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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
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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
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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
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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
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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
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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?
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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
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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
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Early information from measured Early information from measured observables: average volumeobservables: average volume
Circles=Multics dataSquares=Coulomb trajectories
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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