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Introduction

Nucleus-nucleus collisions are the tool to heat and/or compress atomic nuclei. The variation of the collision energy and the system size allows to control the degree to which this happens. In this chapter we will show how this tool can be used to study the phase diagram of nuclear and hadronic matter over a wide range of parameters. A key factor is the availability of a complement of accelerators that provide atomic nuclei with kinetic energies per nucleon ranging from a few tens of MeV to several TeV. In general, increasing the beam energy leads first to heating of the atomic nucleus, eventually, as the beam energy is further increased, to temperatures such that the concept of a nucleus will be replaced by that of a hot hadron gas and finally, at still higher beam energies, the concept of a hadron gas will be
  
Figure: The low temperature, low density part of the phase diagram and the critical region of the liquid-gas phase transition
\begin{figure}\epsfig{file=nnc/fig1.eps, width=\columnwidth}\end{figure}
 

replaced by that of a gas of the fundamental constituents of hadrons, quarks and gluons. To set the scale, typical excitation energies for the three regimes can be characterised by temperatures (i) below 10 MeV, (ii) 10-100 MeV, and (iii) above 100-200 MeV.

  
Figure: The phase diagram of hadronic matter and the hadron gas - quark-gluon plasma phase transition
\begin{figure}\epsfig{file=nnc/fig2.eps, width=\columnwidth}\end{figure}
 

The second relevant parameter to describe the phase diagram is a measure of the density or compression. This will be expressed either in terms of the nucleon (or baryon) density, $\rho$, in units of ground state nuclear matter density $\rho_0$, or in terms of the baryochemical potential $\mu_B$. There may in fact be a third important degree of freedom, not present in atomic nuclei, but possibly at somewhat higher excitation energies: strangeness. Since there is no evidence from experiment yet about the relevance of this degree of freedom, i.e. of hadronic matter with significant strangeness (beyond hypernuclei, that is), this possibility shall only be mentioned as a field for exploration. The regions of interest of the phase diagram are shown in Figures [*] and [*]. At moderate beam energies of the order of a hundred MeV per nucleon the nucleus is heated and compressed rather gently and may take during its decompression and cooling a path that leads into the regions marked in yellow and orange in Figure [*]. In these regions two phases of nuclear matter coexist, the Fermi liquid and a cold gas of nucleons and light nuclei. The system can find itself in the spinodal region of negative pressure and it then breaks up (marked by the red star) into fragments of all sizes in a process called `multifragmentation'. The physics of the liquid-gas phase transition is discussed in the section [*]. When the beam kinetic energy is increased to a few hundred to 1000 MeV per nucleon nuclear matter is compressed to two or three times its normal value and heated to a few tens of MeV. A hot and dense hadron gas is generated who's properties are dominated by the excitations of its original constituents, the nucleons. Meson production is starting to gain significance but the nucleon yield still dominates over the pions by typically one order of magnitude even at the top end of this energy range. This region is interesting because (i) to a very large degree the available energy is channelled into collective degrees of freedom during the cooling and expansion phase and (ii) it allows to sample the properties of hadrons embedded into a dense and hot baryonic medium. Section [*] deals with this energy range. At still higher temperatures and baryon densities there is the boundary from hadron gas to the quark-gluon plasma (QGP), indicated by the blue line in Figure [*]. Along the temperature axis this transition is predicted by Quantum Chromodynamics (QCD). Beyond the phase boundary confinement of quarks and gluons is lifted and chiral symmetry is restored. Present experiments create matter that is initially hot and very dense (up to 10 times normal nuclear matter density; indicated by the pink arrows) while at still higher beam energies achievable at the future colliders extreme heating of an essentially baryon free central region will dominate. Section [*] will address the current level of theoretical understanding as well as the present and future experimental possibilities to study the region of the QCD phase transition and the nature of the quark-gluon plasma. To extract the physics outlined in this chapter requires, beyond the appropriate accelerator facilities, close collaboration between experiment and theory. The specific needs and opportunities connected to the theoretical investigation of this field are discussed in section [*]


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