The nuclear liquid gas phase transition

16/1/06 Eurisol Workshop @ ECT* 1

The nuclear liquid gas phase transition

Francesca Gulminelli LPC Caen and

Institut Universitaire de France

• The status of the art• The isospin degree of freedom transition observables

new phenomenawhat do we need from Eurisol

• Conclusions

p

n

0.1 MeV 1

0.09

0.085

0.08

0.075

0.07

fm-3

fm-3

NM phase diagram

C.Ducoin et al 2005


The status of the art


Boiling nuclei

Nucleus

Density

Tem

per

atu

re70

00

0 0

00

00

0°

0

T critical

SPINODAL multifragmentatio

n

Motivations:• nuclear thermometry•interdisciplinary connections•dense matter and stars

P.J.Siemens Nature 1983


Self similarity and scalings

Au Liquid-Gas

nA=q0A-exp(- c0A) TIsIs PRL2002

EoS PRC2003 Multics PRC2003

J.Finn et al PRL1982

p+Xe 80-350 GeV

A-2.64

Fisher 1967


Caloric CurveAladin PRL1995

Heat (Calories per grams)

Tem

per

atu

re (D

egre

es)

Texas A&M PRC2003


INDRA NPA 2002

Multics NPA 2003

IsisE900A

all

one source

INDRA-Aladin nucl-ex 2005

Fluctuations and negative heat capacity

Nim

rod P

RC

20

04


Bimodality

B.Tamain et al. 2005

Z1

Z2 "reservoir"

T

197Au

197Au

Au+Au 80 A.MeVINDRA@GSI data

order parameter:charge

asymmetryZ1-Z2

Z1-Z2

Z1


Spinodal Decomposition

Sc’= Sc+ts p

n

Spontaneous fluctuation growth inside an Instability region


Spinodal Decomposition

G.Tabacaru et al., EPJA18(2003)103

t


The status of the art

Multifragmentation:• An (out of equilibrium) phase transition• First or second order• If first order, most probably driven by spinodal

instabilities

WCI 2003-2005

world-wide review of the field of dynamics and

thermodynamics with nucleonic degrees of freedom

http://cyclotron.tamu.edu/wci3/


The phase transition with Eurisol


Changing

the isospin content (N/Z) the Coulomb properties

of the fragmenting source:

Muller Serot PRC 1995

N

Z

an extra dimension


From supernovae to neutron stars


New phenomena

Neutron rich nuclei: isospin fractionation

Y=(N-Z)/A0

0

-1

1

-1 1

Gas: + asymmetric

Liquid:+ symmetric

Equilibrium Spinodal

Y

C.D

uco

in n

ucl-th

2005


Isospin fractionation

Y=(N-Z)/A0

0

-1

1

-1 1

Gas: + asymmetric

Liquid:+ symmetric

Equilibrium

Spinodal

Y

C.Ducoin et al nucl-th 2005

Z

counts

I

r(fm)

v/c (x100)

V.Baran et al. PR 2005


Isospin fractionation

112Sn + 112Sn124Sn + 124Sn

5

20

10

2

0 1 2 0 1 2

1

t/3He

11B/11C 7Li/7Be

t/3He

7Li/7Be

11B/11C

rati

o

B(MeV)

LASSA + Miniball PRL 2000Sn+Sn 50 A.MeV

11B/11C7Li/7Be

t/3He

1.3 1.4 1.5N/Z

rati

o

5

10

15

20

NIMROD PRC 2003Sn+Sn 28 A.MeV

n/p5.5 for N/Z=1.48but

thermodynamic characterization needed


Fractionation observables: isoscaling

Y2(N,Z) Y1(N,Z)

= C exp(N+Z)

Lassa+Miniball PRL 2001

Texas A&M PRC 2004

FRS nucl-ex 2005

•Pre-equilibrium effects•Sequential decay (?)

approximately cancel out



Y2(N,Z) Y1(N,Z)

= C exp(N+Z)T.X.Liu et al. PRC 2004

A

primary

C

2 2

sym

1 2

C Z Z4

T A A

2 2

sym

1 2

C

TZ Z

4A A

10 15

secondary

A

Ono PRC 2003

Sensitive to the EOSsymmetry properties



2 2

sym

1 2

C

TZ Z

4A A

2 2

sym

1 2

C Z Z4

T A A

Y2(N,Z) Y1(N,Z)

= C exp(N+Z)

Ono PRC 2003

Sensitive to the EOSsymmetry properties

2 2

1 2

symC4

Z ZAT A

~(N

-Z)/

A

Sensitive to the isotopic content of fragments


First results

Reduced symmetry energy or increased fractionation

disentangle with transport observables

2

2

2

1

4A

Z

A

Z

T

CsymIndra-Aladin PRL 2005

appsymC

Decreasing with centrality

We need:

• IMF isotopic resolution• 4 detection for event sorting• Neutron rich nuclei• E/A>30 MeV


New phenomena

Proton rich nuclei: vanishing limiting temperatures

Bonche Vautherin NPA 1984

N

Z


Y=(N-Z)/A0

0

-1

1

-1 1

Gas: + asymmetric

Liquid:+ symmetric


Y

C.D

uco

in n

ucl-th

2005


Coulomb effects on the phase transition

Energy

12

34

Cou

lom

b in

tera

ctio

n V

C

0 2 4 6 8 10 12 14

CNCharged

CUncharged

Spinodal

200Pb

0 2 4 6 8 10 12 14

Pro

bab

ilit

y

0 4 8 12Energy

Energy

C=N Charged

C= Uncharged

SMM by Raduta2

Z=23, A=50

0.4

0.8

1.2

1.6

2C

ou

lom

b in

tera

cti

on

VC

• Rotation of the order parameter • Reduction of the coexistence

zone

• New decay channels (cf.fission) • Cross over

FG PRL 2003


New phenomena

Proton rich nuclei: vanishing limiting temperatures

Bonche Vautherin NPA 1984

N

Z


Y=(N-Z)/A0

0

-1

1

-1 1

Gas: + asymmetric

Liquid:+ symmetric


Y

C.D

uco

in n

ucl-th

2005

In medium modificationof cluster properties

Ono et al PRC 2004


In medium modification of cluster properties

Reduction of the the surface symmetry term at finite temperature?

Wide isotopic distributions

Ono PRC 2004 Botvina PRL 2005

Reduction of the volumesymmetry term for clusters?


Conclusions

• The physics of hot nuclei

• a unique laboratory for the thermodynamics of open, finite, off-equilibrium systems• a quantitative nuclear metrology

Multics NPA 2003

E/A (A.MeV)

C/A

• What do we need

• 4 detection• wide isotopic resolution

(AZ4 collaboration - FAZIA concept of the EURISOL report)

• wide asymmetry range for the compound• wide asymmetry range for the QP• 30-100 A.MeV beams



Statistical mechanics of small quantum

systems

• Collisions d’ions lourds rélativistes

Excitation Energy (MeV)

10 2 3 4 5 6

Tem

per

atu

re

(MeV

)

0

0.4

0.8

1.2172Yb

Siem-PRC65(2002)044318

• Superfluidité dans les noyaux

Schmidt et al, PRL 79(1997)99

Temperature (K)Hea

t C

apac

ity

(eV

/K)

200 300 400

0

0.4

0.8

0

100

• Transition solide-liquide dans les agrégats

• L’ensemble évaporatif

Brechignac et al, PRL81(98)4612

A.Ono, PRC 59(98)853

GULMINELLI

brechignac: spectre de photodissociation d'agrégats d'atomes de strontium


Clusterization properties at -equilibrium

Path at -equilibrium

for =100 MeV

n (fm-3)

k0 (M

eV)

n/

p

Direction of instability

Instability dir.

T=10 MeV

Slya

Isospin fractionation: n/p < n/p

n (fm-3)

Affects cluster

composition

(less n-rich)

Direction of constant Z/A

Slya SGII SIII

Most instable mode: k0(n, p) (min. of k2C<)

Affects cluster size

/2 = /k0

Instability direction:Eigen-vector corresponding to C<




Equation of state at T=0: symmetry energy

E=E1() + Esymnp

0.2 0.4 0.6

10

20

matter density (fm-3)

Sym

met

ry e

ner

gy (

MeV

)

BPAL32

SkM*

SLy230b

Theoretical uncertainty on the density dependence

Muller Serot PRC 1995


symmetry energy and isospin diffusion

LASSA-Miniball PRL 2004

Sn + Sn 50 A.MeV

112124 124

112

isoscalingY2(N,Z) Y1(N,Z)

= C exp(N+Z)

isospin transport ratio 2xi-x124+124-x112+112 x124+124-x112+112 Ri =

x = isospin sensitive variable

no diffusion

no diffusion

equilibration

data

data


symmetry energy and isospin diffusion

LASSA-Miniball PRL 2004

Sn + Sn 50 A.MeV

112124 124

112

0.2 0.4 0.6

10

20

matter density (fm-3)

Sym

met

ry e

ner

gy (

MeV

)

BPAL32

SkM*

SLy230b

Better agreement with asy-stiffbut

• emission time scales: correlations needed!

data

data


Phase transition and equilibrium

Equilibrium Spinodal Coalescence

Phase coexistence deduced from bimodality does not bear any information on the fragment production mechanism

NM Skyrme Sly4b T=cte

Camille Ducoin, Thèse 2006

Sc= S-E+t

GULMINELLI

une fois qu'on sache bien qu'on étudie liquide-gaz(en admettant qu'on y arrive), ceci n'impliquepas que le système était équilibré!Car si le diagramme de phase exploré par le système est bien (rho_n,rho_p,T) (diagramme qui présente selon la théorie une transition LG), le système peut très bien exploré ce diagramme à l'équilibre ou hors équilibre. Dans les deux cas il y a transition liquide-gaz, mais les observables (par exemple: le contenu isotopique) peuvent etre très différentes. Ceci est le contenu de l'intervention que Camille Ducoin fera à IWM.


Abnormal fluctuations

T

σ2/T2

p = cte

V = cte

The caloric curve depends on the transformation

Fluctuations are unique

Ph.Chomaz, F.G. PRL 2000

energy pressu

re

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The nuclear liquid gas phase transition

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