neutron number n proton number z a sym =30-42 mev for infinite nm inclusion of surface terms in...
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Neutron Number N
Pro
ton
Nu
mb
er Z 3/2AaAaB SV 3/1
)1(
A
ZZaC
A
ZAasym
2)2(
asym=30-42 MeV for infinite NM
Inclusion of surface terms in symmetry
2
23/2 )2()(
A
ZAAaAa SV
symsym
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The National Superconducting Cyclotron Laboratory
@Michigan State University
Isospin Mixing and Diffusion inHeavy Ion Collisions
Betty TsangDresden, 8/2003
Ssym(
Isospin asymmetrynpnp
Can we determine the density dependence of the symmetry energy?
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• Prospects are good for improving constraints further.
• Relevant for supernovae - what about neutron stars?
What is known about the EOS of symmetric matterDanielewicz, Lacey, Lynch (2002)
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The density dependence of asymmetry term is largely unconstrained.
Ssym(
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Measured Isotopic yields
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Isoscaling from Relative Isotope Ratios
Factorization of yields into p & n densities
Cancellation of effects from sequential feedings
Robust observables to study isospin effects
R21=Y2/ Y1
TZTN pne // Zp
Nn ^ ^
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Origin of isoscaling`
Isoscaling disappears when the symmetry energy is set to zero
Provides an observable to study symmetry energy
3/2AaAaB SV 3/1
)1(
A
ZZaC
A
ZAasym
2)2(
R21(N,Z)=Y2 (N,Z)/ Y1 (N,Z)
pn ZNe Zp
Nn ^ ^
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Isoscaling in Antisymmetrized
Molecular Dynamical model
A. Ono et al. (2003)
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Symmetry energy from AMD
(Gogny)>(Gogny-AS)Csym(Gogny)> Csym(Gogny-AS)
Multifragmentation occurs at low density
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EES_fragment
Density dependence of asymmetry energy
S()=23.4(/o)
Results are model dependent
Strong influence
of symmetry term on
isoscaling
=0.36 =2/3
Consistent with many body calculations
with nn interactions
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Sensitivity to the isospin terms in the EOS
Data
Y(N,Z)R21(N,Z)
SMMBUUF1,F3 N/ZP
T Freeze-out source
Asy-stiff term agrees with data better
PRC, C64, 051901R (2001).
~2 ~0.5
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New observable: isospin diffusion in peripheral collisions
• Vary isospin driving forces by changing the isospin of projectile and target.
• Examine asymmetry by measuring the scaling parameter for projectile decay.
ta rg e t
p ro je c tile
symmetric system: no diffusion
weak diffusionstrong diffusion
neutron richsystem
proton richsystem
asymmetric systems
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Isoscaling of mixed systems
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Experimental results
3 nucleons exchange between 112 and 124
(equilibrium=6 nucleons)
Y(N,Z) / Y112+112(N,Z)=[C·exp(N + Z)]
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Experimental results
3 nucleons exchange between 112 and 124
(equilibrium=6 nucleons)
Y(N,Z) / Y112+112(N,Z)=[C·exp(N + Z)]
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The neck is consistent with complete mixing.
Isospin flow from n-rich projectile (target) to n-deficient target (projectile) – dynamical flow
Isospin flow is affected by the symmetry terms of the EoS – studied with BUU model
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Isospin Diffusion from BUU
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Isospin Transport Ratio
112112124124
1121121241242
xx
xxxRi
x=experimental or theoretical isospin observablex=x124+124 Ri = 1.x=x112+112 Ri = -1.
Experimental: isoscaling fitting parameter ; Y21 exp(N+Z)Theoretical : )/()( ZNZN
Rami et al., PRL, 84, 1120 (2000)
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BUU predictions Ssym(
Ssym((
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BUU predictions
Experimental results are in better agreement with predictions using hard symmetry terms
Ssym(
Ssym((
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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
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Acknowledgements
P. Danielewicz, C.K. Gelbke, T.X. Liu, X.D. Liu, W.G. Lynch,
L.J. Shi, R. Shomin, M.B. Tsang, W.P. Tan, M.J. Van
Goethem, G. Verde, A. Wagner, H.F. Xi, H.S. Xu, Akira Ono,
Bao-An Li, B. Davin, Y. Larochelle, R.T. de Souza, R.J.
Charity, L.G. Sobotka, S.R. Souza, R. Donangelo
Bill Friedman