Document 7741647

Report
Q uark-G luon
Plasm a
D e c o n fi n e m
Tem perature
70 000 000 000°
H.Jaqaman et al. PRC27(1983)2782
3000 000 000 000°
Thermodynamical aspects in heavy ion reactions
T critical
G as
Liquid
C oexistence
D ensity
Mauro Bruno
ent
N ucleus
Bologna University
0=250 000 000T/cm3
INFN-Bologna (Italy)
Experimental Investigation of a van der
Waals nuclear fluid-H.I. Collisions
Aims: study thermodynamics of nuclear systems
(finite, charged, 2 components)
observables to identify phase transition
Study:
systems at different excitation energies
peripheral reactions – excitation function
central reactions – well defined excitation energy
Starting from measured reaction products get information on:




primary partitions
equilibrium
critical behaviour
thermodynamical signals
Heavy Ion collisions at intermediate energies
D
E
T
E
C
T
O
R
Expansion
~20 fm/c
(10-22 sec)
~100 fm/c
The decaying system can be identified
and its calorimetric excitation energy
results from the energy balance:
M
E * m0   ( mi  ki )  M n mn  kn 
i 1
~100÷1000 fm/c
Vacuum
(10-6 mb)
4

d
e
v
i
c
e
~1014 fm/c
Sorting the events: multidimensional analysis
assess(1999)
the
Multics-NPA650
329
Peripheral How to
(binary) source equilibration
collisions: •isotropy
two sources
?
•uniform population of the
phase space
•independence on the
entrance channel
•scaling
Central
collisions
25 AMeV
Au+C
*=1.5
Au+Cu Au+Cu
*=3
Central
collisions:
one source
M
T
 p
p
w
(
i
,
j
1
,
3
)
i
j 
i
j
(
k
) (
k
) (
k
)
k

1
Multics-NPA724 (2003) 329
*=4.5
Au+Au 35 AMeV
*=7 A.MeV
Sources at same *: liquid, vapor & droplets
A.Bonasera, Phys.World Feb.1999
Z-2.1
Au nuclei: Multics-NPA650(1999)329
H clusters: B.Farizon, PRL81(1999)4108
Multics: Central from Z0=85 to Z0=100 (lines)
IsAuthe
multifragmentation
a
Multics:
peripheral
Z0=79 (symbols)
Isis: π+Au 8 GeV/c NPA734(2004)487
phenomenon?
Fasa: p,α+Au 4-14 GeV NPA709(2002)392
thermal critical
J.Finn et al PRL1982
p+Xe
80-350 GeV
A-2.64
Self similarity and scaling
Power-laws are free of scales
All the information falls on a single curve
Multics NPA724 (2003) 455
Fisher 1967
nA=q0A-exp(- c0A)
T
Scaled yield: nA/(q0A-
Scaled temperature: A/T
Critical
IsIs PRL2002
exponents
EoS
PRC2003
Can we conclude that the system reached the critical point?
from moment
Au
Liquid-Gas
analysis
|ε|-β
 

 
c eV
m1 = ∑nss ~
m2 = ∑nss2 ~ |ε|-γ
mk = ∑nssk ~ |ε| (τ-1-k)/σ
NO:
The system is finite: power-laws are found at all
σ= (τ-2)/β
densities inside the coexistence region (Lattice-gas)
Canonical thermodynamics
Lattice-gas theory
F.Gulminelli et al. PRL91(2003)202701
Experimentally
probability
probability
Liquid
100
100 Liquid
10
1
Gas
Infinite
System
0.1
10
1
energy
Gas
Finite
System
0.1
energy
The transition
is smoothed
two states
populated at the
same temperature
Microcanonical thermodynamics of finite
systems
Events sorted as a function of E* (calorimetry)
E*= Econfig
+ Ekin
E*= Ecoul(V)+Qv+ Eint(T)+Etr(T)
We can back-trace from data
•the average volume (ρ) of the system
•the temperature T
under the constraint of energy conservation
Multics-Nucl.Phys.A699(2002)795
Early information from measured observables:
average volume
Circles=Multics data
Squares=Coulomb trajectories
Early information from measured observables :
Temperature
Liquid-drop
<Ekin>=(3/2) <m-1>T+<aAIMF>T2
Multics-NPA699(2002)795
T 
Etr
(3 / 2 )m  1
Isotope thermometer
P.M.Milazzo,PRC58(1998) 953
Aladin PRL1995
Indra correlation data
N.Marie,PRC58(1998)256
T, Eint from independent measurements/methods
Microcanonical heat capacity from fluctuations
E*=Econfig+Ekin
(2config= 2kin)
Econfig =Qv+Ecoul(V)
Ekin = Etrasl(T)+Einternal(T)
The system being thermodynamically characterized:
Ph.Chomaz , F.Gulminelli, NPA 647(1999) 153
Ckin/C = 1-2kin/2can
where:
2can=T2Ckin=T2dEkin/dT
Microcanonical fluctuations
larger than the canonical
expectation?
Multics-PLB473 (2000) 219;NPA699 (2002) 795;NPA734 (2004) 512
Heat capacity from fluctuations
Multics:
PLB473 (2000) 219
NPA699 (2002) 795
NPA734 (2004) 512
Indra: NPA699(2002)795
Grey area: peripheral collisions
Points: central collisions:
Au+C
Au+Cu
Au+Au
1-st order phase transition
Liquid-gas phase transition: is the game over?
Au
Liquid-Gas
 

 
c eV
Liquid-drop
Z
B
I
G
Critical
behavior
inside the
coexistence
region
Asym 12
What is left for future measurements?
COINCIDENT EXPERIMENTAL INFORMATION
 A better quantitative
nuclear metrology of hot
nuclei
 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)
Multics E1=20.3 E2=6.50.7
Isis
E1=2.5 E2 =7.
Indra
E2=6.0.5
What is left for future measurements?
an extra dimension
of the EoS
J.Besprosvany and S.Levit - PLB 217 (1989) 1
N=Z
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
T reaches a saturation
at multifragmentation
Proton rich nuclei (A≈100):
vanishing limiting temperature
The saturation value
decreases for increasing size
Starting from the liquid side EP/AP < 25 A MeV AP+T~100
(Laboratori Nazionali di Legnaro-INFN-Italy)
nucl-ex collaboration: garfield apparatus
Side Isotope Array
•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)
Experiments with n-rich/poor systems
32S+58Ni and 32S+64Ni 14.5 AMeV
nucl-ex collaboration&garfield
Experiments with n-rich/poor systems
32S+58Ni and 32S+64Ni 14.5 AMeV
3-IMF events
Tiso ≈ 3.5 MeV
nucl-ex collaboration&garfield
α-α
Before concluding about the
temperature:
thermodynamical
characterization of the source is
needed
isotope emission time scales
have to be 7checked through
p-Li
d-α
correlation functions (intensity
interferometry)
Conclusions
Multics NPA 2004
 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
E*/A (A.MeV)
1+R(q)
1+R(q)
Multics E1=20.3 E2=6.50.7
Isis
E1=2.5 E2 =7.
Indra
E2=6.0.5
We need:
• 4 mass and charge detection
• 20-50 A.MeV radioactive beams
nucl-ex collaboration&garfield

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