Transverse and elliptical flow in asymmetric systems

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Betty Tsang
The National Superconducting Cyclotron
Laboratory _at_Michigan State University
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Transverse and elliptical flow constraints the
EoS of symmetric nuclear matter.
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Relevance to dilute and dense n-rich objects
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Multifragmentation Scenario --consistent with
mixed phase
Time Dependence --Initial compression and energy
deposition -- Expansion -- Cooling -- Fragments
form (freeze-out) -- Fragments decouple
Different Approaches Dynamical (AMD,BNV) Rate
equations (EES) Equilibrium at freeze-out
density (BUU-SMM)
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Isospin mixing
P
T
P
T
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Varying isospin degree of freedom
Gain 24 ns
112Sn112Sn
124Sn124Sn
PRL, 85, 716 (2000)
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Measured Isotopic yields
Shapes are similarMore n-rich isotopes from more
n-rich systemIs Sequential decay effect isospin
independent?Isotopic effects are small how to
quantify them?
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Isoscaling from Relative Isotope Ratios
R21Y2/ Y1
Factorization of yields into p n
densities Cancellation of effects from sequential
feedings Robust observables to study isospin
effects
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Compact representation of isoscaling
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Isoscaling observed in many reactions
PRL, 86, 5023 (2001)
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R21?exp(-?SnN- ?SpZ)/T
R21?exp((-?Sn ?fn)N(-?Sp ?fp ??)Z)/T
R21?exp(-??nN- ??pZ)/T
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Origin of isoscaling

• Isoscaling disappears when the symmetry energy is
  set to zero

• Provides an observable to study symmetry energy

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Role of density dependent asymmetry term-Where
do the fragments originate?-
asy-stiff (F1)
asy-soft (F3)
more symmetric dense region
neutron-rich dense region
more symmetric emitted particles
neutron-rich emitted particles

• Various models predict different dependence on
  density dependence of asymmetry term.
• Equilibrium models fragments originate in
  interior.
• EES model fragments emitted from surface.

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Expanding Emitting Source model W. Friedman
PRC42, 667 (1990)
Thermal instability at low density.
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Density dependence of asymmetry energy
Strong influence of symmetry term on fragment
isotopic ratios
?0.36 ? ?2/3 Consistent with many body
calculations with nn interactions
S(?)23.4(?/?o)?
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Symmetry Terms
Affect neutron star radii, moments of inertia,
central densities.
E(?, ?) E(?, 0)Esym(?) ?2
K(F1) 61 MeV K(F3) -69 MeV
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Sensitivity to the isospin terms in the EOS
F1 agrees with data better
PRC, C64, 051901R (2001).
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Isospin diffusion
P
T
P
T
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Iso-scaling in projectile fragmentation

• Fixed Projectile
• no diffusion a0
• aY(112124)/Y(112112)0.157
• aY(124124)/Y(124112)0.126
• Fixed Target
• aY(124124)/Y(112124)0.401
• aY(124112)/Y(112112)0.448
• a is target dependent
• Isospin diffusion between target and projectile

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Experimental Determination of Isospin diffusion
a? 4Csym(Z2/A2)2-(Z1/A1)2/T -- statistical
models 112112 124124 no isospin gradient, no
diffusion 124112 n-diffusion from proj. to
targ. 112124 n-diffusion from targ. to
proj. a3 (Zb/Ab)2-(Z3/A3)2/ (Za/Aa)2-(Zb/Ab)2
a4 (Z4/A4)2-(Zb/Ab)2/ (Za/Aa)2-(Zb/Ab)2 Exp
erimental results ? 3 nucleons exchange between
112 and 124 (equilibrium6 nucleons)
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Comparison with model (BUU)
a3 (Zb/Ab)2-(Za/Aa)2/ (Z3/A3)2-(Za/Aa)2 a4
(Zb/Ab)2-(Za/Aa)2/ (Zb/Ab)2-(Z4/A4)2
Diffusion determined from 2 symmetric systems
and 1 mixed system
BUU parameters determined from transverse and
elliptical flow data.
E(?, ?) E(?, 0)Esym(?) ?2
Initial results show sensitivity to isospin part
of the EOS Further work is needed
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Summary

• Density dependence of symmetry energy can be
  examined experimentally.
• Existence of isoscaling relations

• Conclusions from multi fragmentation work are
  model dependent
• SMM favors ?2 dependence of S(?).
• EES favors ?2/3 dependence of S(?).
• Isospin Diffusion from projectile fragmentation
  data test the transport model parameters