Phase transitions in nuclei:

from fission to multifragmentation and back

F.Gulminelli – LPC Caen

• First multifragmentation models: ~1980 (L.Moretto, J.Randrup, J.Bondorf, D.Gross)

• First exclusive data on multifragmentation: ~1995 (ALADIN, EOS, INDRA, IsIs)

Multifragmentation: an extension of fission?

J. A. LOPEZ and J. RANDRUP: Nucl. Phys. A512(1990)345; A571(1994)379

N

i iitot

q m rm

2 2

1

1

N

F i iiF

p p rq

1

1

Extended fission coordinate in hyperspace

Conjugated momentum

*N N N

tot

pE q E E V q

m

20

1 1 1 2

, ,

N

s tots

q Tq

E hA E A E

322 2

Partition dependent multi-dimensional fission barrier

Transition current and partial width

E*

=E*

q

V

Multifragmentation: an extension of fission?

J. A. LOPEZ and J. RANDRUP: Nucl. Phys. A512(1990)345; A571(1994)379

E*

=E*

Conditional saddle

Scission

-----------Dissipation (Langevin)

In principle, a very complex many-body dynamics:

• multi-dimensional deformations• pre-saddle emission• dissipation• post-saddle emission

Multifragmentation: an extension of fission?

J. A. LOPEZ and J. RANDRUP: Nucl. Phys. A512(1990)345; A571(1994)379

E*

=E*

Conditional saddle

Scission

-----------Dissipation (Langevin)

In principle, a very complex many-body dynamics:

BUT:• saddle very close to scission

Saddle configurations

Multifragmentation: an extension of fission?

E*

L.Beaulieu et al, Phys.Rev.Lett. 84 (2000) 5971-5974

Experimental evidence: time plays no role in the multi-fragmentation regime

The liquid-gas phase transition of nuclear matter

Gas

Liquid

Density

20

200 M

eV

1 5?

QGP

Tem

pera

tur

e

The liquid-gas phase transition of nuclear matter

Liquid

Gas

Density

20

200 M

eV

1 5?

QGP

Tem

pera

tur

e

Heavy

Ions Collisions

The liquid-gas phase transition of nuclear matter

Liquid

Gas

Density

20

200 M

eV

1 5?

QGP

Tem

pera

tur

e

Heavy

Ions Collisions

Phase transitions in finite systems

Landau Binder PRB 1984

L oorder parameter M

o

L finite

Field H

Transition point

Transition point

Phase transitions in finite systems

Landau Binder PRB 1984K.C.Lee PRE 1996F.Gulminelli Ph.Chomaz PRE 2001

Physica A 2003

L oo

L finite F

M

F

M

order parameter M

Field H

MF

M

P

M.Pichon et al. NPA 2006

Z1

Z2

197Au

197Au

Au+Au 80 A.MeVINDRA@GSI data

Z1-Z2

Z1

Bimodalities in fragmentation distributions

Largest fragment Z1: typicalorder parameter in fragmentation phenomena

Lattice Gas Model :An exact model belonging to the LG Universality Class

Liquid-Gas Transition versus data

*

exp*

*exp

,p E Zp Z dE

p E

1

1

Independent of the incident energy=> of the entrance channel dynamics

Quantitative disagreement !!

=Ebeam(MeV/A)

E.Bonnet et al. 2008

Qualitative agreement

0 .2 .4 A/As

LG

C

LGM with symmetry and Coulomb

, ,i j

i j in n i j c i

i j i j iij

q q pH n n n

r m

2

2

L

G

F

G.Lehaut et al. 2008

Z=54 N=75

LGM with symmetry and Coulomb

L

G

F0. .5 1 Z1/Zs

0. .5 1 Z1/Zs

0. .5 1 Z1/Zs

0. .5 1 0. .5 1 0. .5 1 0. .5 1 Z1/Zs

G.Lehaut et al. 2008

Tem

pera

ture

Nuclear statistical models : MMM

Energy

12

34

Cou

lom

b in

tera

ctio

n V

C

0 2 4 6 8 10 12 14

CNCharged

CUncharged

Spinodal

200Pb

F.Gulminelli et al. PRL91(2003)202701

~Z1

Nuclear statistical models: CTM

G.Chaudhuri et al. nucl-ex 2008

uncharged charged

charged

uncharged

Conclusions Charged systems at finite temperature have a

generic fragmentation pattern with Z1~Ztot/2, Z2~Z1

This hot (asymmetric) « fission » phenomenon can be interpreted as a first order transition

Contrary to fragmentation of neutral systems, this Coulomb-induced transition has no thermodynamic limit => it is not related to the LG universality class but closer to bimodality in fission

This may be what we experimentally observe through multi-fragmentation experiments (projectile fragmentation) (??)