented. Within the framework of transport models the data can be explained assuming in-medium kaon–nucleon potentials. The comparison of K⁺ production excitation functions obtained for Au+Au and C+C collisions with results of transport model calculations favours a soft nuclear equation-of-state.

At the Kaon spectrometer KaoS at SIS/GSI, the production of kaons and antikaons in heavy-ion reactions at a beam energy of 1.5 A GeV has been measured for the collision systems Ni + Ni and Au + Au. The K⁻/K⁺ ratio is found to be constant for both systems and as a function of impact parameter but the slopes of K⁺ and K⁻ spectra differ for all impact parameters. Furthermore, the respective polar angle distributions will be presented as a function of centrality.

A γ-activation method for measuring the thickness of thin CsI(Tl) polycrystalline films deposited by evaporation on large-area (∼150 cm2) backings is described. Scintillators specially prepared to be used in the FASA installation as detectors of intermediate-mass fragment multiplicity were measured. It was shown that the distribution of the film thickness along the scintillator surface can be determined by β-activity scanning. It has been shown that the film thickness decreases from the middle of the backing to its periphery by ≈25% for scintillators with a linear size of 140 mm.

Abstract:: Production cross-sections of charged pions, kaons and antikaons have been measured in C+C and C+Au collisions at beam energies of 1.0 and 1.8 AGeV for different polar emission angles. The kaon and antikaon energy spectra can be described by Boltzmann distributions whereas the pion spectra exhibit an additional enhancement at low energies. The pion multiplicity per participating nucleon M(π+)/part> is a factor of about 3 smaller in C+Au than in C+C collisions at 1.0 AGeV whereas it differs only little for the C and the Au target at a beam energy of 1.8 AGeV. The K+ multiplicities per participating nucleon M(K+)/ part> are independent of the target size at 1 AGeV and at 1.8 AGeV. The K- multiplicity per participating nucleon M(K-)/ part> is reduced by a factor of about 2 in C+Au as compared to C+C collisions at 1.8 AGeV. This effect might be caused by the absorption of antikaons in the heavy target nucleus. Transport model calculations underestimate the K-/K+ ratio for C+C collisions at 1.8 AGeV by a factor of about 4 if in-medium modifications of K-mesons are neglected.

Double differential cross sections for protons, π+and K+are measured in Au + Au collisions at 1.0 GeV/u and Θlab=44°±4° with a new magnetic spectrometer at SIS. The pion spectra show an enhancement at low momenta with respect to a thermal distribution and little dependence on the collision centrality. The high-energetic pions measured in semi-central collisions at approximately midrapidity exhibit an anisotropic azimuthal angular distribution, peaking at 90° and 270° with respect to the reaction plane. The same feature is observed for protons. The kaon to proton ratio increases with the number of participating nucleons, i.e. with the centrality of the collision, whereas the pion to proton ratio stays constant. The first data on subthreshold K+production in a heavy mass collision system are discussed with respect to nuclear matter properties by a comparison to microscopic transport calculations.

Triple differential cross-sections of midrapidity pions from 209Bi+209Bi collisions were measured with the Kaon Spectrometer at SIS at incident energies of 400, 700 and 1000 AMeV. The azimuthal emission pattern of the pions has been investigated in dependence of beam energy and impact parameter. An enhanced emission of pions perpendicular to the reaction plane is observed. The strength of the anisotropy increases with beam energy and pion transverse momentum. In contrast to the nucleons the anisotropy varies only little with the impact parameter. No difference in the behaviour of positive and negative pions is observed.

Abstract:: Multiple emission of intermediate-mass fragments has been studied for the collisions p + Au at 2.16, 3.6 and 8.1 GeV with the FASA setup. The mean IMF multiplicities for events with at least one IMF are equal to 1.7, 1.9 and 2.1 (±0.2) respectively. The multiplicity, charge distributions and kinetic energy spectra of IMF are described in the framework of a intranuclear cascade model followed by the statistical multifragmentation model. However, between the two parts of the calculation the excitation energies and the residual masses and charges are modified to take into account the losses during expansion. The results support a scenario of true thermal multifragmentation of a hot and expanded target spectator.

Positively charged pions and protons from collisions of Ne+NaF and Au+Au at 1 GeV/nucleon incident energy were measured near midrapidity. The center-of-mass pion spectra deviate from a Maxwell-Boltzmann distribution. The slope of the high-energy part of the pion spectra varies significantly with the system mass and little with the size of the reaction zone. While the total pion yield rises linearly with the number of participant nucleons, the highenergy component increases more than linearly.

Transfer reactions induced by 16O and 18O beams on 148Nd were measured with a time-of-flight setup at 72 MeV incident energy. The angular distributions are bell shapes having their maxima at angles somewhat below the grazing angle. The excitation in the final nuclei takes place (if possible) near the optimum Q-value and is spread over 5 MeV for the one-particle transfer reactions and up to 10 MeV for the multiparticle transfers. The cross sections for the individual channels are explained mostly by Q-window considerations. In spite of the differences in the individual channels the total transfer cross section integrated over excitation energy, angle, and all channels turns out to be the same same for both 16O and 18O beams. This cross section amounts to 20 % of the total reaction cross section and nicely fills the gap between the measured fusion cross section and the total reaction cross section obtained from optical model calculations based on elastic scattering data.

Midrapidity protons from209Bi+209Bi collisions were measured with the Kaon Spectrometer at SIS at incident energies of ELab/A=400, 700 and 1000 MeV. Additionally, light fragments were analysed at 400 MeV. We have investigated the azimuthal emission pattern of the particles relative to the reaction plane as function of transverse momentum, bombarding energy and impact parameter. We observe an enhanced emission of particles perpendicular to the reaction plane at all bombarding energies. The ratio of the number of particles emitted out-of-plane/in-plane increases strongly with the particles transverse momentum. The anisotropy decreases with increasing beam energy. Composite particles show a much stronger effect than protons.

Double differential cross sections of positively charged pions and protons have been measured in nuclear collisions of mass-symmetric systems (Ne+NaF, Ni+Ni, Au+Au, Bi+Pb) at incident energies between 0.8 and 1.8 AGeV as a function of the centrality of the reaction. Using a magnetic spectrometer pions and protons were detected with laboratory angles between 40 and 48 degrees, and with momenta up to about 1400 MeV/c. This setting allows for the study of pions and protons emitted close to midrapidity. The center-of-mass pion spectra deviate from a Boltzmann distribution. The inverse slope parameters of the high-energetic pions are smaller than those of the proton spectra and they exhibit a weaker centrality dependence. A scenario is presented where the shape of the pion spectra reflects the decay kinematics of nucleonic resonances embedded in the thermal and the collective motion of the nucleons in the reaction zone. The number of emitted pions per participating nucleon is higher for light than for heavy mass systems. For a given mass system, the total pion multiplicity increases linearly with the number of participating nucleons, whereas the multiplicity of high-energy pions increases more than linearly. This result is consistent with a scenario where the high-energy pions are produced in multiple energetic baryon-baryon collisions occurring in the high-density phase of the collision.

Subthreshold kaon production in197Au+197Au collisions at 1.0 GeV/u has been investigated with the Kaon Spectrometer at SIS. At Tlab=44±4° we found aK+/p ratio of>3 · 10-4 for the momentum range 650 MeV/c to 1150 MeV/c.