Phase transitions in nuclei: from fission to multifragmentation and back F.Gulminelli – LPC Caen
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Transcript of Phase transitions in nuclei: from fission to multifragmentation and back F.Gulminelli – LPC Caen
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) (??)