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Constraining the EoS and Symmetry Energy from HI collisions

Constraining the EoS and Symmetry Energy from HI collisions. Statement of the problem Demonstration: symmetric matter EOS Laboratory constraints on the symmetry energy from nuclear collisions Summary and outlook .

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Constraining the EoS and Symmetry Energy from HI collisions

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  1. Constraining the EoS and Symmetry Energy from HI collisions • Statement of the problem • Demonstration: symmetric matter EOS • Laboratory constraints on the symmetry energy from nuclear collisions • Summary and outlook William Lynch, Yingxun Zhang, Dan Coupland, Pawel Danielewicz, Micheal Famiano, Zhuxia Li, Betty Tsang

  2. EOS: symmetric matter and neutron matter Brown, Phys. Rev. Lett. 85, 5296 (2001) E/A (,) = E/A (,0) + d2S() d = (n- p)/ (n+ p) = (N-Z)/A Neutron matter EOS • The density dependence of symmetry energy is largely unconstrained. • What is “stiff” or “soft” is density dependent

  3. The curvature Knm of the EOS about 0 can be probed by collective monopole vibrations, i.e. Giant Monopole Resonance. • To probe the EoS at 30, you need to compress matter to 30. Need for probes sensitive to higher densities(Why the monopole is not sufficient and Knm is somewhat irrelevant.) • If the EoS is expanded in a Taylor series about 0, the incompressibility, Knm provides the term proportional to (-0)2. Higher order terms influence the EoS at sub-saturation and supra-saturation densities. • The solid black, dashed brown and dashed blue EoS’s all have Knm=300 MeV.

  4. Constraining the EOS at high densities by nuclear collisions Au+Au collisions E/A = 1 GeV) • Two observable consequences of the high pressures that are formed: • Nucleons deflected sideways in the reaction plane. • Nucleons are “squeezed out” above and below the reaction plane. . pressure contours density contours

  5. Constraints from collective flow on EOS at >20. E/A (, ) = E/A (,0) + 2S()  = (n- p)/ (n+ p) = (N-Z)/A1 • The symmetry energy dominates the uncertainty in the n-matter EOS. • Both laboratory and astronomical constraints on the density dependence of the symmetry energy at supra-saturation density are urgently needed. Danielewicz et al., Science 298,1592 (2002). Danielewicz et al., Science 298,1592 (2002). • Note: analysis required additional constraints on m* and NN. • Flow confirms the softening of the EOS at high density. • Constraints from kaon production are consistent with the flow constraints and bridge gap to GMR constraints.

  6. Probes of the symmetry energy E/A(,) = E/A(,0) + d2S() ; d = (n- p)/ (n+ p) = (N-Z)/A • To maximize sensitivity, reduce systematic errors: • Vary isospin of detected particle • Vary isospin asymmetry =(N-Z)/A of reaction. • Low densities (<0): • Neutron/proton spectra and flows • Isospin diffusion • High densities (20) : • Neutron/proton spectra and flows • + vs. - production <0 <0 symmetry energy

  7. Why choose to measure IsospinDiffusion, n/p flows and pion production? • Supra-saturation and sub-saturation densities are only achieved momentarily • Theoretical description must follow the reaction dynamics self-consistently from contact to detection. • Theoretical tool: transport theory: • The most accurately predicted observables are those that can be calculated from i.e. flows and other average properties of the events that are not sensitive to fluctuations. • Isospin diffusion and n/p ratios: • Depends on quantities that can be more accurately calculated in BUU or QMD transport theory. • May be less sensitive to uncertainties in (1) the production mechanism for complex fragments and (2) secondary decay.

  8. soft symmetry energy Bao-An Li et al., PRL 78, 1644 (1997). stiff symmetry energy Measurement of n/p spectral ratios: At E/A = 50 MeV, it probes the pressure due to asymmetry term at 0. • Expulsion of neutrons from bound neutron-rich system by symmetry energy. At E/A=50 MeV, 0 is the relevant domain. • Has been probed by direct measurements of n vs. proton emission rates in central Sn+Sn collisions. • Double ratio removes the sensitivity to neutron efficiency and energy calibration.

  9. Isospindiffusion in peripheral collisions, also probes symmetry energy at <0. { • Collide projectiles and targets of differing isospin asymmetry • Probe the asymmetry =(N-Z)/(N+Z) of the projectile spectator during the collision. • The use of the isospin transport ratio Ri() isolates the diffusion effects: • Useful limits for Ri for 124Sn+112Sn collisions: • Ri =±1: no diffusion • Ri0: Isospin equilibrium mixed 124Sn+112Sn n-rich 124Sn+124Sn p-rich 112Sn+112Sn Systems measure asymmetry after collision Example: proton-rich target P  N neutron-rich projectile

  10. What influences isospin diffusion? • Isospin diffusion equation: • Naive expectations: • D increases with S() • D decreases with np • We tested this by performing extensive BUU and QMD calculations with S() for the form: • S()= 12.5·(ρ/ρ0)2/3 + Sint·(ρ/ρ0) γi • Results: • Diffusion sensitive to S(0.4ρ0) • Diffusion increases with Sint and decreases with i • Diffusion increases with np • Diffusion decreases when mean fields are momentum dependent and neck fragments emerge. • Diffusion decreases with cluster production.

  11. Sensitivity to symmetry energy Stronger density dependence • The asymmetry of the spectators can change due to diffusion, but it also can changed due to pre-equilibrium emission. • The use of the isospin transport ratio Ri() isolates the diffusion effects: Weaker density dependence Tsang et al., PRL92, 062701 (2004) Lijun Shi, thesis

  12. The main effect of changing the asymmetry of the projectile spectator remnant is to shift the isotopic distributions of the products of its decay This can be described by the isoscaling parameters  and : no diffusion Probing the asymmetry of the Spectators Liu et al.PRC 76, 034603 (2007). Tsang et. al.,PRL 92, 062701 (2004)

  13. In statistical theory, certain observables depend linearly on : Calculations confirm this Experiments confirm this Consider the ratio Ri(X), where X = , X7 or some other observable: If X depends linearly on 2: Then by direct substitution: Determining Ri()

  14. The main effect of changing the asymmetry of the projectile spectator remnant is to shift the isotopic distributions of the products of its decay This can be described by the isoscaling parameters  and : 1.0 0.33 Ri() -0.33 -1.0 Probing the asymmetry of the Spectators Liu et al.PRC 76, 034603 (2007). Tsang et. al.,PRL 92, 062701 (2004)

  15. Quantitative values • Reactions: • 124Sn+112Sn: diffusion • 124Sn+124Sn: neutron-rich limit • 112Sn+112Sn: proton-rich limit • Exchanging the target and projectile allowed the full rapidity dependence to be measured. • Gates were set on the values for Ri() near beam rapidity. • Ri()  0.470.05 for 124Sn+112Sn • Ri()  -0.44 0.05 for 112Sn+124Sn • Obtained similar values for Ri(ln(Y(7Li)/ Y(7Be)) • Allows exploration of dependence on rapidity Liu et al., (2006) Liu et al.PRC 76, 034603 (2007).  v/vbeam

  16. Comparison to QMD calculations • IQMD calculations were performed for i=0.35-2.0, Sint=17.6 MeV. • Momentum dependent mean fields with mn*/mn =mp*/mp =0.7 were used. Symmetry energies: S() 12.3·(ρ/ρ0)2/3 + 17.6·(ρ/ρ0) γi • Experiment samples a range of impact parameters • b5.8-7.2 fm. • larger b, smaller i • smaller b, larger i mirror nuclei

  17. GDR: Trippa, PRC77, 061304 Danielewicz, Lee, NPA 818, 36 (2009) Bao-An Li et al., Phys. Rep. 464, 113 (2008). PDR: A. Klimkiewicz, PRC 76, 051603 (2007). Diffusion is sensitive to S(0.4), which corresponds to a contour in the (S0, L) plane. Tsang et al., PRL 102, 122701 (2009). ImQMD fits for S0=30.1 MeV fits to IAS masses ImQMD CONSTRAINTS fits to ImQMD fits for variable S0 Expansion around r0: • Symmetry slope L & curvature Ksym • Symmetry pressure Psym

  18. Why probe higher densities?Example: EoS neutron star radius • The neutron star radius is not strongly correlated with the symmetry pressure at saturation density. • This portends difficulties in uniquely constraining neutron star radii for constraints at subsaturation density. L • The correlation between the pressure at twice saturation density and the neutron star radius is much stronger. • additional measurements at supra-saturation density will lead to stronger constraints. • Would be advisable to have multiple probes that can sample different densities

  19. Larger values for n/  p at high density for the soft asymmetry term (x=0) causes stronger emission of negative pions for the soft asymmetry term (x=0) than for the stiff one (x=-1). - /+ means Y(-)/Y(+) In delta resonance model, Y(-)/Y(+)(n,/p)2 In equilibrium, (+)-(-)=2( p-n) The density dependence of the asymmetry term changes ratio by about 10% for neutron rich system. High density probe: pion production Li et al., arXiv:nucl-th/0312026 (2003). soft soft stiff stiff t (fm/c) • This can be explored with stable or rare isotope beams at the MSU/FRIB and RIKEN/RIBF. • Sensitivity to S() occurs primarily near threshold in A+A

  20. Au+Au Preliminary results puzzling Riken Future determination of the EoS of neutron-rich matter ? FRIB S() MeV GSI MSU Isospin diffusion, n-p flow Xiao, et al., arXiv:0808.0186 (2008) Reisdorf, et al., NPA 781 (2007) 459. Pion production

  21. Double ratio involves comparison between neutron rich 132Sn+124Sn and neutron deficient 112Sn+112Sn reactions. Double ratio maximizes sensitivity to asymmetry term. Largely removes sensitivity to difference between - and +acceptances. Double ratio: pion production Yong et al., Phys. Rev. C 73, 034603 (2006) soft stiff

  22. Summary and Outlook • Heavy ion collisions provide unique possibilities to probe the EOS of dense asymmetric matter. • A number of promising observables to probe the density dependence of the symmetry energy in HI collisions have been identified. • Isospin diffusion, isotope ratios, and n/p spectral ratios provide some constraints at 0, . • + vs. - production, neutron/proton spectra and flows may provide constraints at 20 and above. • The availability of fast stable and rare isotope beams at a variety of energies will allow constraints on the symmetry energy at a range of densities. • Experimental programs are being developed to do such measurements at MSU/FRIB, RIKEN/RIBF and GSI/FAIR

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