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Phase transition in Phase transition in NucleiNuclei
Olivier LOPEZOlivier LOPEZ
Séminaire 1-2-3 – Décembre 2006 - LPC CaenSéminaire 1-2-3 – Décembre 2006 - LPC Caen
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Phase diagram of NMPhase diagram of NM
2020
0 M
eV
1 5?Density
Tem
pera
ture Gas
Liquid
QGP
Hadron
200 AGeV
LG Coexistence
100 AMeV
20 AMeV
50 AMeV
Big Bang
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Underlying PhysicsUnderlying Physics DFT approach to nuclear physics: towards an universal functionalDFT approach to nuclear physics: towards an universal functional
Study the energy functional for asymmetric nuclear matterStudy the energy functional for asymmetric nuclear matter Constrain the isovector part of the energy (symmetry energy)Constrain the isovector part of the energy (symmetry energy) Produce sub- and super-saturation density matter through HI-induced Produce sub- and super-saturation density matter through HI-induced
reactionsreactions
Nuclear matter phase diagram and finite nuclei phase Nuclear matter phase diagram and finite nuclei phase transitionstransitions
Scan the low-temperature region of the nuclear matter phase diagramScan the low-temperature region of the nuclear matter phase diagram Characterize the phase transition (location, order, critical points,…)Characterize the phase transition (location, order, critical points,…) Evidence finite size effects (anomalies in thermodynamical potentials)Evidence finite size effects (anomalies in thermodynamical potentials) Complementary to the ALICE Physics program at higher energy (QGP)Complementary to the ALICE Physics program at higher energy (QGP)
From finite nuclei to dense nuclear matterFrom finite nuclei to dense nuclear matter Constrain Mean-Field models for AstrophysicsConstrain Mean-Field models for Astrophysics Study the structure and pahse properties of Neutron Star crustsStudy the structure and pahse properties of Neutron Star crusts Understand the dynamics of supernova type II explosion (EOS)Understand the dynamics of supernova type II explosion (EOS)
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Density Functional Density Functional TheoryTheory
Self-consistent mean field calculations (and extensions) are probably the only possible framework in order to understand the structure of medium-heavy nuclei. E = < | H | >
H = < | Heff | > = E[]
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Symmetry energy Symmetry energy (basics)(basics)
Standard Bethe-Weisäcker formula for Binding Standard Bethe-Weisäcker formula for Binding Energy :Energy :
E = -aE = -avvA + aA + assAA2/32/3 + a + accZZ22/A/A1/31/3+a+asymsym(N-Z)(N-Z)22/A + /A +
Symmetry Energy : Symmetry Energy : EEsymsym = a = asymsym(N-Z)(N-Z)22/A/A is therefore the is therefore the change in nuclear energy associated to the changing of change in nuclear energy associated to the changing of proton-neutron asymmetry N-Zproton-neutron asymmetry N-Z
In nuclear matter (isoscalar+isovector) : In nuclear matter (isoscalar+isovector) :
E(E(nn, , pp) = E) = E00(() + E) + E11((nn, , pp)) with with EE11((nn, , pp) = S() = S()()(nn--pp)/)/22
Pressure : P = Pressure : P = 22E/E/
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Symmetry Energy Symmetry Energy (questions)(questions)
Little is known Little is known at super and at super and sub-saturation sub-saturation densitydensity
Dependence on Dependence on the neutron-the neutron-proton proton asymmetry ?asymmetry ?
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Phase transition and Phase transition and Neutron starsNeutron stars
(Extended) MF theories with a density functional constraint in a large density domain are a unique tool to understand the structure of neutron stars.
Multifragmentation and Phase transition
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MultifragmentationMultifragmentationas a possible as a possible signature ofsignature of
the liquid-gas phase the liquid-gas phase transitiontransition
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Threshold for Threshold for MultifragmentationMultifragmentation
From G. Bizard et al., Phys. Lett. B 302, 162 (1993)
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Hot nuclei and de-Hot nuclei and de-excitationexcitation
1 3 8 E*/A (MeV)
Evaporation
~ 0
T < 5 MeV
Vaporization
<< 0
T>15 MeV
Multifragmentation
< 0
T= 5-15 MeV
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Simultaneous emission for fragments : ff < n
Equilibrated system in (,T) plane :Isotropic emission
Nuclear system at sub-saturation density :
/0 << 1
Multifragmentation as a signal of liquid-gas phase
transition?
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Multifragmentation as a Multifragmentation as a simultaneous processsimultaneous process
FF
~ n
R(FF
) =
Ncorr
(FF
) - Nuncorr
(FF
)
Ncorr
(FF
) + Nuncorr
(FF
)
Angular correlation functions :
From D. Durand, Nucl. Phys. A 630, 52c (1998)
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Multifragmentation as an Multifragmentation as an equilibrated process…equilibrated process…
Mass scaling
Universality
The “rise and fall” of MF emission
From A. Schuttauf et al., Nucl. Phys. A 607, 457 (1996)
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Multifragmentation at low Multifragmentation at low density …density …
58Ni+197Au central collisions
Volume
Statistical weight :
W = eS(V,T)
V=(1+)V0 with >0
Statistical Multifragmentation Model (SMM)
From N. Bellaize et al., Nucl. Phys. A 709, 367 (2002)
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Multifragmentation and Multifragmentation and statistical descriptionstatistical description
Reaction dynamics and Reaction dynamics and Fermi motion is not taken Fermi motion is not taken into account → into account → additional additional free parameter Efree parameter Eradrad (radial flow) for (radial flow) for Statistical ModelsStatistical Models
Is explicitly incorporated Is explicitly incorporated in dynamical (semi-in dynamical (semi-classical) approaches like classical) approaches like HIPSE or QMD, (quantal) HIPSE or QMD, (quantal) like AMD/FMD…like AMD/FMD…
From N. Bellaize et al., Nucl. Phys. A 709, 367 (2002)
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Heavy Ion Phase Space ExploratorD. Lacroix, A. Van lauwe and D. Durand, Phys. Rev. C 69, 054604
(2004)
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Signals of Phase Signals of Phase transitionstransitions
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Signals of phase Signals of phase transitiontransition
Caloric curve: Caloric curve: T=f(E*)T=f(E*)
E*/A
T
5 10
5
SMMA=100
Free nucleons gasE* T
Fermi gasE* T2
10coexistence
Back-bending
From J. Pochodzalla et al., Phys. Rev. Lett. 75, 1040 (1995)
From INDRA collaboration (1999)
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Signals of (1st order) Phase Signals of (1st order) Phase transitiontransition
Abnormal energy Abnormal energy fluctuationsfluctuations
Energy
C
T
S
Entropy
Temperature
Specific heat
T-1 = (dS/dE)V
C = dE/dT
Latent Heat
C C1 + C2 = C1
2
C1 - 12/T2
C = ( E/ T) = -T2(2S/ E2)
T-1 = (S
If one divides the system in two independent subsystems (1)+(2) :
Et = E1 + E2
And we get for the partial energy fluctuations of system (1) :
12 = T2 C1C2/(C1+C2)
Thermodynamical relations :
(true at all thermodyn. conditions)
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Signals of (1st order) Phase Signals of (1st order) Phase transitiontransition
M. D’Agostino et al., Physics Letters B 473, 219 (2000)
N. Le Neindre, PHD Thesis Caen (1999)
Peripheral Au+Au reactions Central Xe+Sn reactions
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Liquid-gas phase Liquid-gas phase transitiontransition
Critical phenomena : Critical phenomena : power laws, scalings, power laws, scalings, exponentsexponents
Caloric curves : Caloric curves : back-bendingback-bending Universal scaling : Universal scaling : -scaling (order-disorder)-scaling (order-disorder) Disappearance of collective properties : Disappearance of collective properties : Hot GDR, Hot GDR,
Shape transition (Jacobi)Shape transition (Jacobi) Abnormal fluctuations : Abnormal fluctuations : negative negative
capacities/susceptibilitiescapacities/susceptibilities Charge correlations : Charge correlations : spinodal decompositionspinodal decomposition Bimodality : Bimodality : order parameter for phase transitionorder parameter for phase transition
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The case of The case of BimodalityBimodality
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Bimodality : theoretical Bimodality : theoretical aspectsaspects
Related to a convex Related to a convex intruder of the intruder of the S(X)S(X)
Appearance of a Appearance of a double-humped double-humped distri-bution for the distri-bution for the proba-bility proba-bility distribution distribution PP of of the order the order parameter parameter XX
Examples : Examples :
X=EX=E
X=VX=VFrom Ph. Chomaz, M. Colonna and J. Randrup, Phys. Rep. 389, 263 (2004)
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Bimodality : Bimodality : experimental resultsexperimental results
Peripheral Peripheral Au+Au reactions Au+Au reactions at E/A=80 MeVat E/A=80 MeV
Transverse Transverse energy sorting energy sorting (→ T)(→ T)
Bimodality of Bimodality of ZZmaxmax, Z, Zasymasym is is observed in the observed in the third panelthird panel
From M. Pichon, B. Tamain et al., Nucl. Phys. A 779, 267 (2006)
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Bimodality : interpretationBimodality : interpretation
Normal density (J) vs dilute (E*) system ?
From O. Lopez, D. Lacroix and E. Vient, Phys. Rev. Lett. 95, 242701 (2005)
Same T
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FuturesFutures
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SPIRAL/SPIRAL2SPIRAL/SPIRAL2
Isospin dependence of Isospin dependence of the level-density the level-density parameter for parameter for medium-sized nucleimedium-sized nuclei
Limiting temperature Limiting temperature for nucleifor nuclei
Cluster emission Cluster emission threshold for p-rich threshold for p-rich nuclei around A=115 nuclei around A=115 for moderate E*/A for moderate E*/A (~1-2 MeV)(~1-2 MeV)
Isospin dependence of Isospin dependence of the liquid-gas phase the liquid-gas phase transitiontransition
Mass splitting of p-n in Mass splitting of p-n in asymmetric nuclear asymmetric nuclear mattermatter
Link to astrophysics Link to astrophysics and compact nuclear and compact nuclear matter (NS)matter (NS)
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INDRA-SPIRAL experiments : INDRA-SPIRAL experiments : statusstatus
E494S : Isospin dependence of the level-density parameterE494S : Isospin dependence of the level-density parameter
3333,,36,4036,40Ar + Ar + 58,60,6458,60,64Ni at E/A=11.1-Ni at E/A=11.1-11.711.7 MeV => Pd isotopes, E*/A=2-3 MeV => Pd isotopes, E*/A=2-3 MeVMeV
Coupling with VAMOSCoupling with VAMOS Scheduled in March-April 2007 (moving D5-G1 is planned 01/07)Scheduled in March-April 2007 (moving D5-G1 is planned 01/07)
E475S : Emission threshold for complex fragments from E475S : Emission threshold for complex fragments from compound nuclei of A=115 and N~Z (p-rich)compound nuclei of A=115 and N~Z (p-rich)
7575,78,82,78,82Kr + Kr + 4040Ca at E/A=5.5 MeVCa at E/A=5.5 MeV Done in March 2006 (calibration under progress)Done in March 2006 (calibration under progress)
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Isospin dependence of the level-Isospin dependence of the level-density parameter density parameter aa
E* dependence : a = A
with : = 1/(K+E*/A) K =7 , =1.3
N-Z dependence is assumed
(A) a = A e-(N-Z)2 (B) a = A e-(Z-Z0)2
From S. I. Al-Quraishi et al., Phys. Rev. C 63 (2005), 065803
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Long-term rangeLong-term range
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Need for new detectors
4 array (exclusive measurements)
Low Energy thresholds (E/A<1 MeV/u)
Very High angular resolution (<0.5°)
Mass and charge identification (1<A<100)
Modularity / Flexibility (coupling/transportation)
FAZIAFour pi A and Z Identification Array
INDRA
CHIMERA
LHASSA
MINIBALL/MSU
ALADIN
ISIS
NIMROD
EOS
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FAZIA : next generation FAZIA : next generation 44 array array
Compactness of the device Ebeam from barrier up to 100 A.MeV Telescopes: Si-ntd/Si-ntd/CsI Possibility of coupling with other detectors Complete Z (~70) and A (~50) id. Low-energy & identification threshold Digital electronics for energy, timing and
pulse-shape id.
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FAZIA projectFAZIA project
Visit us at http://fazia.in2p3.frVisit us at http://fazia.in2p3.frCourtesy of JM Gautier (LPC Caen)
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FAZIA : next-gen 4FAZIA : next-gen 4 array array
Digital electronicsDigital electronics Pulse Shape Pulse Shape
AnalysisAnalysis
36Ar 40Ar
E/A= 7.8 MeV
CIME / GANIL Sept. 06Tandem Orsay (2003)
E/A= 6.2 MeV
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Long-term range is: Long-term range is: EURISOLEURISOL
(I) Density dependence of the nuclear symmetry energy (DDSE)
56Ni - 74Ni, 106Sn -132Sn, E/A = 15 – 50 MeV (II) Neutron-Proton effective mass splitting (N
PMS)56Ni - 74Ni, 106Sn - 132Sn , E/A=50-100 MeV (III) Isospin-dependent phase transition (IDPT)56Ni - 74Ni, 106Sn -132Sn, 200Rn - 228Rn, E/A = 30 –
100 MeV (IV) Isospin fractionation, Isoscaling (IFI)56Ni - 74Ni, 106Sn -132Sn, 200Rn - 228Rn, E/A = 30 –
100 MeVKey Points are : large panoply of beams (light, medium, large A) over the maximal N/Z extension Beam energy range around and above the Fermi domain (15-100AMeV) Beam intensity around 106-108pps, small emittance, good timing (<1ns)
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Phase transition in Phase transition in Nuclei Nuclei
To be continued…To be continued…
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Nature of Phase transitions
Solid, liquid and gas phases Plasma (electrons, QGP, ...) Magnetic properties in solid state matter
(para/ferromagnets) Bose-Einstein condensates Superfluidity (Cooper pairs) Fund. symmetries breakings (matter/antimatter,
electroweak, …) Nuclei ! …
Phase transitions reflect the self-organization of a system and are ruled by common properties such as predicted by universality classes and Renormalization Group theory.
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Dynamics of the phase transitionDynamics of the phase transitionSpinodal decomposition?Spinodal decomposition?
Boltzman-Langevin (Stochastic Mean-Field)
A. Guarnera et al, Phys. Lett. B 403, 191 (1997)
Metastable regions
Spinodalregion
“GANIL” trajectory
T (MeV)
10.3
10-15
R 10 fmPrivileged wavelength are formed : R ~10 fm
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Symmetry Energy Symmetry Energy (future)(future)
Neutron-proton Neutron-proton asymmetry is different asymmetry is different between the bulk and between the bulk and surface for exotic surface for exotic nucleinuclei
Modified BW formula : Modified BW formula :
E = -aE = -aVVA + aA + assAA2/32/3 + a + acc + + + +
For A>>1, → aFor A>>1, → asymsym, for, for small A → weakening of SEsmall A → weakening of SE
proton
neutron
r
(r)
Z2
A1/3 1 + A-1/3asym/asym
(N-Z)2
A
asymV
V S
asymV
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Multifragmentation as an Multifragmentation as an equilibrated process…equilibrated process…
129Xe+natSn at 50AMeV; Multifragmentation
cos (cm
)-1 +1
dNdcos(
cm)
Isotropic emissionin cm frame
From N. Marie et al., Phys. Lett. B 391, 15 (1996)
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Phase transition and Phase transition and critical phenomenacritical phenomena
Power laws and scalingPower laws and scaling
Power law of the A-distribution :
P(A) = A-f(A)cc
3D Ising Model : = 2.2 = 0.66
Experimentally : = 2.12 ± 0.13 = 0.64 ± 0.04
From M. D’Agostino et al., Nucl. Phys. A 650, 329 (1999)
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Bimodality : exp. resultsBimodality : exp. results
Observed Observed whatever the whatever the sortingsorting
Characteristic Characteristic of a 1of a 1stst order order phase phase transitiontransition
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0
0.5
1
1.5
2
c(mb)
1.2 1.25 1.3 1.35 1.4 1.45 1.5
N/Z
Exp.
Calc.
Figure 1. Carbon emission in 4He + 116,124 Sn. Data from Ref. 5.From J. Brzychczyk et al., Phys. Rev. C 47, 1553 (1993)
4He+116-124Sn E=180 MeV
Statistical Models and Statistical Models and drip linesdrip lines
Enhancement of Enhancement of
Carbon emission Carbon emission for for
p-rich nucleip-rich nuclei
Hauser-Feshback Hauser-Feshback
calculations calculations (BUSCO) (BUSCO)
for Ba isotopesfor Ba isotopes
130Ba
138Ba
124Ba
E*/A ≈ 1.5 MeV
7575,78,82,78,82Kr + Kr + 4040Ca at E/A=5.5 MeV forming CN Ca at E/A=5.5 MeV forming CN 115-122115-122Ba !Ba !