Transcript Transverse and elliptical flow in asymmetric systems

B  aV A  a S A
2/3
2
Z ( Z  1)
(
A

2
Z
)
   aC
 a sym
1/ 3
A
A
Proton Number Z
asym=30-42 MeV for infinite NM
( A  2Z )
(a sym A  a sym A )
2
A
V
Neutron Number N
S
2
2/3
Inclusion of surface
terms in symmetry
Can we determine the density dependence of the
symmetry energy?
 E(, )  E(, 0)Ssym() 2
 Isospin asymmetry:   (n p)/ (n p)
Isospin Mixing and Diffusion in
Heavy Ion Collisions
Betty Tsang
Dresden, 8/2003
The National Superconducting
Cyclotron Laboratory
@Michigan State University
What is known about the EOS of symmetric matter
Danielewicz, Lacey, Lynch (2002)
• Prospects are good
for improving
constraints further.
• Relevant for
supernovae - what
about neutron stars?
E(, )  E(, 0)Ssym() 2
The density dependence
of asymmetry term is
largely unconstrained.
Measured Isotopic yields
Isoscaling from Relative Isotope Ratios
R21=Y2/ Y1
e
N n / T  Z p / T
( )
N ^
^
 ( ) 
n
Z
p
Factorization of yields
into p & n densities
Cancellation of effects
from sequential feedings
Robust observables to
study isospin effects
Origin of isoscaling`
R21(N,Z)=Y2 (N,Z)/ Y1 (N,Z)
N n  Z p
e
N ^ Z
^
 ( n ) ( p )
Isoscaling disappears
when the symmetry
energy is set to zero
Provides an
observable to study
symmetry energy
B  aV A  a S A
2/3
2
Z ( Z  1)
(
A

2
Z
)
   aC
 a sym
1/ 3
A
A
A. Ono et al. (2003)
Isoscaling in
Antisymmetrized
Molecular Dynamical
model
Symmetry energy from AMD
a(Gogny)>a(Gogny-AS)
Csym(Gogny)> Csym(Gogny-AS)
Multifragmentation occurs at low density
Density dependence of asymmetry energy
Strong
influence of
symmetry term
on isoscaling
a=0.36  =2/3
S()=23.4(/o)
Results are model dependent
Consistent with
many body
calculations
with nn
interactions
Sensitivity to
the isospin
terms in the
EOS
P
T
BUU
F1,F3
N/Z
SMM
Y(N,Z)
R21(N,Z)
Freeze-out
source
Data
~2
~0.5
Asy-stiff
term
agrees
with
data
better
PRC, C64, 051901R (2001).
New observable: isospin diffusion in peripheral collisions
symmetric system: no diffusion
projectile
target
asymmetric systems
• Vary isospin driving
forces by changing the
isospin of projectile and
target.
• Examine asymmetry by
measuring the scaling
parameter for projectile
decay.
strong diffusion
weak diffusion
proton rich
system
neutron rich
system
Isoscaling of mixed systems
Experimental results
Y(N,Z) / Y112+112(N,Z)=[C·exp(aN + bZ)]
3 nucleons
exchange
between 112
and 124
(equilibrium=6
nucleons)
Experimental results
Y(N,Z) / Y112+112(N,Z)=[C·exp(aN + bZ)]
3 nucleons
exchange
between 112
and 124
(equilibrium=6
nucleons)
The neck is consistent
with complete mixing.
Isospin flow from nrich projectile (target)
to n-deficient target
(projectile) – dynamical
flow
Isospin flow is affected
by the symmetry terms
of the EoS – studied
with BUU model
Isospin Diffusion from BUU
Isospin Transport Ratio
2 x  x124124  x112112
Ri 
x124124  x112112
Rami et al., PRL, 84, 1120 (2000)
x=experimental or theoretical isospin
observable
x=x124+124  Ri = 1.
x=x112+112  Ri = -1.
Experimental: isoscaling fitting
parameter a; Y21 exp(aN+bZ)
Theoretical :   ( N  Z ) /( N  Z )
BUU predictions
E(, )  E(, 0)Ssym() 2
Ssym()  () 
BUU predictions
E(, )  E(, 0)Ssym() 2
Ssym()  () 
Experimental
results are in
better
agreement with
predictions
using hard
symmetry
terms
Summary
 Challenge: Can we constrain the density
dependence of symmetry term?
 Density dependence of symmetry energy can be
examined experimentally with heavy ion
collisions.  Existence of isoscaling relations
 Isospin fractionation: Conclusions from multi
fragmentation work are model dependent;
sensitivity to S().
 Isospin diffusion from projectile fragmentation
data provides another promising observable to
study the symmetry energy with Ri
Acknowledgements
Bill Friedman
P. Danielew icz , C.K. Gelbke, T.X. Liu, X.D. Liu, W .G. Ly nch,
L.J. Shi, R. Shomin, M.B. Tsang, W .P. Tan, M.J. Van
Goet hem, G. Verde, A. W agner, H.F. Xi, H.S. Xu, Akira O no,
Bao-An Li, B. Dav in, Y. Larochelle, R.T. de Souz a, R.J.
Charity, L.G. Sobotka, S.R. Souz a, R. Donangelo