WCI3

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WCI3
Radial Flow
F. Rami C.O.Dorso
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The Radial Flow Experimental facts

• Generally defined (in experimental papers)
• as an azimuthally symmetric collective
• expansion of the emitting source

• ? Consensual definition
• - expanding source not necessarily
• spherical
• - same over a broad range of energies
• (MSU/GANIL ? SPS and RHIC)

• Predicted by Hydrodynamical model
• Bondorf et.al. NPA296(1978)320, Siemmens
• Rasmussen PRL 42(1979) 880
• (Stoecker Greiner, Phys. Rep. 137 (1986) 227)

• Observed for the first time in central
• AuAu collisions at 150AMeV (FOPI_at_GSI)

? Large fraction of the initial KE (30) is
converted into the collective expansion ?
Implications on collision dynamics and
underlying reaction mechanisms
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Extensive studies over the last 12 years

• Since the first experimental observation of the
  radial flow, there have been
• extensive experimental studies over a very
  broad energy range going from a
• few tens of MeV/nucleon (MSU, GANIL) up to
  ultra-relativistic energies
• (AGS, SPS and RHIC)

• Data around (and above) the Fermi energy (E/A lt
  few 100 MeV)

Accelerators SARA (Grenoble) NSCL (MSU) GANIL
(Caen) BEVALAC (Berkeley) SIS-GSI (Darmstadt)
R.T. de Souza et al, Phys. Lett. B 300 (1993) 29
S.G. Jeong et al, PRL 72 (1994) 3468
W.C. Hsi et al, PRL 73 (1994) 3367 D.
Heuer et al, Phys. Rev. C 50 (1994) 1943
M.A. Lisa et al, PRL 75 (1995) 2662 G.
Poggi et al, Nucl. Phys. A 586 (1995) 755
J.C. Steckmeyer et al, PRL 76 (1996) 4895
S.C. Jeong et al, Nucl. Phys. A 604 (1996) 208
M. D'Agostino et al, Phys. Lett. B 371
(1996) 175 R. Pak et al, Phys. Rev. C 54
(1996) 1681 N. Marie et al, Phys. Lett. B 391
(1997) 15 W. Reisdorf et al, Nucl. Phys.
A 612 (1997) 493 T. Lefort et al, PRC 62
(2000) 031604 B. Borderie et al, Nucl.
Phys. A 734 (2004) 495 A. Lefèvre et al,
Nucl. Phys. A 735 (2004) 219
Detectors (large acceptance) AMPHORA _at_
SARA 4?-array _at_ MSU MINIBALL _at_ MSU,
SIS MURTONNEAU _at_ GANIL INDRA _at_ GANIL, SIS EOS _at_
BEVALAC, AGS FOPI _at_ SIS
This list is not exhaustive
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How to observe the Radial Flow?
Prerequisite ? Isolate the emission source

• At high energies (E/A gt 100 MeV) one can
  produce a single 'fused'
• nuclear system (the fireball) in highly central
  collisions

• At lower energies one can produce nuclear
  sources via binary dissipative
• processes (? quasi-projectiles and
  quasi-targets)
• The initial mass and excitation energy of the
  source depend on the
• collision impact parameter

• Several centrality selection criteria are used in
  heavy-ion experiments
• -Total particle multiplicity
• -Total detected charge
• -Ratio of transverse to longitudinal kinetic
  energies (ERAT)
• -Flow angle
• -Principle Component Analysis (PCA)

• The choice of the appropriate selection criterion
  (or combination of criteria)
• depends on the experimental setup (and the
  bombarding energy)

• Centrality should be selected in a similar way
  in model
• calculations (Monte Carlo codes detection
  filter)

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How to observe the Radial Flow?
The radial expansion of the source adds KE to
the particle distributions ? superposition of two
effects Thermal (random) Collective
ltEgt 3/2 T 1/2 mv2

• Heavy particles more sensitive to radial flow
• Experimentally, Signals of collective
  expansion
• should appear as an extra KE in the fragments

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How to characterize the Radial Flow?
Usual Approach
Use statistical models that include a radial flow
component

• At high energies Use the Blast wave formalism
  (Siemens Rasmussen)
• ? Fit the data for different species
  (simultaneously ? mass dependence)
• Results ? T and ?flow
• Generally done at mid-rapidity (?cm900) to
  avoid possible contamination
• of spectator matter and directed flow

• At low energies Use statistical model
  simulations that include the radial
• expansion (WIX, SIMON, )
• ? Compare to the data with different
  assumptions on the radial flow
• Results ? Eflow and sharing of the total
  available energy among
• thermal and collective
  components

Problem ? To which extent the extracted
values depend on model
asssumptions? Not always
clear, in particular at low energies close to
the threshold where the signal is
very small (difficult to
extract accurately!)
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Kinetic energy spectra of light particles
M Lisa et al (EOS), PRL 75 (1995) 26662

• Measured light charged isotopes (Z1,2)
• in central AuAu from 0.25 to 1.15AGeV
• at ?cm900

• analyzed using the Blast wave formalism

Results

• A purely thermal model (?flow0) cannot
• reproduce simultaneously all data

• Fit ? ?flow 0.32 ? 0.05 at E1 AGeV
• ? Large collective flow (45 to 60 of
• total KE)

• Source shape spherical

• FOPI ? Similar results in the 100-250AMeV
• energy range
• (Poggi el al, Nucl. Phys. A 586
  (1995) 755 )

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Kinetic energy spectra of heavy fragments
S.G.Jeong et al (FOPI), PRL 72 (1994) 3468
Au on Au _at_ 150 AMeV, central
Advantage of measuring heavy fragments ? more
sensitive to flow (less affected by thermal
fluctuations) ? provide cleaner
characterization of the radial flow ? Check
the mass dependence (next slide)
Centrality via Erat
Exp. Data (int 25-45), symbols
FREESCO w/coulomb (no flow)
qmd
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The mass dependence
W.Reisdorf et al (FOPI), NPA612(97)493

• A quasi-linear dependence is clearly
• observed for heavy fragments
• ? common flow velocity to all
• detected fragments

AuAu

• The energy taken up by the
• radial flow was estimated
• to be 60 of the available
• kinetic energy at E250AMeV
• (blast model)

Z 2 ? A assumed

• Event topology isotropic within 20

(C.Roy et al (FOPI), Z. Phys. A358 (1997) 73)
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Radial flow energy in AuAu _at_ 100 AMeV
W.C.Hsi et al (Miniball _at_ GSI), PRL 73 (1994) 3367

• Measured KE spectra of IMFs
• in central AuAu collisions at
• E/A 100 MeV
• Extracted values of the expansion
• energy independently for each
• fragment ( 3 rel. Max. dist.)
• Typical values -gt 1/3 to 1/2 of
• the available c.m. energy
• (consistent with FOPI data)

• Mean radial collective energy not
• linear with A, suggesting that
• not all fragments participate
• equally in the collective expansion

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Radial flow energy in 40Ar45Sc _at_ 35-115 AMeV
R.Pak et al (MSU), Phys. Rev. C 54 (1996) 1681

• Measured transverse KE as a function of angle and
  impact parameter
• for 40Ar45Sc at beam energies from 35 to 115
  AMeV

• Agreement with predictions
• of BUU and WIX calculations

? The radial flow accounts for half of the
emitted particle's energy for the heavier
fragments (Z?4) at the highest beam energy
WIX assuming 50 available energy goes into
collective motion
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Radial flow energy in 64ZnnatTi _at_ 35-79 AMeV
J.C.Steckmeyer et al (GANIL), PRL 76 (1996) 4895

• Measured 64Zr natTi reaction at
• E 35 to 79 AMeV
• Source fast quasiprojectile
• ? Observed even in the most
• central events (b ? 2fm)
• Comparisons with WIX and EUGENE
• ? estimate of the radial flow energy
• at E 79 AMeV
• between 1.8 and 2.7 AMeV
• Shape found to be isotropic

• Similar studies of quasiprojectile sources
• in 36Ar27Al from 55 to 95 AMeV (GANIL)
• Jeong et al, Nucl. Phys. A 604 (1996) 208

? Eflow grows with excitation energy ? At E/A10
MeV Eflow 1.02.2AMeV
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Comparison of data to SMM calculations
Radial flow energy in Central AuAu _at_ 35 AMeV
DAgostino et al, Phys. Lett. B 371 (1996) 175
Mean c.m. KE per nucleon at 90o
Cont. lines SMM predictions at ?0/3 no
flow Dashed lines SMM predictions at ?0/6
Eflow 0.8 AMeV
Charge distribution of the six heaviest fragments
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Comparison of dynamic observables to SMM through
PCA analysis
Au Au central collisions _at_ 35 AMeV Nucl. Phys.
A633 (1998) 547
Mean cm kinetic energy per nucleon Points
experiment Cont. line SMM
prediction Dashed line SMM predictions
1.1 MeV radial flow
Mean cm kinetic energy (full points) of the
heaviest fragments (b) and all but the heaviest
(c) compared to SMM predictions 1.1 MeV radial
flow (open points)
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Radial flow from INDRA _at_ GANIL
N.Marie et al, Phys. Lett. B 391 (1997) 15

• Measured KE of IMFs in central
• XeSn collisions at 50 AMeV
• Comparison with SIMON calculations
• with and without collective motion
• Main conclusion
• The results indicate a fast
• disintegration process of the
• system with a radial collective
• motion of about 2 AMeV

Mass dependence clearly observed
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Radial flow from INDRA _at_ GANIL
J.Frankland et al, Nucl. Phys. A 689 (2001) 940

• Data for 129Xe natSn _at_ 32AMeV
• and 155Gd natU _at_ 36AMeV
• ? Radial flow energy estimated from
• stochastic mean field simulations
• (BNVBOB)

B.Borderie et al, Nucl. Phys. A 734 (2004) 495

• Data for several reactions at incident
• energies between 32 and 52 AMeV
• Radial flow energy deduced
• from comparisons with SMM

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Radial flow from INDRA _at_ GSI
A.Lefèvre et al, Nucl. Phys. A 734 (2004) 219

• Central collisions of 129Xe natSn _at_ 50AMeV
  
• and 197Au 197Au _at_ 60, 80 and 100 AMeV
• ? Comparisons to MMC-NS calculations
• (Microcanonical Multifragmentation Model
• with Non-spherical Sources)
• ? Data can be reproduced if an expanding
• prolate source aligned along the beam
• direction is assumed (flow not included
• in energy balance)

Eflow
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Excitation function of the Radial Flow

• Data for ? reactions
• No significant system-size
• dependence if expresed in
• terms of Eflow per nucleon

• Discrepancy between
• EOS and FOPI/IMF
• Importance of including
• IMFs in the extraction
• of radial flow energy
• (IMF contribution to the
• total emitted charge is
• found to be significant
• up to Ebeam 600 AMeV)

Onset of expansion at Ebeam ? 30 AMeV

• Broad systematics
• Better understanding of the origin of flow and
  disentangle ? contributions
• - Thermal pressure (dominant at low energy)
• - Influence of Coulomb repulsion
• - Compressional effects

• Need for detailed comparisons with theoretical
  models

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What is the radial flow
The existence of a collective degree of freedom
related to the presence Of a isotropic radial
velocity distribution not generated by coulomb
interaction
Its influence on I Fragment formation
Caloric Curve of fragmenting
system Dynamical properties of IMF spectra
In other words its competition with the thermal
part of the energy and Coulombian part.
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Theoretical models
Theoretical models
Dynamical Models N-body approaches CMD QMD
AMD 1-body approaches BUU, BNV, LV ,
etc. BOB Hydrodynamics Blast
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Theoretical models
Theoretical models
Statistical models Microcanonical Canonical Gra
nd-canonical Sequential evaporation EES (with
expansion and contraction) GEMINI SIMON HIPSE
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Classical Molecular Dynamics
Bonsera et.al, Campi et.al. Dorso
et.al. Interaction potentials Lennard Jones,
Illinois, QCNM Flow Intrinsic to the
development of the dynamics Results Pedagogical?
Non-equilibrium Fragments Local
Equilibrium? Challenge evolve into more
realistic/nuclear
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CMD (LJ) 1
X.Campi.et.al.
Interaction potential
Fragment definition
Given a pair of particles they belong to the Same
cluster if
This fragment definition si shown to
be Equivalent to Coniglio-Klein (Ising Model)
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CMD (LJ) 1
Asymptotic fragment kinetic energies related to
initial density Non-equilibrium effect.
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CMD (LJ) 2
CMD Dorso
A.Chernomoretz, F.gulminelli, M.ison
C.O.DorsoPRC 69 (2004),034610
Caloric curve Confined system
ECFM indicates fragments are formed Very early in
the evolution. The system Reaches local
equilibrium allowing to Define an effective
local temperature
ECRA fragments
Evolution of Fragment Mass Distributions Upon
removal Of container
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CMD (LJ) 2
What is freeze out?
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CMD (LJ) 2
Influence of flux on the CC of an Expanding system
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Quantum Molecular Dynamics
System described in terms of unsymmetrized
gaussian wave packets
Equations of motion
Interaction potential
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Quantum Molecular Dynamics
Sources of flow
At variance with CMD High transparency
At 50A MeV (XeSn) High Transparency, no signals
of equilibration, The observed apparent flosw is
not real but reflects initial fermi motions
Coulomb barrier,etc. At 200A MeV Smaller mean
free path, Small fragments show strong radial
flow due to Strong forces in the central region
of the reaction.
Phys.let. B 506 (2001) 261
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Brownian One Body model
P. Chomaz, M.Colonna, A. Guarnera, J.Randrup PRL
73(1994)3512
Allows for the analysis of fragmentation in terms
of spinodal decomposition
The starting point is the boltzmann kinetic
equation augmented to include higher order
correlations
, with
In order to accelerate the calculation process,
the following approximation Is used
, with
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Brownian One Body model

• In NPA 689(2001)940 the analysis of HIC is
  performed according to
• BNV simulation which provides initial
  configuration to be fed in BOB
• BNV calculation is stopped at maximum
  compression and BOB evolution is turned on. At 80
  fm/c the system enters the spinodal region
• At 250fm/c fragments are well separated and
  excited
• Finally fragments relax via statistical decay

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Statistical Models
Statistical models come in many
flavors Microcanonical (Randrup, Gross, Raduta,
Das Gupta, etc.) Canonical (Bondorf, Gross etc.
) Grand canonical (Randrup, etc.) In what
follows we pick (arbitrarily) one of the
realizations (WIX)
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WIX
J.Randrup Comp. Phys. Com 77(1993) 153
The explosive transformation of a given source in
assumed to happen in a Statistical
(microcanonical) manner. The density of states is
accordingly
The collective expansion is taken into account by
considering that the velocity Of the explosion
products can be decomposed in thermal
collective components vnUnVn. Vn is
characterized by a Maxwell-Boltzmann distribution
while Un is assumed homogeneous
The total kinetic energy can be separated in two
parts
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WIX
Mass dependence of the Energy spectra
Kinetic energy spectra of final Fragments as a
function of the flow energy
No flow
Flow
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Microcanonical Lattice Gas with Flow
Protons and neutrons in a lattice. Proton-neutron
bond-5.33 MeV. Coulomb is taken into account.
Configurations are sampled with MMC, the weight
given by
Configurations are accepted according to (Ray
prescription)
Momenta is assigned to particles according to
Ekin. Flow is included by adding pf(i)
cri-rcm
Finally, fragments are recognized by
MSTE prescription
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Microcanonical Lattice Gas with Flow
Lattice gas fragment mass distributions are
impervious to Flow
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Equilibrium under Flow?
F.Gulminelli P.Chomaz PRE 66 (2002) 46108
In the frame of information theory Given the
observables ?E? (average energy) and ?p(r)?
(average local radial Momentum), the probability
of a microstate n is given by
? and ?(r) are Lagrange multipliers. Imposing
?p(r)?m?r (self similar)
And the ?E? reads
There are divergences due to r2 terms
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Equilibrium under Flow?
Divergences are cured by introducing a confining
pressure which fixes the Freeze out volume
Collective motion is less effective than random
motion in producing fragmets
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Expanding Emitting Source
W.Friedman PRL60(1988)2125, PRC 42(1990) 667
In this model the dynamics is given in ?(t) -gt
A(t) and R(t) In the frame of a system with
varying ?(t) induced by emission diven by
emission rates according to Weisskopf detailed
balance

• Energies
• Collective kinetic energy of the residue
• Collective compressional energy of the residue
• Thermal excitation of the residue
• Kinetic energy of the emitted fragment
• Separation energy of the emitted fragment

Changes in the thermal energy of the
residue particle emission -gt taken at constant
density density variation -gt isotropic expansion
Changes in density driven by thermal pressure and
collecitve compressional energy
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91Zr at Tmax15,20,25 MeV T falls exponentially
until 5 MeV
At 5MeV the mass of the instantaneous Residue
declines sharply
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Conclusions and outlook
The presence of radial flow is well established
both Experimentally And Theoretically The
dynamical origin of Radial flow is not on firm
basis, competition Between compression and
thermal effects. Dynamical models should be
improved to fully understand the
mechanism Through which initial collective motion
(colliding nuclei) is transformed into random
thermal motion and back into collective (at
least partially in The from of radial
motion) When are fragments formed? Early
fragment formation, or Freeze out Formation, or
spinodal decomposition? Further exploration on
the effect of flow on CC
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Thanks to X. Campi V. Viola F. Gulminelli M.
Bruno J. Randrup R. De Souza M. Rivet V.
Kamaukhov D. Lacroix
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SLAFNAP6
Iguazú, Argentina. October 3 to 7, 2005
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NUCLEAR STRUCTURE Nuclear Structure
Experiments and Models Radioactive Beams
Applications to Lepto-Nuclear- and
Astroparticle-Physics Superheavy Systems New
Facilities NUCLEAR REACTIONS Near-Barrier
Phenomena Radioactive Beams Weakly Bound
Systems Nuclear Astrophysics New Facilities
NUCLEAR PHYSICS APPLICATIONS Medicine and
Biology Environmental Science Materials Science
Energy Production Art and Archeology
SUBNUCLEAR PHYSICS Exotic Hadrons
Quark-Gluon Plasma Aspects of Non-Perturbative
QCD NUCLEAR THERMODYNAMICS AND DYNAMICS
Nuclear Fragmentation Phase Transformations in
Nuclear Systems Isospin Dynamics