Bimodalities

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Bimodalities
A compilation of models and data
O. Lopez, M.F. Rivet
WCI3 Town Meeting, College Station (Texas)
February, 12-17 2005
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Bimodalities part 1
Theoretical bases
LOPEZ/RIVET, WCI3 Town Meeting, College Station
(Texas) February, 12-17 2005
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Bimodalities foundation
Bimodality of the magnetization in a finite Ising
ferromagnet at phase transition Binder Landau
PRB30 (1984)
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(Texas) February, 12-17 2005
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Bimodality of order parameter distribution new
definition of a 1st order phase transition in
finite system Chomaz et al. PRE64 (2001)
1/ Equivalent to Yang-Lee theorem (stand. def. at
thermodynamic limit) Chomaz/Gulminelli
Physica A330 (2003)
and to
3/ If XE, negative heat capacity
LOPEZ/RIVET, WCI3 Town Meeting, College Station
(Texas) February, 12-17 2005
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Phase transition definition and statistical
ensembles
Clt0 the order parameter (E ) must be
controlled
microcanonical ensemble
Bimodality and Yang-Lee Th. extensive variable
(E, V ) should be free to fluctuate
Canonical ensemble
LOPEZ/RIVET, WCI3 Town Meeting, College Station
(Texas) February, 12-17 2005
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Relaxed condition Gaussian ensemble as
interpolating ensemble
N particles in sample, N in heat bath, vary N
from 0 to 8
a ? 1/N
Bimodality obtained for large N (small a)
canonical and not for small N µcanonical
Challa Hetherington PRL60 (1988)
LOPEZ/RIVET, WCI3 Town Meeting, College Station
(Texas) February, 12-17 2005
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LG Phase transitions different possible order
parameters
Canonical Lattice gas model in the first
order phase transition region. Chomaz et al. PRE
64 (2001)
LOPEZ/RIVET, WCI3 Town Meeting, College Station
(Texas) February, 12-17 2005
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Bimodalities part 2
Experimental facts
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(Texas) February, 12-17 2005
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Bellaize et al, Nucl. Phys A709 (2002) INDRA
collaboration
Bimodalities experimental overview
Observation of a bimodality in fragment size
asymmetry for E4 (32) and E5 (52) MeV/n
(from SMM)
LOPEZ/RIVET, WCI3 Town Meeting, College Station
(Texas) February, 12-17 2005
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Bimodalities experimental overview
Borderie et al, Journal of Physics G (2002) R217
INDRA collaboration
32-50 MeV/nucleon 129XenatSn A 180-220,
Central collisions (qflow)
Ratio between Liquid and Gas phase
LOPEZ/RIVET, WCI3 Town Meeting, College Station
(Texas) February, 12-17 2005
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Bimodalities experimental overview
Lautesse et al, PRC 2005, in press INDRA
collaboration
32 MeV/nucleon 58NinatNi
A 100, central collisions (DFA)

• Data exhibit 2 fragmentation patterns
• Evaporation-Residue (GEMINI-like)
• multifragmentation (SMM-like)

LOPEZ/RIVET, WCI3 Town Meeting, College Station
(Texas) February, 12-17 2005
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Bimodalities experimental overview
M. Pichon, Thèse LPC Caen (2004) http//tel.ccsd.c
nrs.fr/documents/archives0/00/00/74/51
80 MeV/nucleon 197Au 197Au
A 160-180, peripheral reactions (QP)
LOPEZ/RIVET, WCI3 Town Meeting, College Station
(Texas) February, 12-17 2005
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Bimodalities experimental overview
D'Agostino et al, 5th Italy-Japan Symposium
Naples 2004 MULTICS-MINIBALL collaboration
35 MeV/nucleon 197Au197Au
A 180, peripheral reactions (QP)
The same signal is observed
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(Texas) February, 12-17 2005
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Trautmann et al, private communication
(2005) ALADIN collaboration
Bimodalities experimental overview
1000 MeV/nucleon 197Au197Au
A 130, peripheral collisions (QP)
Wait final remarks
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(Texas) February, 12-17 2005
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Bimodalities experimental overview
Ma et al, Nucl-ex/0410018 NIMROD Collaboration
47MeV/nucleon 40Ar27Al,48Ti,58Ni
A 24-40, peripheral reactions (QP)
A crossover between gas and liquid phase for
E/A 5.5 MeV (exc5-6)
LOPEZ/RIVET, WCI3 Town Meeting, College Station
(Texas) February, 12-17 2005
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Bimodalities part 3
Models and simulations
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(Texas) February, 12-17 2005
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nucl-th/0412111 N. Buyukcizmeci, R. Ogul, A.S.
Botvina
Bimodalities Statistical Multifragmentation Model
Calculations for different nuclei From EA2-20
MeV
2 classes of events are seen depending on the
size of Amax
(A)
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(Texas) February, 12-17 2005
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D. Cussol Private communication (2005)
Bimodalities Classical Molecular Dynamics
Bimodality in A1-A2 is observed for 3 simulation
sets - central collisions (blt0.1) - peripheral
collisions (QP) - thermalized systems (r0/r8)
The transition is located at different
excitation energies Eleastbound lt E/N lt
2Eleastbound
What is its meaning ? Role of the deposited
energy ?
LOPEZ/RIVET, WCI3 Town Meeting, College Station
(Texas) February, 12-17 2005
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Lopez and Lacroix, Preliminary results (2005)
Bimodality Heavy Ion Phase Space Exploration Van
Lauwe et al, PRC 69, 054604 (2004)
80 MeV/nucleon XeSn, Et12QC bins (QP)
The transition is governed by the transferred
spin to the QP source
Bimodality and Phase Transition (not LG)
LOPEZ/RIVET, WCI3 Town Meeting, College Station
(Texas) February, 12-17 2005
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Bimodalities part 4
Questions and (some) answers
LOPEZ/RIVET, WCI3 Town Meeting, College Station
(Texas) February, 12-17 2005
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Bimodalities general overview of experimental
data
Results from Reaction type Size (A) Bimodality in
INDRA Central 200 Z1-Z2
INDRA Central 200 Zliq-Zgas ()
INDRA Central 100 Asym123
INDRA Peripheral 160-180 Z1-Z2
MULTICS/MINIBALL Peripheral 180 Z1-Z2
ALADIN Peripheral 130 Z1-Z2
NIMROD Peripheral 24-40 Zliq-Zgas ()
Amax a better order parameter ?
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(Texas) February, 12-17 2005
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In experiments, we never observe a bimodality of
Amax, but for some asymmetry parameter (Aasym,
Z1-Z2, ) , Why ?
LOPEZ/RIVET, WCI3 Town Meeting, College Station
(Texas) February, 12-17 2005
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Event sorting is not enough canonical ?
Lattice-gas F. Gulminelli
Bimodality is observed in Aasym but not in Amax
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(Texas) February, 12-17 2005
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What is the influence of out-of-equilibrium
effects ?
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(Texas) February, 12-17 2005
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F. Gulminelli Phase coexistence in
Nuclei Habilitation Université de Caen (2003)
Bimodality Lattice-gas model and
out-of-equilibrium effects
Bimodality and radial flow
Bimodality is still present even for 100 of
radial flow (as compared to E)
Similar conclusions are observed in presence of
transparency (longitudinal flow) F. Gulminelli
and Ph. Chomaz Nucl. Phys. A734 (2004) 581
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(Texas) February, 12-17 2005
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What is the influence of Coulomb interaction ?
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Bimodalities Influence of Coulomb
Gulminelli et al PRL 91, Number 20 (2003)
Bimodality in IMMM (Isobar Microcanonical
Multifragmentation Model)
A multicanonical approach allows the mapping
between Coulomb and uncharged systems
Inclusion of Coulomb deforms the event
probability structure of the phase space but the
bimodal character still remains for small systems
but not for the heavier ones
Size dependence ?
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(Texas) February, 12-17 2005
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Is the asymmetry parameter a good order parameter
?
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Bimodality of Amax (order parameter) only when
there is a 1st order PT
Aasy (Amax A2)/(Amax A2) may lead to
ambiguity on the order of the PT but not on
the existence of a PT
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Bimodalities some questions

• What is the best order parameter Amax vs.
  (Amax-A2), (Amax-A2-A3), ?

• What about the event sorting canonical vs. X ?

• Some alternative explanations may exist
• spin, geometry effect, boundary
  conditions,

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(Texas) February, 12-17 2005
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Bimodalities to go further from the exp. side
Correlation between bimodality and the other
proposed signals for the LG phase transition
Abnormal energy fluctuations (negative heat
capacity)
Scaling laws (universal fluctuations, Fishers,
Zipfs, )
Space-time correlations (emission times,
correlation functions)
Improve the validity of the signal
LOPEZ/RIVET, WCI3 Town Meeting, College Station
(Texas) February, 12-17 2005
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BIMODALITIES
The discussion is now OPEN
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(Texas) February, 12-17 2005
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Bimodalities summary
Definition Bimodality is the presence of two
components in an event probability distribution
of an order parameter for a finite system it is
related to the coexistence of two phases for the
considered system
Generic features
It is related to the abnormal convexity of the
entropy or other thermodynamical potentials

It is then a 1st order phase transition
It should be observed in a canonical treatment
of data or at least in the framework of
gaussian ensembles
It is a signature of the liquid-gas phase
transition in nuclear matter if
Order parameter is the density (rliq-rgas) or
Energy
LOPEZ/RIVET, WCI3 Town Meeting, College Station
(Texas) February, 12-17 2005
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Bimodalities what could be in the Consensus
From the theoretical side
The relationship between phase coexistence and
bimodality is clearly established for finite
systems
The order parameter for the Liquid-Gas phase
transition is (rliq-rgas) or E and is related to
the biggest fragment (Amax) for LG (but not only
!)
From the experiment side
Two decay modes are observed they correspond to
the fragmentation threshold and the route from
residue-evaporation to multifragmentation
They are observed both in peripheral and central
collisions
LOPEZ/RIVET, WCI3 Town Meeting, College Station
(Texas) February, 12-17 2005