Mauro Bruno Bologna University

INFN-Bologna (Italy)

Gas

Quark-Gluon Plasma

Nucleus Density

Tem

per

atu

re

70 0

00 0

00 0

00°

30

00 0

00 0

00 0

00°

0=250 000 000 T/cm3

T critical

Liquid

Coexistence

H.Jaqaman et al. PRC27(1983)2782

Thermodynamical aspects in heavy ion Thermodynamical aspects in heavy ion reactionsreactions

Experimental Investigation of a van Experimental Investigation of a van der Waals nuclear fluid-H.I. Collisionsder Waals nuclear fluid-H.I. Collisions

Aims:Aims: study thermodynamics of nuclear systems study thermodynamics of nuclear systems (finite, charged, 2 components)(finite, charged, 2 components) observables to identify phase transitionobservables to identify phase transition

Study:Study: systems at different excitation energies systems at different excitation energies peripheral reactions – excitation functionperipheral reactions – excitation function central reactions – well defined excitation central reactions – well defined excitation energyenergy

Starting from measured reaction products get information Starting from measured reaction products get information on:on:

primary partitionsprimary partitions equilibriumequilibrium critical behaviourcritical behaviour thermodynamical signalsthermodynamical signals

Heavy Ion collisions at intermediate Heavy Ion collisions at intermediate energiesenergies

Vacuum (10-6 mb)

~100 fm/c

DDEETTEECCTTOORR

~20 fm/c(10-22 sec)

~100÷1000 fm/c

~1014 fm/c

Expansion

nnni

M

ii kmMkmmE

)(*1

0

The decaying system can be identified and its calorimetric excitation energy results from the energy balance:

4device

Central collisions: one source

),(i,j wppT kM

k

k

j

k

iij31

1

)()()(

Central collisionsAu+C Au+Cu Au+Cu Au+Au*=1.5 *=3 *=4.5 *=7 A.MeV

Nucl.Phys.A 724 (2003) 455

25 AMeV 35 AMeVCentral collisions

Au+C Au+Cu Au+Cu Au+Au*=1.5 *=3 *=4.5 *=7 A.MeV

Nucl.Phys.A 724 (2003) 455

Central collisionsAu+C Au+Cu Au+Cu Au+Au*=1.5 *=3 *=4.5 *=7 A.MeV

Nucl.Phys.A 724 (2003) 455

25 AMeV 35 AMeV

Multics-NPA724 (2003) 329

Multics-NPA650 (1999) 329Peripheral (binary)

collisions: two sources

Sorting the events: multidimensional Sorting the events: multidimensional analysisanalysisHow to assess the How to assess the

source source equilibration ? equilibration ? •isotropy•uniform population of the phase space•independence on the entrance channel•scaling

Sources at same Sources at same **: liquid, vapor & droplets: liquid, vapor & droplets

Multics: Central from Z0=85 to Z0=100 (lines)Multics: Au peripheral Z0=79 (symbols)

Isis: π+Au 8 GeV/c NPA734(2004)487Fasa: p,α+Au 4-14 GeV NPA709(2002)392

A.Bonasera, Phys.World Feb.1999A.Bonasera, Phys.World Feb.1999

Au nuclei: Multics-NPA650(1999)329H clusters: B.Farizon, PRL81(1999)4108

Is the multifragmentation a thermal critical Is the multifragmentation a thermal critical phenomenon?phenomenon?

Z-2.1

Au Liquid-Gas

c eV

IsIs PRL2002

J.Finn et al PRL1982

p+Xe 80-350 GeV

A-2.64nA=q0A-exp(- c0A) T

Fisher 1967Multics NPA724 (2003) 455

Power-laws are free of scalesAll the information falls on a single curve

Scaled yield: nA/(q0A-Scaled temperature: A/T

EoS PRC2003

Critical Critical exponents exponents

from from moment moment analysisanalysis m1 = ∑nss ~ |ε|-β

m2 = ∑nss2 ~ |ε|-γ

mk = ∑nssk ~ |ε| (τ-1-k)/σ

σ= (τ-2)/β

Self similarity and scalingSelf similarity and scaling

NO: The system is finite: power-laws are found at all densities inside the coexistence region

(Lattice-gas)

Can we conclude that the system reached the critical Can we conclude that the system reached the critical point?point?

energy

1

10

100

0.1pro

bab

ility

energy

1

10

100

0.1pro

babili

ty

Canonical thermodynamicsCanonical thermodynamicsLattice-gas theoryLattice-gas theory

Liquid

Liquid

Gas

Gas

Infinite System

FiniteSystem

The transition is smoothed

two states populated at the same temperature

F.Gulminelli et al. PRL91(2003)202701Experimentally

Microcanonical thermodynamics of finite Microcanonical thermodynamics of finite systemssystems

We can back-trace from data •the average volume (ρ) of the system

E*= Econfig + Ekin

E*= Ecoul(V)+Qv+ Eint(T)+Etr(T)

Events sorted as a function of E* (calorimetry)

•the temperature T

under the constraint of energy conservationMultics-Nucl.Phys.A699(2002)795

Early information from measured Early information from measured observables: average volumeobservables: average volume

Circles=Multics dataSquares=Coulomb trajectories

Early information from measured Early information from measured observables : Temperatureobservables : Temperature

Isotope thermometer P.M.Milazzo,PRC58(1998) 953

Indra correlation dataN.Marie,PRC58(1998)256

<Ekin>=(3/2) <m-1>T+<aAIMF>T2 Multics-

NPA699(2002)795

1)2/3(

m

ET tr

T, Eint from independent measurements/methods

Liquid-drop

Aladin PRL1995

Microcanonical heat capacity from Microcanonical heat capacity from fluctuationsfluctuations

E*=Econfig+Ekin (2config= 2

kin)

Ph.Chomaz , F.Gulminelli, NPA 647(1999) 153

Ekin = Etrasl(T)+Einternal(T)

Econfig =Qv+Ecoul(V)

The system being thermodynamically characterized:

Multics-PLB473 (2000) 219;NPA699 (2002) 795;NPA734 (2004) 512

Microcanonical fluctuationslarger than the canonical expectation?

Ckin/C = 1-2kin/2

can

where:

2can=T2Ckin=T2dEkin/dT

Heat capacity from fluctuations Heat capacity from fluctuations

Grey area: peripheral collisions

Points: central collisions:

Indra: NPA699(2002)795

Au+C Au+Cu Au+Au

Multics:PLB473 (2000) 219NPA699 (2002) 795NPA734 (2004) 512

1-st order phase transition1-st order phase transition

Au Liquid-Gas

c eV

Liquid-gas phase transition: is the game Liquid-gas phase transition: is the game over? over?

Critical behavior inside the coexistence region

Liquid-dropZ

B

I

GAsym 12

What is left for future measurements? What is left for future measurements? COINCIDENT EXPERIMENTAL INFORMATIONCOINCIDENT EXPERIMENTAL INFORMATION

Multics E1=20.3 E2=6.50.7Isis E1=2.5 E2 =7.Indra E2=6.0.5

Coincident experimental information are needed on:•critical partitioning of the system, fluctuations•calorimetric excitation energy•isotopic temperature•proximity of the decay products

4π mass and charge detection !!

Multics NPA 2004

E*/A (A.MeV)

A better quantitative nuclear metrology of hot nuclei

What is left for future What is left for future measurements?measurements?an extra dimension an extra dimension of the EoSof the EoS 2-nd generation devices and

exotic beams are needed, to fully investigate the phase transition

by changing:•the Coulomb properties •the isospin content (N/Z) of the fragmenting source

N=Z

J.Besprosvany and S.Levit - PLB 217 (1989) 1

T reaches a saturation at multifragmentation The saturation value decreases for increasing size

Proton rich nuclei (A≈100): vanishing limiting temperature

Starting from the liquid side EStarting from the liquid side EPP/A/APP < 25 A MeV < 25 A MeV AAP+TP+T~100 ~100

(Laboratori Nazionali di Legnaro-INFN-Italy)(Laboratori Nazionali di Legnaro-INFN-Italy)

•Low energy thresholds (ionization chambers as ΔE)•High granularity: 400 ΔE-E telescopes 4o-150o

•A identification (1<=Z<=8) up to 90o

•Digital electronics for CsI pulse-shape discrimination (A identification Z<=4)

Side Isotope Arraynucl-ex collaboration: garfield apparatusnucl-ex collaboration: garfield apparatus

Experiments with n-rich/poor systemsExperiments with n-rich/poor systems 3232S+S+5858Ni and Ni and 3232S+S+6464Ni 14.5 AMeVNi 14.5 AMeV

nucl-ex collaboration&garfieldnucl-ex collaboration&garfield

Experiments with n-rich/poor systemsExperiments with n-rich/poor systems 3232S+S+5858Ni and Ni and 3232S+S+6464Ni 14.5 AMeVNi 14.5 AMeV

3-IMF events3-IMF events

Tiso ≈ 3.5 MeV

Before concluding about the temperature:thermodynamical characterization of the source is neededisotope emission time scales have to be checked through correlation functions (intensity interferometry)

α-α

p-Li7 d-α

nucl-ex collaboration&garfieldnucl-ex collaboration&garfield

1+

R(

q)

ConclusionsConclusions The physics of hot nuclei: a unique laboratory

• for the thermodynamics of finite, charged, 2-component systems• for a quantitative nuclear metrology• for interdisciplinary connections

Multics E1=20.3 E2=6.50.7Isis E1=2.5 E2 =7.Indra E2=6.0.5

We need: • 4 mass and charge detection• 20-50 A.MeV radioactive beams

Multics NPA 2004

E*/A (A.MeV)

1+

R(

q)

nucl-ex collaboration&garfieldnucl-ex collaboration&garfield