Nuclear Matter Joachim Stroth, GSI/Univ. Frankfurt Nuclear Matter Course I Properties of strongly...

Nuclear MatterJoachim Stroth, GSI/Univ. Frankfurt

Nuclear Matter

Course IProperties of strongly interacting systems

Course IICreating and investigating nuclear matter under extreme conditions

Joachim Stroth, GSI/Univ. Frankfurt


Discovery of the Micro-Cosmos

It all started with the observation of Radioactivity. In the late 19th Century Henri Becquerelle discovered Ionising Radiation emerging from Uranium. We now know that and -Rays stem from transitions in the nucleus. This event can be viewed as the birth of Nuclear Physics.

Further Discoveries:

– In Cathode Rays:Electron (Thompson)

– In Cosmic Rays:Positron, Myon (Anderson), Pion (Powell)

– With Accelerators:Anti-Proton, and and and

Decay patterns for the dacay of pions of the type + + + e+ + 3


The Atomic Nucleus

Ernest Rutherford, the real father of nuclear physics found something very heavy and tiny in the interior of atomic nuclei.

The observed angular distribution of -particles was in agreement with the assumption of pure electromagnetic scattering off an object with

– M >> M

– R < 3 10 –14 m

The probability for an interaction can be calculated for thin targets:

%3g200

106.0

cm

g1cm1010d

24

2224

mol

A

mol

AAu =×

×===== −

MN

xM

NMA

NAA

AP ρσσσ


Electron Beam as Particle Microscope

Scattering of electrons off point-like objects is ...

.. excellently described by:

Exchange of PhotonsExchange of Photons

⎟⎠

⎞⎜⎝

⎛ −=Ω 2

sin1)(

)(4d

d

Formula-Mott

224

22 θ

βσ

qc

EZe

ee

e

EEv

ppq

′−=

′−=

e

E,pE´,p´

Z


The Charge Distribution of Nuclei

Experiments on elastic scattering of Electrons at Energies of < 1 GeV ( 0.2fm)

22 )(d

d

d

d

Mott

qFΩ

=Ω

σσ

Nobel Price Nobel Price in Physics 1961in Physics 1961

HofstaedterHofstaedter

e e

Z

Fourier-Transform ofthe Form Factor yields the Charge DistributionCharge Distribution

Pb

Ca

0 2 4 6 8 10R [fm]

0.02

0.08

ρ [f

m-3]

[Grad]

dσ/

dΩ[

rel.

Ein

h.]

20 30 40 50 60

100

10-2

10-4

10-6

10-8

10-10

48Ca

40Ca


Digging deeper with Deep-Inelastic Scattering


The Form Factor of Protons


Struktur des Nukleons

Experiments with Electron Beams at the SLAC up to 20 GeV ( 0.1fm)

Essential Observations:

– Nucleons do have diffuse surfaces

– Nucleons can be transformed into excited states

– Nucleons are composite particles which contain point-like constituents

Nobel Price 1990Nobel Price 1990

Kenndall, Friedmann, TaylorKenndall, Friedmann, Taylor


Constituents of the Atomic Nucleus

<qq> 0

<qq> = 0

Protons

Neutrons

up- and down-Quarks

Gluons and virtual Quarks and Anti-Quarks

R 1fm; m 1GeV

Nucleus (R 1-10 fm)

R < 10-4 fm; m 10 MeV

Strong Interaction: QCD

99.9% of the Matter around us 99.9% of the Matter around us consits out of Nucleonsconsits out of Nucleons


The Nucleon is a Complex Object

Hadrons are very complex excitations of valence quarks in the present of quark and gluon condensates.


The Particle ZooAccording to current understanding point-like particles


The Particle Zoo II

Bosons carry the interaction.


The Nature of the Strong ForceAlong the successful description of electro-weak interaction by gauge theory, the strong interaction can be described by the exchange of gluons.

Property QED QCD

Charge electric colour

Bosons photon(carries no charge)

gluons(carry charge)

Mass of boson 0 0

Screening reduces bare charge

amplifies bare charge

Strength s= 25


QCD: Confinement

If the distance between two quarks gets larger, more and more gluons contribute to the interaction between the quarks. Hence the potential energy grows with increasing distance.At some point, enough energy is stored in the field to produce a pair of quarks out of the vacuum.

Krr

crV s +−=

34

)(hα


The Origin of Matter

Criteria of Sacharov for the cre-ation of matter out of radiation:

C and CP ViolationThe decay rate of quarks and anti-quarks are different

Violation of Baryon Number ConservationLeptons decay in quarks and vice versa

No thermal equillibriumB=0 if baryon number is not onserved

10-43s

10-10s

10-34s

GUT

QGP

Hadronisation

t

x

Matter was produced about 1 s second after the Big Bang

Since particles are always produced in pairs, why is there only matter and no anti-matter left


Production of Heavy Nuclei

In the Bing Bang only the light-est nuclei could be formed !

Production of heavier nuclei:

– Thermonuclear burning in starsup to Iron !

– Supernova Explosions:Neutron absorbtion with subsequent beta-decay !

• r-processNeutron Drip Line

• s-process

1 10

1E-90

1E-80

1E-70

1E-60

1E-50

1E-40

1E-30

1E-20

1E-10

1

HAGEDORNProduction in Secondary Reaction

Rel

ativ

e Y

ield

Atomic Mass Number


Nuclear Matter has Exotic Properties

Let‘s quote some macroscopic properties of Nuclear Matter

Nuclear matter is extremely heavy 280 Million Tons per cm280 Million Tons per cm33

– Less than a mm3 is enough to built an aircraft carrier.

– However, if one would burn it completely, the energy gain would be equivalent to 50 GW for a whole year.

Although we know Nuclear Matter only in small portions inside atoms, it exists in nature also in big portions:

– Neutron Stars have a diameter of typically 10 km.


The Equation of State

Around normal nuclear ground-state density the compressibility can be determined from Giant Monopole Resonances.

At higher densities the proper-ties can only be extracted from experiment on the basis of theoretical models.

Conditions: E/A(ρ) = -16 MeV

(E/A)(ρ)/ρ

Compressibilityρ(E/A)/ ρ200 - 400 MeV

Com

pre

ssio

nal

En

ergy

E/A

Density

hard EoS = 380 MeVsoft EoS = 200 MeV


The Effective Interactions between Nucleons

Hideki Yukawa described in 1934 the force between nucleons as an exchange of virtual particles. If the exchanged particles carry mass, the range of the interaction is finite:

⎭⎬⎫

⎩⎨⎧−=

hmcr

r

grV exp

4)(

2

π

fm7.0MeV1372

fmMeV20022

2 ≈×

≈→≈Δ→≈ΔΔ Dhh ctcmctE

Meson Mass[MeV]

TypeI[JP]

140 1[0-]

σ 400-1200 0[0+]

ρ 770 1[1-]


Nuclei can be described assuming nucleons moving independently in a mean nuclear potential:

– PhenomenologicalSquare-well, Harmonic, Woods-Saxon

– Self-consistentHartree-Fock

The Formation of Nuclei

Nuclei form because of the strong effective interaction between nucleons. Although this „residual“ interaction is weaker than the bare strong force between quarks and gluons, it still overcomes Coulomb repulsion of protons by far.

⎟⎟⎠

⎞⎜⎜⎝

⎛⎥⎦

⎤⎢⎣

⎡ −+

=

d

arrV

exp1

1)(


The Nucleus as a Liquid Drop

The nucleus in the ground state is cold Fermi liquid. At moderate excitation energies (E/nucleon << EB) nuclei behave like little droplets of water.

The Coulomb Barrier:

Potential energy of two touching spheres (if r=R0)


Heating Nuclear Matter

Nuclei store additional energy by transfering nucleons into levels between the Fermi-surface and the barrier:

– Single Particle excitations

– Collective Excitations

It can thermalize by forming a Compound Nucleus

And cool down by

– (Fragmentation)

– Particle Decay (,p,n)

– Electromagnetic transitions ()

At E/A of 5 MeV the nuclei transform to a gas of nucleons.


Hadronic Matter

Nucleons are composite particles and can therefore transform into excited states. Is the temperature of nuclear matter high enough, internal degrees of the nucleons are excited.

e.g.: N + N = N + Δ= N + N +

These excited states are often called resonances, since their decay width is rather large (due to the strong interaction).

ρ

k,

p,n

N(1440)

N(1520)

M[GeV]

0

1

a1

Mesonen

Baryonen


The Melting of Resonances

Exiting nucleons by inelastic electron scattering

– on liquid hydrogen (protons):Resonances are clearly visible (most prominent the Δ33)

– on nuclei:no higher-lying resonances seem to survive


QCD: Spontaneous Breaking of Chiral Symmtery

The groundstate of QCD is characterized by a non-vanishing field of quark – anti-quark pairs, the so-called chiral condensate.

This is a non-perturbative effect of QCD


ρ

k,

p,n

N(1440)

N(1520)

M[GeV]

0

1

a1

Vakuum<qq> 0

Mesonen

Baryonen

ρ

k,

p,n

N(1440)

N(1520)

M[GeV]

0

1a1

Vakuum<qq> > 0

Mesonen

Spontaneously Broken Chiral Symmetry

How can almost massless quarks combine to hadron with a mass of typicall 1 GeV and more?

The ground state of QCD is spotaneously broken – the vaccum is filled by a condensate of scalar quark – anti-quark pairs!

Light mesons (M<<1 GeV), , K

No parity doubletts M(ρ) M(a1)

The bare quarks gain dynamically mass by coupling to the quark – ant-quark pairs.

ρ

k,

p,n

N(1440)

N(1520)

M[GeV]

0

1

a1

Vakuum<qq> 0

Mesonen

Baryonen


Probing the Chiral Condensate

Expectation value of the chiral condensate in a simplified model, as a function of baryon density and temperature of nuclear matter.Already in ordinary nuclei the condensate is reduce as compared to vacuum.


Medium Modifications of Hadrons

Spectral function of the ρ-meson in medium


The Quark-Gluon Phase of Nuclear Matter At very high energies and/or densities quarks are deconfined


Characteristic Energy Regimes

Heavy Ion Accellerators around the world

Coulomb Barrier

Fermi-Energy Regime

Resonance Matter

Quark-Gluon Matter

E/nucl. [GeV] 0,01 0,1 10 100 10000

Tandems, Linacs

Cyclotrons Synchrotrons (recently also colliders)

Many Univ. and Instituts

GANIL, MSU, RIKEN

GSI(SIS), LBL(Bevalac),

BNL(AGS)

CERN(SPS) BNL(RHIC), CERN(LHC)

in 2006


Dissipative Collisions

In a kinematically complete experiment the following obsevables are derived:

– T CM scattering angle

– TKEL Total Kinetc Energy Loss

– MR,E Mass of Recoil Ion and Ejectile

The data show evidence for a smooth transfer of collective energy of motion into internal degrees od freedom


Multi-Fragmentation

The ALADIN Experiment!Projectile Fragmentation in inverse Kinematics

– Forward focusing (4 detection)

– No detector Thresholds


The Liquid-Gas Phase Transition

Results of the ALADIN collaboration show evidence for transition from a liquid to a vapour phase of nuclear matter.


Creating Nuclear Fireballs

At energies above a few 100 MeV/u the non-overlapping parts of the nuclei are abraised and continue on straight trajectories.

Nucleons in these „pole caps“ are called spectators.

The nucleons in the overlapp zone form the fireball and are called participants.

A correlation plot of the two helps to select impact parameter, which is no direct observable:

– ZSUM (Small Angle Hodoscope) Sum of all Charge

– M (Large Angle Hodoscope) Multiplicity


Cross Properties of Expanding Fireballs

A nuclear fire ball is a hot, rapidly expanding gas of hadrons.

Below some critical density, all collisions between the particle stop and the system freezes out.

In the spectrometer all particles are identified by their mass and charge.

From the spectral shape it can be inferred, that the energy of the particles is composed of a thermal and collective part

Kinetic Energy of a Particle:Ek = Eth + Eflow = 3/2 kT + m/2flow2


A Typical 4 Experiment

Particle IDentification:

– Momentum from the bending in a magnetic field

– Chargeby Ionization Power

– Mass from time-of-flight (combined with momen-tum measurement)

Z

pB =ρ

2

d

dZ

x

E∝

p

m =


Particle Spectra

The emission pattern of part-icles show a rich structure if correlated with the reaction plane.

[ ])2cos(2)cos(21d

d21 Ψ+Ψ+∝

Ψvv

σ


Creation of New Particles (Resonance Matter)

Short-lived particles (resonances) can be detected via particle correlations.

Observable Invariant Mass

e.g.: N+N N+Δ33 N+N+∑== iinv pPPPM ;νμ

Resonance

Mass[MeV]

I(JP)

P11 1440 ½(½+)

D13 1520 ½(1½-)

S11 1535 ½(½-)

P33 (Δ33) 1232 1½(1½+

)


Pions are Complicated

The pion is the lightest hadron. Its existence in nuclear matter is tightly linked to the excitation of the Δ33 resonance.

Data described by „two temperatures“ fit

⎥⎦⎤

⎢⎣⎡+⎥⎦

⎤⎢⎣⎡∝

22

113

3

expexpdp

dT

ECTEC

σ

Δ33

hole


Strangeness Production

The KAOS Spectrometer features a compact dipole combined with a large quadrupole to enlarge acceptance.Various focal-plane detectors allow a dedicated kaon trigger.

At 1 AGeV the energy in a single nucleon nucleon is not sufficient to produce kaons.

In contrast to pion production is the kaaon production rising as the number of participating nucleons increases.

Clear evidence for multi-step production mechanism

N K+, ΔN K+N


Medium Modification of KaonsIn medium kaons/anti-kaons experience a density dependent potential which lowers/increases their effective mass. Hence the production of anti-kaons close to the production threshold is enhanced.


A Thermal Model for the Fireball

The Thermal Model assumes that all particles stem from a thermalized fireball, where all inelastic collisions stop at the same temperature.

By adjusting only two parameters, the baryon chemical potential and the temperature, relative particle yields can be explained.

( )∫

⎭⎬⎫

⎩⎨⎧ ±−−

=1

1exp

d

2

2

2

iSiBi

ii

SBET

ppg

μμπ

ρ


Central Collision of two Gold NucleiAbout 95% of the velocity of light

Simulation: Univ. Frankfurt, Institut für Theoretische Physik


p

n

Δ++

K

ρ= 2-3ρ0

T < 100 MeV

e.g. Au+Au @ 1 GeV/u

Probing the Interior of Fire Balls

p

e+

e-

ρ


The HADES-Spectrometer

GeometryGeometry

inin

Online Pattern RecognitionOnline Pattern Recognition

RICH (Ring Imaging Cherenkov

Detectors)

TOF (Organic Scintillators)

SHOWER (Lead-Shower Detector)

TrackingTracking

ILSE (Super Conducting Magnet)

MDC (Multiwire Drift Chambers)


Low-mass Dilepton Pairs

Sensitive to changes of in-medium properties of vector mesons (restoration of chiral symmetry)

Experimental findings:

– Strong enhancement of lepton pairs below the vector meson region

– Enhancement already at Bevalac energies


Ultra Relativistic Collisions


Multistrange Hyperons

Strangeness enhancement in the QGP should influence in particular the production of multi-strange baryons (hyperons).

Strong enhancement of Ω over over found (ΩΩ : AA/pp = 17/1 : AA/pp = 17/1)

WA97 F. Antinori et al, Nucl. Phys. A 661 (1999) 130c


The Suppression of Charmonium

Anomalous suppression if screening in a deconfined phase occurs.

– Effect establishes as a function of centrality

NA50


Composition of a Neutron Star

Each arrow indicatesa different model for the neutron star

Each model represents an other EOS


The Phase Diagram of Nuclear Matter …

... yet another version


Experimental Concept

Detector components: Detector components:

1. magnet (1-2T)

2. Silicon pixel/strip detectors:

, , , Ω

3. RICH: particles with = 10-100:

electrons, (pions, kaons)

4. TRD: electrons ( 2000): J/

5. TOF-start (diamond pixel

detector) and TOF-stop (RPC):

particle identification

( pions, kaons, protons, …)

1.-5. needed for D mesons

Trigger:Trigger:1. level: reactions, centrality, hits in TRD and

RICH2. level: electrons, momentum, hit matching,

rings in RICH3. level: displaced vertex

Nuclear Matter Joachim Stroth, GSI/Univ. Frankfurt Nuclear Matter Course I Properties of strongly...

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