1. Nuclear matter 1) Introduction 2) Nuclear matter in the ground state 3) Hot and dense nuclear matter 4) State equation of nuclear matter 5) Phase diagram and phase transitions 6) Study of hot and dense nuclear matter properties 7) Collision of relativistic heavy nuclei 8) Quark-gluon plasma Simulation of creation of hot and dense nuclear matter zone in the heavy ion collisions

2. Introduction What do we study? Study of properties of unlimited block of nuclear matter → necessity to separate influence of: 1) reaction dynamics 2) finality of nuclear matter volume Study of thermodynamic properties (state equation) of nuclear matter in different conditions, phase transitions between different states of nuclear matter: 1) In the ground state 2) Hot and dense state Why do we study? In very dense and hot state → important for understanding of properties of matter during Universe creation and inside of many astrophysical objects Very high density and temperature → possibility of quark-gluon plasma creation Matter in very dense and hot state can be at active galaxy centers – picture of one Seyfert galaxy – obtained by Hubble telescope (NASA)

3. How do we study? Nuclear physics: In the ground state - giant resonances – vibration of nuclei depends on nuclear matter compressibility Hot and dense – heavy ion collisions  compression and heating of nuclear matter Collisions of the heaviest nuclei with different energies – achievement of the highest – present top is RHIC at Brookhaven, LHC at CERN (2007) Experiment for hot and dense nuclear matter studies ALICE prepared for LHC accelerator build up at laboratory CERN Astrophysics – research of neutron star properties (stability, dependency of size on mass) and history of supernova explosion Supernova explosion remnant at Large Magellanic Cloud – Hubble telescope picture (NASA)

4. Nuclear matter in the ground state Usual nuclear matter (mixture of protons and neutrons): Information about binding energy of nuclear matter for T=0 and ρ=ρ 0 → volume contribution at Weizsäcker formula (drop model) determines binding energy B/A = 16 MeV Studies of equation of state of nuclear matter at ground state → history of nuclear vibration is given by nuclear matter compressibility: 1) oscillations (volume increasing and decreasing) of nucleus 2) giant dipole resonances – relative motion of proton and neutron liquid 3) vibration of nucleus Oscillations Giant dipole resonances Vibrations Description of nuclear matter – QCD calculation on the lattice using quantum chromodynamics Dependency of nuclear matter properties on ratio between proton and neutron numbers (isotopic composition) Neutron liquid in the ground state: Occurrence inside neutron stars. Nuclear matter with strangeness in the ground state: Influence of strangeness on nuclear matter properties – interaction between lambda particles - Brookhaven (system consisted of proton, neutron and two lambdas) Occurrence - maybe inside neutron stars.

5. Hot and dense nuclear matter Necessity of nuclear matter study not only at the ground state but also for different temperatures (energy densities) and densities Temperature increasing → increasing of kinetic energy of nucleons → transformation of kinetic energy to excitation energy → phase transitions between different forms of nuclear matter: 1) excitation of nucleons to resonances (Δ a N*) 2) higher temperature (energy density) → transition from nuclear liquid to hadron gas 3) even higher → quark-gluon plasma Can be studied from the history of compression, heating and following expansion during atomic nuclei collisions with high energy ( E > 100 MeV/A) ↔ permeation of colliding nuclei does not happen (confirmed by Bevalac during seventies) Device for study of heavy nuclei collision FOPI on SIS accelerator – energy ~ 1 GeV/A

6. Equation of state of nuclear matter Nuclear matter properties can be described at equilibrium state by two variables density ρ and temperature T and equation of state, which is relation for pressure P = f(ρ,T). We use energy per one nucleon E/A instead of pressure and we fix temperature: E/A=f(ρ) | T=const Relation between pressure and temperature is (for equilibrium state entropy S is constant): For T = 0 minimum E/A = -B/A = -16 MeV will be for ρ 0 = 0.16 nucl./fm -3 (2.6∙10 17 kg/m 3 ) Nuclear matter equation of state E/A = f(ρ) for different variants of stiffness ρ [nucleon/fm 3 ] B/A[MeV/nucleon]

7. Radius of curvature of function E/A = f(ρ) for ρ → ρ 0 where is minimum of energy and then it is valid: it gives nuclear matter compressibility (K = compression module): Compressibility is defined in classical thermodynamics by equation (change of pressure as dependency on relative change of density): Nuclear physics → we are working with number of nucleon density and binding energy per nucleon. Compressibility we involve in the form: We substitute expression for pressure: In minimum region ρ = ρ 0 →: Larger energy change with density change → larger resistance against compression → harder equation of state K > 290 MeV → hard equation of state K < 290 MeV → soft equation of state Stiffness of equation of state depends on shape of central part of nuclear potential (its repulsive part) Experiments with α particles scattering on Sm nuclei → K ~ 240 MeV

8. Phase diagram and phase transitions Nuclear matter can be in different phases for different densities, temperatures or also strangeness. Phase and phase transitions between them can be displayed by phase diagram: 1) phase transition of nuclear liquid to hadron gas T C  5 MeV 2) phase transition from hadron gas to quark-gluon plasma T C  200 MeV, ρ C  5-8 ρ 0 ) Phase diagram of nuclear matter with marking of different phases and phase transitions plasma ice vapor water atomic nucleus nuclear collision neutron star early universe Density Temperature hadron gas quark-gluon plasma nuclear liquid nuclear condensate Early Universe Quark-gluon plasma Neutron star Baryon density Temperature strangelets hadron gas nuclear liquid nuclear condensate gas-plasma coexistence

9. Phase transitions. We have three transition types – different dependency of temperature changes (T C - critical temperature – temperature of phase transition): First order transition: Second order transition: Continuous transition: I. order transition: 1) parallel existence of two phases during phase transition 2) existence of overcooled or superheated forms of matter in appropriate phase 3) stopping of parameter changes (temperature, increasing of expansion) II. order transition:1) impossibility of parallel existence of two phases Energy density Temperature Energy density Temperature Energy density Temperature

10. Phase transition of nuclear liquid in hadron gas. Similarity of potential shape  similarity between phase transition of nuclear matter (nuclear liquid  hadron gas) and H 2 O (water to water vapor) Phase transitions of nuclear matter and water (H 2 O) and shape of appropriate potentials Device ALADIN at GSI Darmstadt, where phase transition of nuclear liquid to hadron gas was studied Nuclear matter Potential Distance Potential Vapor Water Temperature [ o C] Energy [meV/molecule] Temperature Energy JINR Nuclear liquid Hadron gas

11. Study of hot and dense nuclear matter properties Necessity of determination of physical quantities – density, temperature and changes of nuclear matter physical properties as function f = f(ρ,T) Nuclear methods: Collisions of heavy nuclei → creation of hot and dense nuclear matter zone Determination of temperature in different moments: spectra of different particles Determination of density Determination of equation of state stiffness (compressibility coefficient): Collision history (expansion history and asymmetry of particle emission) Astrophysical methods: Detector STAR working on RHIC accelerator (colliding beams of heavy nuclei with 200 GeV/nucleon) and reconstruction of collision by this experiment 1) Study of neutron star properties Determination of density (mass, volume – ρ = ρ(r) ) Determination of temperature using spectrum (surface – inside is more difficult) Stability depends on equation of state of neutron liquid 2) Study of supernova explosion history Explosion history depends on nuclear matter equation of state Released energy magnitude, character of emitted spectrum

12. Signs of quark-gluon plasma creation: Experiments on SPS at CERN observe: 1) Achievement of needed temperature and energy density 2) History of expansion 3) Increasing of strange particle production 4) Suppression of J/ψ meson production 5) Chiral symmetry restoration Observation of new phenomena on RHIC accelerator at years 2002 – 2004: 6) Jet production suppression Thousands of particles are created during collisions. Most of them is necessary detect and determine their properties. Collision of gold nuclei at STAR experiment on RHIC accelerator of colliding beams ( 100 + 100 GeV/a ) First evidence of observation of quark-gluon plasma creation on SPS accelerator at CERN. NA44, NA45/CERES, NA49, NA50, NA52, NA57/WA97 and WA98 experiments report together discovery of this matter at year 2000. Collision of accelerated lead nucleus with target nucleus, NA49 experiment on SPS accelerator (158 GeV/n) SPSRHIC Transition from fixed target to colliding beams: Energy accessible in centre of mass: 13 GeV/n200 GeV/n Comparison with p-p collisions results after normalization on number of nucleon-nucleon collisions

13. Jet production – visualization of quarks Example of four jet creation observed by OPAL experiment on LEP accelerator (Searching of Higgs particle) Created hadron jet has direction and total energy of original quark Collision of quark with very high energy → creation of couple of directed flow of particles interacting by strong interaction - „jets" Quark with very high energy creates great number of quark antiquark pairs they hadronised later Quark Jet

14. Suppression of jet production (jet quenching) Passage of jet partons through quark-gluon plasma (QGP) → energy and momentum losses → jet suppression (they are not in normal hadron mass) → proof of QGP creation 3) Suppression of jet production (particles with high p t ) and jet pairs Observed by experiments on RHIC accelerator Jet productions in different collisions were compared: 1) d-Au - QGP can not be created → only saturation and Cronin effect 2) Au-Au - QGP can be created → also production suppression Suppression of jet pair production is observed only in Au-Au collisions → QGP is created ? Nucleus-nucleus collision: jet production is influenced by these phenomena: 1) Cronin effect – multiple scattering→ smear of transverse momenta → shift to higher p t → production increasing 2) Saturation – big parton density → decreasing of jet production increasing with energy lower energies higher energies

15. Au + Au experimentd + Au control experiment Suppression of particles with high transversal momentum R AA – relation between numbers of measured and extrapolated from nucleon-nucleon collisions Experimental results: Dramatic difference of behavior in the case of Au+Au and d+Au collisions as dependency on collision centrality Konečná dataPředběžná dataKonečná dataPředběžná data Konečná data Croninův jev pouze Croninův jev i potlačení výtrysků Konečná dataPředběžná data Croninův jev i potlačení výtrysků pouze Croninův jev Experiment Phenix

16. What further? Necessity of study of properties of new matter state – its equation of state Some properties agrees with original assumptions about quark-gluon plasma, some are nearer to „color glass condensate“ We study so far only strongly interacting particles (99,9 % created particles are hadrons), photons and leptons only from secondary processes → indirect signals – information is partly loosed Urgent study of photons and leptons created directly in plasma → direct signals from quark-gluon plasma Determination of phase transition order – big importance for Big Bang history RHIC 200 + 200 GeV/nucleonLHC 3500 + 3500 GeV/nucleon