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The National Superconducting Cyclotron Laboratory @ Michigan State University

Exploring the symmetry energy. in nuclear equation of state. with heavy ions. Betty Tsang. The National Superconducting Cyclotron Laboratory @ Michigan State University. The density dependence of asymmetry term is largely unconstrained.

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The National Superconducting Cyclotron Laboratory @ Michigan State University

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  1. Exploring the symmetry energy in nuclear equation of state with heavy ions Betty Tsang The National Superconducting Cyclotron Laboratory @Michigan State University

  2. The density dependence of asymmetry term is largely unconstrained. Transverse and elliptical flow constraints the EoS of symmetric nuclear matter.

  3. Nuclei+e- Stability of Neutron Star and its structure Nuclei+dripped n +e- Sizes of nuclei with n-halo and n-skin EOS ? ? exotics 10 km o 5o 0 Relevance to dilute and dense n-rich objects

  4. P T 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)

  5. P T Isospin mixing P T P T

  6. Enrichment of n in the gas D b r µ e p Depletion of p in the gas Varying isospin degree of freedom Gain 24 n’s 112Sn+112Sn 124Sn+124Sn PRL, 85, 716 (2000)

  7. 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?

  8. Isoscaling from Relative Isotope Ratios R21=Y2/ Y1 Factorization of yields into p & n densities Cancellation of effects from sequential feedings Robust observables to study isospin effects

  9. Compact representation of isoscaling

  10. Y2/ Y1 Isoscaling observed in many reactions PRL, 86, 5023 (2001)

  11. P T Q Value, Sep. E ECoulEsym b Separation Energy ECoulEsym Chemical Potentials ECoul Esympn R21exp[(-Sn·N- Sp·Z)/T] R21exp[((-Sn+ fn*)·N+(-Sp +fp*+ )·Z)/T] R21exp[(-n·N- p·Z)/T]

  12. Origin of isoscaling • Isoscaling disappears when the symmetry energy is set to zero • Provides an observable to study symmetry energy

  13. Various models predict different dependence on density dependence of asymmetry term. Equilibrium models: fragments originate in interior. EES model: fragments emitted from surface. SMM EES Role of density dependent asymmetry term-Where do the fragments originate?- asy-stiff (F1) asy-soft (F3) neutron-rich dense region more symmetric dense region more symmetric emitted particles neutron-rich emitted particles

  14. n, lcp evap. 11 MeV fragments 13 MeV multifragmentation 14 MeV 15 MeV vaporization Expanding Emitting Source model W. Friedman PRC42, 667 (1990) Thermal instability at low density.

  15. EES_fragment 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)

  16. Mass Radii Symmetry Terms • Affect neutron star radii, moments of inertia, central densities. E(, ) = E(, 0)+Esym() 2 K(F1) = +61 MeV K(F3) = -69 MeV

  17. BUU SMM Y(N,Z) R21(N,Z) P N/Z F1,F3 T Freeze-out source Data Sensitivity to the isospin terms in the EOS F1 agrees with data better PRC,C64, 051901R (2001).

  18. Isospin diffusion P T P T

  19. Iso-scaling in projectile fragmentation • Fixed Projectile: no diffusion: a=0 a=Y(112+124)/Y(112+112)=0.157 a=Y(124+124)/Y(124+112)=0.126 • Fixed Target: a=Y(124+124)/Y(112+124)=0.401 a=Y(124+112)/Y(112+112)=0.448 a istarget dependent Isospin diffusion between target and projectile

  20. Experimental Determination of Isospin diffusion a 4Csym[(Z2/A2)2-(Z1/A1)2]/T -- statistical models 112+112;124+124no isospin gradient, no diffusion 124+112 n-diffusion from proj. to targ. 112+124 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] Experimental results 3 nucleons exchange between 112 and 124 (equilibrium=6 nucleons)

  21. 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

  22. 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

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