Title:

Introduction to Relativistic Heavy Ion Collisions

by L.P. Csernai

(John Wiley & Sons, Chichester, 1994) ISBN 0 471 93420 8

310 pages, 11 chapters (Norwegian Library Record - Bibsys) . . . Click on the icon above --> Full Text, PDF -->

PREFACE

This book is based on my courses given at the University of Minnesota, Michigan State University and University of Bergen between 1985 and 1992. It is written for advanced undergraduates, or beginning graduate students in physics both for experimentalists and theorists. The book contains more material than necessary for a one semester course to allow for some selection.

The purpose of the book is to give a general introduction to all beginners in the field of high energy heavy ion physics. It tries to cover a wide range of subjects from intermediate to ultra-relativistic energies, so that it provides an introductory overview of heavy ion physics, in order to enable the reader to understand and communicate with researchers of neighbouring or related fields.

Some familiarity with basic nuclear physics, statistical physics and special relativity is assumed. The book is essentially based on a simple introduction to relativistic kinetic theory, with ample examples from the field of heavy ion physics. It introduces the basic variables used in the field. Then collective macroscopic features of the dense and high temperature matter is discussed. Collective fluid dynamical approaches are introduced in a greater detail, and simple (frequently analytically solvable) models are presented. The properties of the nuclear Equation of State are discussed at an introductory level, mentioning some results from the recent years.

The connections between the collective dynamical descriptions and the experimentally measurable quantities are shown, and the mass and energy scaling of data is used to discuss the observability of dissipative properties of the high energy matter. Microscopic an inherently nonequilibrium descriptions are discussed only briefly.

Recent advances in the search for the Quark Gluon plasma are discussed in an extended chapter. Finally a few interesting connections to astrophysics are mentioned.

The book containes assignments with solutions of a wide range of different difficulties. The excercises are important, because some basic information is introduced via the excercises only.

The sections indicated by (*) are recommended for additional reading, and should not be included necessarily in a regular course. The presentation of the subject in the indicated sections is concise, thus the study of the original literature is advised to those who are interested in the subject particularly and in detail.

Laszlo P. Csernai

November, 1992

ERRATUM in Postscript (104 kB). The ERRATUM includes not only usual misprints but corrections to some formulae and problem solutions, so it is important to download. Revised on Aug. 1, 2002. Please if you observed other misprints which are not included yet in the ERRATUM, notify me by E-mail to csernai@ift.uib.no

CHAPTER Preface

CHAPTER 1 Basic Phenomenology of Heavy Ion Collisions
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Section 1.1 Introduction ** 1.1.1 The Quark Gluon Plasma ** 1.1.2 The nuclear Equation of State ** 1.1.3 New collective phenomena ** 1.1.4 Particle production
Section 1.2 Energy domains of heavy ion physics ** 1.2.1 Intermediate energy reactions ** 1.2.2 Relativistic heavy ion reactions ** 1.2.3 Ultra-relativistic heavy ion reactions ++ Stopping region ++ Transparent region
Section 1.3 Heavy ion experiments ** 1.3.1 Acceptance ** 1.3.2 Event selection ++ Event trigger ++ Selection trigger ** 1.3.3 Physical event tape ** 1.3.4 Detector filters ** 1.3.5 Outline
Section 1.4 General features of heavy ion physics
Section 1.5 Connections to other fields of physics ** 1.5.1 Nuclear physics ** 1.5.2 Particle physics ** 1.5.3 Statistical physics ** 1.5.4 Relativistic fluid dynamics ** 1.5.5 Astrophysics
Section 1.6 Why a theoretical treatment is important?
Section 1.7 Outline of the book
Section 1.8 Assignment 1 ** 1.8.1 Solutions to Assignment 1
Section References

CHAPTER 2 Introduction to Relativistic Kinetic Theory
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Section 2.1 Basic definitions of microscopic quantities ** 2.1.1 Phase-space variables ** 2.1.2 Properties of the rapidity ** 2.1.3 Some typical rapidities
Section 2.2 Basic definitions of macroscopic quantities
Section 2.3 Energy-momentum tensor ++ Hydrodynamic flow ** 2.3.1 Local Rest frame: (LR) ++ Eckart's Definition ++ Landau's definition ** 2.3.2 Other macroscopic quantities -- Special cases - Eckart's definition - Landau's definition ** 2.3.3 Decomposition of the energy-momentum tensor -- Special cases
Section 2.4 J "F u ttner distribution ** 2.4.1 Normalization ** 2.4.2 Transformation properties of f(x,p). ++ In the configuration space ++ In the momentum space:
Section 2.5 Mixtures
Section 2.6 Assignment 2 ** 2.6.1 Solutions to Assignment 2
Section References

CHAPTER 3 Relativistic Boltzmann Transport Equation
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Section 3.1 Particle conservation
Section 3.2 Collisions
Section 3.3 Non-relativistic limit
Section 3.4 An example for the solution
Section 3.5 Relativistic Boltzmann equation for mixtures
Section 3.6 Conservation laws ** 3.6.1 Conservation of particle number ** 3.6.2 Conservation of charge ** 3.6.3 Conservation of energy and momentum
Section 3.7 Boltzmann H-theorem -- Consequence:
Section 3.8 Equilibrium distribution function
Section 3.9 Zeroth order approximation -- Assumption:
Section 3.10 Assignment 3 ** 3.10.1 Solutions to Assignment 3
Section References

CHAPTER 4 Equation of State
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(Additions are taken from: Phase coexistence in finite quark-gluon plasma, L.P. Csernai and Z. Neda, Phys. Lett. B337 (1994) 25.)

Section 4.1 Intermediate Energy EOS ** 4.1.1 Bulk nuclear matter ++ Nuclear compressibility ++ Thermodynamical variables ++ A simplified Equation of State ++ Phase coexistence between liquid and gas phases ++ Critical exponents ++ Fragment mass distributions ++ Law of Mass Action ** 4.1.2 Finite systems and fragment abundances ++ Phase transition in finite systems ++ Droplet and bubble formation
Section 4.2 The Nuclear EOS and Quark Gluon Plasma ** 4.2.1 Hadronic Equation of State ++ Compressional part of the nuclear EOS ** 4.2.2 QGP Equation of State ++ Phase mixture ** 4.2.3 QGP phase transition and nuclear compressibility ** 4.2.4 Dependence of phase transition on the nuclear EOS
Section 4.3 EOS from microscopic theory ** 4.3.1 Momentum dependent interaction ** 4.3.2 Momentum distribution ** 4.3.3 The partition function
Section 4.4 Assignment 4 ** 4.4.1 Solutions to Assignment 4
Section References

CHAPTER 5 Relativistic Fluid Dynamics
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Section 5.1 Energy domains, stopping power ** 5.1.1 Stopping energy region ** 5.1.2 Transparent reactions, mid rapidity region ** 5.1.3 Transparent reactions, fragmentation region
Section 5.2 Perfect fluid dynamics
Section 5.3 Numerical solutions ** 5.3.1 Equation of state ** 5.3.2 Flow characteristics from numerical solutions - In the Eulerian fluid dynamics - Physically ** 5.3.3 Conclusions
Section 5.4 Numerical methods ** 5.4.1 The Particle in Cell (PIC) method ** 5.4.2 The Flux Corrected Transport algorithm (FCT)
Section 5.5 Simple analytic solutions --- Shock waves ** 5.5.1 Taub adiabat for finite particle densities -- 1 Parallel projection. -- 2 Orthogonal projection. ** 5.5.2 Relativistic detonations -- Minimum energy to reach a new phase: ** 5.5.3 Detonations to QGP ** 5.5.4 Detonations in baryon free plasma ** 5.5.5 Deflagrations from QGP (*)
Section 5.6 Assignment 5 ** 5.6.1 Solutions to Assignment 5
Section References

CHAPTER 6 Simple models
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Section 6.1 Applicability of simple models -- Spherical models: -- Landau model: -- Bjorken model:
Section 6.2 The Bjorken model ** 6.2.1 Entropy conservation ** 6.2.2 Multiplicity estimate in ultra-relativistic collisions ** 6.2.3 Inclusion of phase transition in the Bjorken model (*) ** 6.2.4 Baryon recoil in the Bjorken model (*)
Section 6.3 Spherical expansion ** 6.3.1 Fireball model ** 6.3.2 Blast-wave model ++ Basic assumptions of the Blast Wave model ** 6.3.3 An approximate spherical solution
Section 6.4 The Landau model ** 6.4.1 Physical assumptions ** 6.4.2 Quasi-analytic solution ** 6.4.3 Numerical solution
Section 6.5 Assignment 6 ** 6.5.1 Solutions to Assignment 6
Section References

CHAPTER 7 Measurables
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Section 7.1 The freeze out process ** 7.1.1 Formal treatment of the freeze out
Section 7.2 Baryon measurables ** 7.2.1 Rapidity distribution ** 7.2.2 Transverse Momentum Spectra ** 7.2.3 Collective Sidewards Flow ** 7.2.4 Average Transverse Momentum
Section 7.3 Pion Measurables -- Rapidity Distribution: -- Transverse Momentum Spectrum -- Collective Sidewards Flow -- Average Transverse Momentum
Section 7.4 Calculation of cross sections ** 7.4.1 Inclusive and exclusive cross sections ** 7.4.2 Double and triple differential cross sections ** 7.4.3 Boosting thermal distributions ** 7.4.4 Spherical expansion
Section 7.5 Results of three dimensional calculations ** 7.5.1 Fragment emission at the end of the flow
Section 7.6 Global flow analysis ** 7.6.1 Global flow analysis in fluid dynamics ** 7.6.2 Decomposition of the global flow tensor
Section 7.7 Transverse Flow Analysis ** 7.7.1 Determination of the reaction plane (A) ++ Test of the reaction plane ** 7.7.2 Self correlations (B)
Section 7.8 Assignment 7 ** 7.8.1 Solutions to Assignment 7
Section References

CHAPTER 8 Scaling of the hydrodynamical model
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Section 8.1 Similarity in classical fluid dynamics ** 8.1.1 Application to heavy ion collisions
Section 8.2 Scaling properties of cross sections
Section 8.3 Scaling properties of the transverse flow ** 8.3.1 Global flow tensor ** 8.3.2 Transverse Momentum Analysis ** 8.3.3 Fragment flow and scaling ** 8.3.4 Fragment flow - mass dependence (*)
Section 8.4 Scaling violations ** 8.4.1 Scaling violation in transverse flow ** 8.4.2 Disappearance of the transverse flow
Section 8.5 Assignment 8 ** 8.5.1 Solutions to Assignment 8
Section References

CHAPTER 9 Direct Solutions of Kinetic Theory
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-- The Chapman-Enskog method:
Section 9.1 Viscous Fluid Dynamics ** 9.1.1 Entropy production ** 9.1.2 Shock front profiles
Section 9.2 Multi Component Fluid Dynamics
Section 9.3 Solutions on microscopic level ** 9.3.1 Intranuclear cascade models ** 9.3.2 Mean field models: BUU - VUU - BN - LV ** 9.3.3 Models of Molecular Dynamics
Section 9.4 Assignment 9 ** 9.4.1 Solution to Assignment 9
Section References

CHAPTER 10 Search for Quark Gluon Plasma
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Section 10.1 Introduction ** 10.1.1 Theoretical expectations -- QCD Predictions ++ Global Characteristics of the Collision -- Energy density: -- Baryon density: -- Freeze-out volume: ** 10.1.2 Experimental facilities
Section 10.2 Quarks and gluons
Section 10.3 Lattice QCD -- Pure gluon theory: (N-f =0) -- Four degenerate flavors: -- N-f = 2 or 2 + 1 : ** 10.3.1 The lattice formalism ** 10.3.2 The order of the phase transition -- Pure gluon matter: -- Calculations with dynamical quarks: -- Finite baryon chemical potential: ** 10.3.3 Critical temperature ** 10.3.4 The Equation of State ** 10.3.5 Screening lengths ** 10.3.6 Summary of present results
Section 10.4 Surface tension, viscosity and nucleation
Section 10.5 Nuclear stopping power ** 10.5.1 Proton nucleus collisions ** 10.5.2 Heavy ion collisions -- Expectations for higher energies ** 10.5.3 Stopping in theoretical models -- String models:
Section 10.6 Reaction models ** 10.6.1 Fluid dynamical results ++ Detailed numerical models ** 10.6.2 Microscopic string models -- Hadron - hadron reactions: -- Strings: -- Heavy ion reactions: ++ Monte-Carlo model families: -- A) Naive string models: -- B) String models with rescattering: -- C) String models with string fusion: -- D) Parton cascade models: ++ Monte-Carlo models and Quark Gluon Plasma
Section 10.7 On some suggested signals ++ Collective flow, Pt- spectra, thermodynamic variables -- Transverse flow -- The shape of the pion spectra: ** 10.7.1 Strangeness and Anti-baryon enhancement ** 10.7.2 Heavy quark bound states ** 10.7.3 Electromagnetic probes -- Photons: -- Di-leptons: ** 10.7.4 Exotic signals
Section 10.8 Assignment 10 ** 10.8.1 Solution to Assignment 10
Section References

CHAPTER 11 Connections of astrophysics and Heavy Ions
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Section 11.1 Neutron and hybrid stars ** 11.1.1 Pulsars and neutron stars ** 11.1.2 Supernova explosions
Section 11.2 Implications on the early universe ** 11.2.1 Strangelets
Section References