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

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

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)

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[]

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/

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 ?

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

MultifragmentationMultifragmentationas a possible as a possible signature ofsignature of

the liquid-gas phase the liquid-gas phase transitiontransition

Threshold for Threshold for MultifragmentationMultifragmentation

From G. Bizard et al., Phys. Lett. B 302, 162 (1993)

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

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?

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)

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)

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)

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)

Heavy Ion Phase Space ExploratorD. Lacroix, A. Van lauwe and D. Durand, Phys. Rev. C 69, 054604

(2004)

Signals of Phase Signals of Phase transitionstransitions

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)

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)

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

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

The case of The case of BimodalityBimodality

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)

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)

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

FuturesFutures

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)

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)

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

Long-term rangeLong-term range

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

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.

FAZIA projectFAZIA project

Visit us at http://fazia.in2p3.frVisit us at http://fazia.in2p3.frCourtesy of JM Gautier (LPC Caen)

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

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)

Phase transition in Phase transition in Nuclei Nuclei

To be continued…To be continued…

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.

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

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

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)

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)

Bimodality : exp. resultsBimodality : exp. results

Observed Observed whatever the whatever the sortingsorting

Characteristic Characteristic of a 1of a 1stst order order phase phase transitiontransition

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 !