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

IntroductionWhat 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)

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)

Nuclear matter in the ground stateUsual nuclear matter (mixture of protons and neutrons):Information about binding energy of nuclear matter for T=0 and ρ=ρ0 → volume contribution at Weizsäcker formula (drop model) determines binding energy B/A = 16 MeVStudies 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 nucleus2) giant dipole resonances – relative motion of proton and neutron liquid3) 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.

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 gas3) 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

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

konstS

2 AE

P

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 ρ0 = 0.16 nucl./fm-3 (2.6∙1017 kg/m3)

Nuclear matter equation of state E/A = f(ρ) for different variants of stiffness

ρ [nucleon/fm3]

B/A

[MeV

/nu

cleo

n]

0A

E

Radius of curvature of function E/A = f(ρ) for ρ → ρ0 where is minimum of

energy and then it is valid:

it gives nuclear matter compressibility (K = compression module):

0

2

2

AE

K

Compressibility is defined in classical thermodynamics by equation (change of pressure as dependency on relative change of density):

constS

PK

Nuclear physics → we are working with number of nucleon density and binding energy per nucleon. Compressibility we involve in the form:

constS

P9K

We substitute expression for pressure:

constS

2

2

2 AE

AE

29K

In minimum region ρ = ρ0 → :

0AE

0const,S

2

2

20

AE

9K

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

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 TC 5 MeV2) phase transition from hadron gas to quark-gluon plasma TC 200 MeV, ρC 5-8 ρ0)

Phase diagram of nuclear matter with marking of different phases and phase transitions

plasma

ice

vapor

water

atomicnucleus

nuclear collision

neutron star

early universe

Density

Tem

pera

ture

hadrongas

quark-gluonplasma

nuclear liquid

nuclearcondensate

Early Universe

Quark-gluonplasma

Neutron star

Baryon densityT

empe

ratu

re

strangelets

hadron gas

nuclearliquid nuclear

condensate

gas-plasmacoexistence

Phase transitions.

We have three transition types – different dependency of temperature changes (TC - 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 transition2) existence of overcooled or superheated forms of matter in appropriate phase3) stopping of parameter changes (temperature, increasing of expansion)

II. order transition:1) impossibility of parallel existence of two phases

Energy density

Tem

per

atu

re

Energy density

Tem

per

atu

re

Energy density

Tem

per

atu

re

Phase transition of nuclear liquid in hadron gas.

Similarity of potential shape similarity between phase transition of nuclear matter (nuclear liquid hadron gas) and H2O (water to water vapor)

Phase transitions of nuclear matter and water (H2O) and shape of appropriate potentials

Device ALADIN at GSI Darmstadt, where phase transition of nuclear liquid to hadron gas was studied

Nuclear matter

Pot

enti

al

Distance

Distance

Pot

enti

al

Vapor

WaterTem

per

atu

re [

o C]

Energy [meV/molecule]

Tem

per

atu

re

Energy

JINR

Nuclearliquid

Hadrongas

Study of hot and dense nuclear matter propertiesNecessity 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 densityDetermination 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 historyExplosion history depends on nuclear matter equation of stateReleased energy magnitude, character of emitted spectrum

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)

SPS RHIC

Transition from fixed target to colliding beams:Energy accessible in centre of mass:

13 GeV/n 200 GeV/n

Comparison with p-p collisions results after normalization on number of nucleon-nucleon collisions

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 greatnumber of quark antiquark pairsthey hadronised later

Quark

Quark

Jet

Jet

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 pt) and jet pairs

Observed by experiments on RHIC acceleratorJet 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 pt → production increasing

2) Saturation – big parton density → decreasing of jet production increasing with energy lower energies

higher energies

Au + Au experiment d + Au control experiment

Suppression of particles with high transversal momentum

RAA – 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 data Předběžná dataKonečná data Předběžná dataPředběžná dataKonečná data

Croninův jev

pouze Croninův jev

i potlačení výtrysků

Konečná data Předběžná data

Croninův jev i potlačení výtrysků

pouze Croninův jev

Exp

erim

ent

Ph

enix

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 loosedUrgent 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/nucleon LHC 3500 + 3500 GeV/nucleon