% % Lecture presentation aid for the textbook: % % Laszlo P. Csernai: " Introduction to Relativistic Heavy Ion Collisions" % (John Wiley and Sons Ltd, Chicester, New York, Brisbane, Toronto, % Singapore, 1994; ISBN - 0-471-93420-8) % % Transparencies for Lecture 1 / Chapter 1 % % The following file is containing transparencies in plain LaTeX format. % Figures are usually not included, they can be pasted from the printed % textbook. Empty space is left for this purpose. Some LaTeX figures are % included in the files. 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Csernai: Inroduction to Relativistic Heavy Ion Collisions (Wiley, 1994)} \put(10,235){\parbox[t]{170mm}{\Large\sf \parskip=0.3cm #1}}\end{picture} }%end transparencyframe % \begin{document} \pagestyle{plain} % transparency ===================================================== \transparencyframe{ \vskip 2truecm \begin{center} {\LARGE\bf Introduction to }\\[1ex] {\LARGE\bf Relativistic Heavy Ion Collisions}\\[2ex] {\sc L\'aszl\'o P. Csernai} \end{center} \vskip 1.5truecm John Wiley and Sons Ltd, Chicester, New York, Brisbane, Toronto, Singapore, 1994 ISBN - 0-471-93420-8 \vfill }%end tr-page \newpage % transparency ===================================================== \transparencyframe{ \vspace*{-1.5cm}\chapter{Basic Phenomenology of Heavy Ion Collisions} \section{Introduction} {\bf 1970's, early 1980's:} Bevatron in Berkeley, Dubna Syncrophasotron p accelerators converted to accelerate heavy ions.\\ Accelerators for nuclear research: increased energy $\Longrightarrow$ Beams of heavy nuclei: NSCL/MSU in East Lansing, GSI in Darmstadt, GANIL, Saclay, Celsius ring in Uppsala, etc.. {\bf Mid 80's:} Large proton accelerators converted: Alternating Gradient Synchrotron (AGS) at Brookhaven National Laboratory (BNL) \& Super Proton Synchrotron (SPS) at the European Center for Nuclear Research (CERN). {\bf Mid 90's:} Heavy ions at the planning phase for Large Hadron Collider (LHC) of CERN. Why did high energy nuclear physics become so much the center of interest again? {\bf The main reason is the exploration of the Quark-Gluon Plasma (QGP).} }%end tr-page \newpage % transparency ===================================================== \transparencyframe{ \vspace*{-1.5cm}\subsection{The Quark Gluon Plasma} \B Early 70's: deep inelastic electron collisions on protons $\Longrightarrow$\\ $\exists$ internal structure in nucleons: {\bf quarks} and {\bf gluons}. \B Quantum Chromodynamics (QCD), conclusion: single free quarks (q) or gluons (g) cannot be observed in laboratories. \B In physical vacuum q \& g-s are {\bf confined} by the strong interaction. This is represented by the quantum number {\bf ``color''}, and all particles are colorless. \B At high energy densities (like Early Universe) colored objects may propagate longer distances. \B QGP in laboratory in heavy ion reactions at 10 - 100\agev\ \\ (10 - 100 fm$^3$ \& 2 - 10 fm/c). \subsection{The nuclear Equation of State} \B At $\approx$ 100 A$\cdot$ GeV, number of particles involved in a reaction may go up to several thousand: Sufficient for statistical and kinetic approach. \B The thermodynamical properties of the matter in statistical equilibrium are described by an Equation of State, (EOS) with interesting features: - i) phase transition from continuous nuclear liquid into a nuclear vapor of fragments and nucleons: the nuclear liquid-gas phase transition, or multifragmentation. - ii) the compressibility of nuclear matter at and high densities - iii) the phase transition to QGP $\exists$ nonequilibrium: transport coefficients, in-medium cross sections. }%end tr-page \newpage % transparency ===================================================== \transparencyframe{ \vspace*{-1.5cm}\subsection{New collective phenomena} \B Hot and compressed nuclear matter behaves like a {\bf compressible fluid} and fluid dynamical effects are observed in these reactions. - $\exists$ Sidewards flow, bounce-off, - Squeeze out of the hot zone between the two nuclei, orthogonally to the reaction plane - Transverse flow decreases with decreasing energy, goes to zero at around 100 \amev\ and turns to a negative angle flow. (Nucl. attraction) \subsection{Particle production} In HI reactions new particles are produced \B Collective effects, Fermi motion, $\Longrightarrow$ at low energies where, in free nucleon-nucleon collisions, production is not possible. \B Production of exotic particles, such as strangelets, is also predicted. }%end tr-page \newpage % transparency ===================================================== \transparencyframe{ \vspace*{-1.5cm}\section{Energy domains of heavy ion physics} Energies from 100 \amev\ beam energy to 10 A$\cdot$TeV. $\Longrightarrow$ \\ $\exists$ many different collision processes and physical phenomena, Will concentrate on features common to the whole heavy ion research: relativistic statistical description, collective phenomena which can not be studied elsewhere. The energy region can be divided: - i) intermediate energy heavy ion reactions, - ii) relativistic energy heavy ion reactions, - iii) ultra-relativistic heavy ion reactions. \subsection{Intermediate energy reactions} Properties around the normal nuclear density, $n_0$. Beam energies: 10 - 100 \amev. {\bf The nuclear liquid-gas phase transition:} Low excitations: the nuclear matter is bound due to the attractive nuclear interaction. - In HI coll. compress the nuclear matter to 1-2 $n_0$ and heat up the matter to 10 - 20 MeV. - Then expand nearly adiabatically to densities below $n_0$. In final state smaller nuclear fragments are formed, the nucl. vapor is condensed to form droplets. This is the nuclear multi-fragmentation. Critical phenomena, can be studied. NSCL at Michigan State University, UNILAC and SIS at GSI in Darmstadt Germany, GANIL in Caen France, CELSIUS in Uppsala Sweden, etc. }%end tr-page \newpage % transparency ===================================================== \transparencyframe{ \vspace*{-1.5cm}\subsection{Relativistic heavy ion reactions} Energy range, 100 \amev - 10 \agev $\Longrightarrow$ \\ Nuclear matter is compressed and heated more than at lower beam energies. \B Compressibility and other basic properties of the nuclear EOS and nuclear interactions can be tested. - This energy range has astrophysical relevance to neutron stars and supernova explosions. - Nuclear incompressibility,\\ - Transport coefficients,\\- In medium cross sections,\\ - Momentum dependence of the nucleon-nucleon interaction, etc., are studied. - Collective processes are well established both experimentally and theoretically. The most dominant is the collective sidewards flow in the reaction plane. Used to extract the EOS and transport properties. \bigskip SIS at GSI Darmstadt, the heavy ion accelerator in Dubna, SATURN in Saclay France and earlier the BEVALAC at LBL in Berkeley, }%end tr-page \newpage % transparency ===================================================== \transparencyframe{ \vspace*{-1.5cm}\subsection{Ultra-relativistic heavy ion reactions} From 10 \agev\ beam energy. Lowest estimated QGP threshold. \B $\exists$ two regimes:\\ - i) {\em stopping region:} baryons from the projectile and the target are (partly) stopped by each other $\leadsto$ baryon rich matter\\ - ii) {\em transparent region:} baryons are far apart in the phase space, \& cannot slow down completely. \subsubsection{Stopping region} SPS at CERN and AGS at BNL, $\leadsto$ stopping up to 60 \agev Theoretical estimates: Stopping up to 200 or 800 \agev - Study: highly excited {\bf baryon rich} matter, or baryon rich QGP. - Astrophysical relevance: hybrid stars, i.e. neutron stars with dense quark matter core. \subsubsection{Transparent region} Middle zone in the reaction will be {\bf baryon free.} Energy deposited in this region may form a baryon free QGP. - Theoretical calculations are more straightforward. - Astrphysical relevance: Early universe before hadrons were formed. LHC heavy ion collider at CERN, RHIC at BNL. (TEVATRON at Fermilab: $p+\bar{p}$) }%end tr-page \newpage % transparency ===================================================== \transparencyframe{ \vspace*{-1.5cm}\section{Heavy ion experiments} New experimental approach required. LOW ENERGY NUCLEAR PHYSICS: \\ \B Most frequent is an elastic collision (target and projectile maintain their integrity and their internal quantum state).\\ \B Inelastic processes: one or both of the outgoing particles may be in excited states, and even some extra particle(s) may be created.\\ \B Final multiplicity is rather small. Consequently one or at most two outgoing particles are detected.\\ \B Reaction plane cannot be reliably identified (e.g. not measured neutrals). Thus azimuth averaged cross sections are given. RELATIVISTIC HEAVY ION COLLISIONS:\\ \B Multiplicities are large, at 100 \amev\ beam energy; about 10 - 100 secondaries; at 100 \agev\ produced particles may exceed 1000.\\ \B Large multiplicity $\leadsto$ special experimental requirements.\\ \B Event by event detection is desirable.\\ \B Measure all emitted particles simultaneously. - Consequence --- highly segmented detector arrays: the MSU 4$\pi$ detector, the BEVALAC Plastic Ball, or the large detector arrays at the CERN-SPS and BNL-AGS.\\ - Alternatively large volume track detectors like the streamer chamber, time projection chamber (TPC) or stacks of nuclear emulsion. %High energy particle detectors %are using top technology, but heavy ion detectors have %special extra features. With these advanced detectors %the increasing multiplicity does not seem to be an obstacle at the %first sight, but the track recognition problem becomes %increasingly difficult at very large multiplicities. Recently new %techniques are experimented with, like neural networks, to solve %the track recognition problem. % %The relativistic heavy ion experiments thus are large scale %efforts %involving several dozen researchers usually and large systems %of equipment, similarly to modern particle physics experiments. % Experimental tasks:\\ (i) equipment design and construction,\\ (ii) data taking,\\ (iii) data evaluation (!!!) }%end tr-page \newpage % transparency ===================================================== \transparencyframe{ \vspace*{19cm} Figure 1.1 {\it The layout of the SPS at CERN, Geneva. From [7] } }%end tr-page \newpage % transparency ===================================================== \transparencyframe{ \vspace*{19cm} Figure 1.2 {\it The layout of the RHIC at Brookhaven National Laboratory. From [9] } }%end tr-page \newpage % transparency ===================================================== \transparencyframe{ \vspace*{-1.5cm}\subsection{Acceptance} Detectors: limited size, given geometry $\leadsto$ forward / backward problem. - Target (mostly) in vacuum $\leadsto$ soft particles ($<$ 20 - 30 MeV) lost. - Acceptance of the detector: no orthogonal cuts in parallel and orthogonal momenta $\leadsto$ To construct spectra is difficult. \subsection{Event selection} $\exists$ Head on or only grazing collisions. Assumption: more central the collision $\leadsto$ more outgoing particles. Probability of $b\pm d b$ increasing as $\propto \ 2\pi b$. E.g.: 25 \% highest multiplicity 1/2 of impact parameters. \B Impact parameter selection: not exact, $\exists$ random fluctuations. Selected set of data, $M\epsilon S$, corresponds to a set with distribution of impact parameters, $P_M(b)$. This distribution is not known. }%end tr-page \newpage % transparency ===================================================== \transparencyframe{ \vspace*{-1.5cm}\subsubsection{EVENT TRIGGER} Select e.g. 25 \% of the highest multiplicity collisions: \B 1) we have to determine how much is 100 \% of the collisions: (It is possible that some particles are missed, thus some low multiplicity events are not detected at all.) \subsubsection{SELECTION TRIGGER} \B 2) Then after a complete sample, select a SUBSET of violent events. - Multiplicity measured with a detector of $4 \pi$ acceptance: OK - Reduced triggering device or software selection criteria are used. Impact parameter distribution of the SUBSET is basically unknown: $\leadsto$ Simulations with a theoretical model. \subsection{Physical event tape} The above features are quite general in heavy ion experiments. Primary data are quite different in different experiments, Data evaluation: converting {\bf primary data} to a physical data set: \B The detected particles and their characteristics. A set of events with all characteristic data on each emitted particle is than stored on a physical data tape. Used to evaluate the desired cross section, momentum distribution, correlation, etc. }%end tr-page \newpage % transparency ===================================================== \transparencyframe{ \vspace*{-1.5cm}\subsection{Detector filters} \B Some theoretical models produce "physical data tapes"\\ Called: {\em event generators}. 1) Theoretical models: not limited by detector acceptance. 2) Theoretical set of events might not correspond to the experimentally selected set. - Some experimental groups provide computer codes to simulate their detector acceptance and triggering. The theoretical data tape should then be filtered through the particular detector acceptance program and the resulting {\em filtered} theoretical data can be compared to experimental data. (Not frequently done) - Experimental groups perform simpler theoretical calculations to make extrapolations to a given region of the phase space. These extrapolated data are then published usually (directly comparable to theoretical results. \subsection{Outline} Experimental methods of representing the primary physical data\\ are presented, but experimental techniques are not discussed. The most important measurables will be discussed, \\ after the introduction of basic theoretical aspects of a nonequilibrium, high energy, many-body system. }%end tr-page \newpage % transparency ===================================================== \transparencyframe{ \vspace*{-1.5cm}\section{General features of heavy ion physics} $\exists$ some common aspects of heavy ion reaction dynamics. \B The energies are large enough and the masses of ions are also large $\leadsto$ heavy ions considered as classical particles. Their De Broglie wavelength is much less than typical nuclear sizes. Quantum effects in microscopic dynamics only: in the EOS, transport coefficients, kinetic theory. At relativistic and ultra-relativistic energies: even nucleons can be considered as classical particles. \B This and the short range of the nuclear interaction $\leadsto$\\ {\bf geometrical concepts} apply (e.g.): total cross section, separation of {\em participant} and {\em spectator} regions. In reality the separation between spectators and participants is not exact. With increasing energy, however, it gets better. \vspace*{6.5cm} Figure 1.3 {\it Spectators and participants in a heavy ion collision. From [10] } }%end tr-page \newpage % transparency ===================================================== \transparencyframe{ \B Most interesting phenomena: in the {\bf participant zone}. However, e.g. spectators may form (somewhat excited, irregularly shaped), extremely neutron rich light fragments not produced in laboratory before. (C.f.: heavy nuclei are much more neutron rich, N/A, than light ones.) Realistically the nucleons do not propagate along exactly straight trajectories. Fluid dynamical model: considerable collective sideward motion is generated. \vspace*{10cm} Figure 1.4 {\it Final state in a collision of Ne+U in the fluid dynamical model. The dotted line encloses a region of temperature $T> 10$ MeV, other lines are encircling the regions of high density in the target and projectile residues. The arrows indicate the flow velocity field. From [13] } }%end tr-page \newpage % transparency ===================================================== \transparencyframe{ \vspace*{-1.5cm}\section{Connections to other fields of physics} \subsection{Nuclear physics} \B Nuclear equation of state (EOS). In low energy nuclear reactions the EOS could be studied at essentially zero temperature and at densities very close to the ground state. At relativistic energies Heavy Ion reactions map out a much larger domain of the field of thermodynamical variables. \B Nucleon-nucleon interaction. Basic for microscopic dynamics, and determines the non-equilibrium or transport properties of the nuclear matter. \subsection{Particle physics} \B Hadronic collision phenomenology. Basis of many reaction models directly (like string Monte Carlo models), and many other models extract features from hadron physics. Necessary to extract the colective nuclear processes from the simple superposition of many independent hadronic collisions. \B Nonperturbative QCD. Numerical studies, ``Lattice QCD'': equilibrium and nonequilibrium QCD. - Subthreshold particle production: Fermi motion, but also collective effects (like cumulative production). }%end tr-page \newpage % transparency ===================================================== \transparencyframe{ \vspace*{-1.5cm}\subsection{Statistical physics} \B Heavy ion reaction: dynamical system, few hundred nucleons. - Deviations from infinite matter limit are important. - Signs of collective matter behaviour can be clearly observed. Statistical physics of small but collective systems. \B Quark Gluon Plasma: number of quanta increases. - Continuum, finite particle effects are small. - Dynamical process: phase transitions in a dynamical system: An open field of research. Heavy ion physics may contribute to this field at two points: i) the dynamics of the phase transitions in "small" systems, and ii) the dynamics of the phase transitions in ultra-relativistic systems where the energy of the system is much higher than the rest mass of the particles. \B Transport theory at high energies. Many numerical reaction models were developed based on transport theory, and the field is in rapid development today. \subsection{Relativistic fluid dynamics} Terrestial possibility to test the solutions of relativistic fluid dynamics. \B Relativistic detonations and deflagrations. \B Multicomponent fluid dynamical models. }%end tr-page \newpage % transparency ===================================================== \transparencyframe{ \vspace*{-1.5cm}\subsection{Astrophysics} Most interesting connection to other fields of physics: Models of the early universe, of neutron stars, supernova explosions, quark stars, etc. \B EOS: Studies by both astrophisicists and heavy ion researchers. Conclusions from heavy ion data should be checked against the known astrophysical information. - E.g.: Compressibility from HI data $\Longleftrightarrow$ Mass of the neutron stars $\leadsto$ Heavy ion data should not support neutron star masses which contradict to the observations; i.e. smaller maximum mass than the observed maximum. - Early universe: strongly influenced by the phase transitions in the highly energetic matter, particularly by the formation of hadrons. \section{Why a theoretical treatment is important?} These lectures: both for theorists and experimentalists as an {\em introduction} to the field: introductory knowledge mainly from the theoretical side. Theorists should also be aware of experimental possibilities and limitations which are mentioned in the book. Both experimentalists and theorists should be familiar, on the other hand, with the basic theoretical concepts of the field. }%end tr-page \newpage % transparency ===================================================== \transparencyframe{ \vspace*{-1.5cm}\section{Outline of the course} {\it Lectures 2 and 3:} Introduction to transport theory of relativistic systems. Examples from heavy ion physics. Basics of equilibrium and non-equilibrium systems and how systems evolve towards equilibrium. {\it Lecture 4:} Nuclear equation of state (EOS), static equilibrium system. {\it Lecture 5:} Relativistic fluid dynamics. Dynamical systems which are locally eqilibrated but not globally. Heavy ion reactions in the "ideal" case belong to this category, if the system is sufficiently large. {\it Lecture 6:} Simple reaction models are presented, widely used both by theorists and experimentalists in the recent years. These are all simple fluid dynamical models. {\it Lecture 7:} Experimental observables. Connections to the collective properties. {\it Lecture 8:} Energy and mass scaling of the observables are discussed, i.e. how can one compare experimental reasults measured at different beam energy or in different colliding systems. {\it Lecture 9:} Kinetic reaction models not assuming a priory equilibrium are introduced. Since most of these are numerical microscopic models we constrain ourselves to the presentation of the basic features and the results of these models. {\it Lecture 10:} Overview of the search for quark gluon plasma is given. More information on the EOS based on Lattice QCD. Reaction dynamics is discussed in different energy regions, {\it Lecture 11:} Connections between astrophysics and heavy ion reactions are presented. }%end tr-page \newpage % transparency ===================================================== \transparencyframe{ \vspace*{-1.5cm}\section{Assignment 1} {\bf Assignments are important: Some of the concepts used in the field are introduced in assignments! Brief solution is provided in the textbook. } \subsection*{Participants and Spectators} \begin{description} \item[1.a] Calculate the number of participant nucleons in a central S + Pb reaction, assuming that the nuclei have sharp surfaces and their density distribution is uniform, $n_0=0.17/$fm$^3$. \item[1.b] What is the center of mass kinetic energy of the participants in the laboratory frame if the Sulphur projectile had a beam kinetic energy of $\varepsilon_S^{(kin.)} = 200$GeV per nucleon in the lab, and the Lead was a fixed target. What is the average excitation energy of the participant nucleons. \end{description} }%end tr-page \end{document}