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The National Superconducting Cyclotron Laboratory Michigan State University

Constraints on the Density dependence of Symmetry Energy in Heavy Ion Reactions. 5th ANL/MSU/JINA/INT FRIB Workshop on Bulk Nuclear Properties Nov 19-22, 2008 MSU. S( r). The National Superconducting Cyclotron Laboratory Michigan State University. Betty Tsang.

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The National Superconducting Cyclotron Laboratory Michigan State University

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  1. Constraints on the Density dependence of Symmetry Energy in Heavy Ion Reactions 5th ANL/MSU/JINA/INT FRIB Workshop onBulk Nuclear Properties Nov 19-22, 2008 MSU S(r) The National Superconducting Cyclotron Laboratory Michigan State University Betty Tsang

  2. Extracting Density dependence of Symmetry Energy in Heavy Ion Reactions F1 Outline: What does HIC have to offer? What are the pitfalls (in theory)? What constraints do we have now? (Are the constraints believable or reliable?) What research directions are we going towards FRIB? F3

  3. Extracting Density dependence of Symmetry Energy in Heavy Ion Reactions F1 F3 Micha Kilburn HIC provides a range of density determined from incident energy and impact parameter

  4. E/A=1600 MeV 200 MeV 50 MeV Pions, n, p fragments Bulk nuclear matter properties from Heavy Ion Central Collisions Highest density reached by central collisions depends on incident beam energy. Types of particles formed depend on emission times and density.

  5. Danielewicz, Lacey, Lynch, Science 298,1592 (2002) pressure contours • Experiment: measure collective flow (emission patterns) of particles emitted in Au+Au collisions from (E/A~1-8 GeV). • Transport model (BUU) relates the measurements to pressure and density. density contours

  6. Danielewicz, Lacey, Lynch, Science 298,1592 (2002) Pressure (MeV/fm3) Equation of State of Nuclear Matter E/A(,) = E/A(,0) + d2S() ; d = (n- p)/ (n+ p) = (N-Z)/A

  7. ?? Danielewicz, Lacey, Lynch, Science 298,1592 (2002) Pressure (MeV/fm3) Equation of State of Nuclear Matter E/A(,) = E/A(,0) + d2S() ; d = (n- p)/ (n+ p) = (N-Z)/A • Newer calculation and experiment are consistent with the constraints. • Transport model includes constraints in momentum dependence of the mean field and NN cross-sections

  8. Proton Number Z Crab Pulsar Neutron Number N Hubble ST Experimental Techniques to probe the symmetry energy with heavy ion collisions at E/A<100 MeV Isospin degree of freedom • Vary the N/Z compositions of projectile and targets 124Sn+124Sn, 124Sn+112Sn, 112Sn+124Sn, 112Sn+112Sn • Measure N/Z compositions of emitted particles • n & p • isotopes • p+ & p- at higher incident energy

  9. Heavy Ion collision: 124Sn+124Sn, E/A=50 MeV b=0 fm multifragmentation gi=2.0 gi=0.5 subnormal density b=7 fm gi Esym=12.7(r/ro)2/3+19(r/ro) Neck fragments Around incident energy: E/A<100 MeV: Reaction mechanism depends on impact parameters n & p are emitted throughout Charged fragments (Z=3-20) are formed at subnormal density

  10. Classes of models used to interpret experimental results Symmetry energy included in the nuclear EOS for infinite nuclear matter at various density from the beginning of collision. Symmetry energy included in the form of fragment masses – finite nuclei & valid for ro only. EOS extrapolated using statistical model is questionable. • I. Transport models: • Describe dynamical evolution of the collision process • Self consistent mean field • n-n collisions, • Pauli exclusion • Uncertainties • Semi-classical • Approximations needed to make computation feasible. • II. Statistical models: • Describe longer time scale decays from single source. • nuclear mass, • level densities, • decay rates • Uncertainties • Source parameters: Ao, Zo, Eo, Vo, J • Information obtained is for finite nuclei, not for infinite nuclear matter Theory must predict how reaction evolves from initial contact to final observables

  11. Experimental Observable : Isospin Diffusion --Isospin Transport Ratio 124 Isospin diffusion occurs only in asymmetric systems A+B 112 No isospin diffusion between symmetric systems 124 112 Ri = -1 124 112 Ri = 1 Non-isospin diffusion effects same for A in A+B & A+A ;same for B in B+A & B+B Rami et al., PRL, 84, 1120 (2000) Non-isospin transport effects are “cancelled”?? xAB, yABexperimental or theoretical observable forAB yAB= a xAB+b Ri(xAB )= Ri(yAB )

  12. Probe the symmetry energy at subsaturation densities in peripheral collisions, e.g. 124Sn + 112Sn Isospin “diffuse” through low-density neck region Projectile 124Sn Target 112Sn stiff • Symmetry energy drives system towards equilibrium. • stiff EOS  small diffusion; |Ri|>>0 • soft EOS  fast equilibrium; Ri0 soft Experimental Observable : Isospin Diffusion x(calc)=d

  13. gi pBUU: S=12.7(r/ro)2/3+ 12.5(r/ro) gi~2 0.69g1.05 stiffness stiffness g IBUU04 : S~31.6(r/ro) Constraints from Isospin Diffusion Dataof calculation! M.B. Tsang et. al., PRL 92, 062701 (2004) L.W. Chen, … B.A. Li, PRL 94, 032701 (2005) Observable in HIC is sensitive to r dependence of S and should provide constraints to symmetry energy

  14. F2 F1 stiff F3 soft gi S=12.7(r/ro)2/3+17.6(r/ro) ImQMD F1=2u2/(1+u) F2=u F3=u Y(n)/Y(p) u = • n and p potentials have opposite sign. • n & p energy spectra depend on the symmetry energy  softer density dependence emits more neutrons. Experimental Observables: n/p yield ratios =0.3 Uasy (MeV) • More n’s are emitted from the n-rich system and softer iso-EOS.

  15. minimize systematic errors Double Ratio Data : Famiano et al. PRL 97 (2006) 052701 n/p Double Ratios (central collisions) 124Sn+124Sn;Y(n)/Y(p) 112Sn+112Sn;Y(n)/Y(p) Will repeat experiment for better accuracy

  16. minimize systematic errors Double Ratio Double Ratio Center of mass Energy n/p Double Ratios (central collisions) 124Sn+124Sn;Y(n)/Y(p) 112Sn+112Sn;Y(n)/Y(p) • Effect is much larger than IBUU04 predictions  inconsistent with conclusions from isospin diffusion data. Famiano et al. RPL 97 (2006) 052701

  17. Nuclear Collisions simulations with Transport Models – Nuclear EOS included from beginning of collisions BUU models: Semiclassical solution of one-body distribution function. Pros Derivable, approximations better understood. Cons Mean field no fluctuations BUU does not predict cluster formation QMD: Molecular dynamics with Pauli blocking. Pros Predicts cluster production Cons Cluster properties (masses, level densities) approximate Need sequential decay codes to de-excite the hot fragments Code used: ImQMD At high incident energies, cluster production is weak  the two models yield the same results. Clusters are important in low energy collisions.

  18. Cluster effects are important for low energy nucleons but cannot explain the large discrepancy between data and IBUU04 calculations Cluster effects Zhang et al. PLB 664 (2008)145

  19. Analysis of n/p ratios with ImQMD model Esym=12.5(r/ro)2/3+ 17.6(r/ro) gi 0.4gi 1.05 Data need better measurements but the trends and magnitudes still give meaningful 2 analysis at 2 level

  20. b~5.8 – 7.2 fm Impact parameter is not well determined in the experiment gi S=12.5(r/ro)2/3+ 17.6(r/ro) Analysis of isospin diffusion data with ImQMD model x(data)=a x(QMD)=d Equilibrium Ri=0 No diffusion Ri=1; Ri=-1 0.4gi 1

  21. b~5.8 – 7.2 fm New analysis on rapidity dependence of isospin diffusion ratios – not possible with BUU type of simulations due to lack of fragments. gi S=12.5(r/ro)2/3+ 17.6(r/ro) Analysis of rapidity dependence of Ri with ImQMD model x(data) =f(7Li/7Be) x(QMD)=d Equilibrium Ri=0 No diffusion Ri=1; Ri=-1 0.4gi 1

  22. 0.45gi 0.95 0.4gi 1.05 0.4gi 1 Consistent constraints from the 2analysis of three observables S=12.5(r/ro)2/3+ 17.6(r/ro) 0.4gi 1 g IBUU04 : S~31.6(r/ro) 0.69g1.05 approximation For the first time, we have a transport model that describes np ratios and two isospin diffusion measurements gi How to connect different representations of the symmetry energy

  23. gi g S=12.5(r/ro)2/3+ 17.6(r/ro) S~31.6(r/ro) 0.69g1.05 IBUU04 0.4gi 1 ImQMD IBUU04 IQMD • Expansion around r0: • slope L & curvature Ksym LSymmetry pressure Psym

  24. gi g S=12.5(r/ro)2/3+ 17.6(r/ro) S~31.6(r/ro) 0.69g1.05 IBUU04 0.4gi 1 ImQMD IBUU04 IQMD dRnp=0.04 fm

  25. gi S=12.5(r/ro)2/3+ Cs,p(r/ro) ImQMD Vary Cs,p and i 2s2 analysis No constraints on So

  26. gi Esym=12.5(r/ro)2/3+ Cs,p(r/ro) Constraints from masses and Pygmy Dipole Resonances

  27. gi Esym=12.5(r/ro)2/3+ Cs,p(r/ro) Constraints from masses and Pygmy Dipole Resonances

  28. gi Esym=12.5(r/ro)2/3+ Cs,p(r/ro) Current constraints on symmetry energy from HIC

  29. Constraints on the density dependence of symmetry energy Au+Au FRIB No constraints between r0 and 2r0 ?

  30. Outlook 2020? FRIB FAIR Precision measurements in FRIB

  31. FRIB MSU Outlook FAIR MSU (2009-2012) : E/A<100 MeV measure isospin diffusion, fragments, residues, p,n spectra ratios and differential flow  improve constraints on S(r), m*, snn, spp, snp at r<ro MSU (~2013) : E/A>120 MeV  measure p+, p- spectra ratios constraints at ro<r<1.7ro -- Bickley

  32. FRIB MSU GSI Outlook ? FAIR GSI (2011) : E/A~400 – 800 MeV measure p,n spectra ratios and differential flow  determine constraints S(r), m*, snn, spp, snpat 2.5ro<r<3ro Lemmon, Russotto et al, experimental proposal to GSI PAC

  33. Riken FRIB MSU GSI Outlook ? FAIR Riken (2013-2017) : E/A=200-300 MeV measure p+, p- spectra ratios, p,n, t/3He spectra ratios and differential flow  determine S(r), m*, snn, spp, snpat r~2ro Riken (2011) : E/A>50 MeV  measure isospin diffusions for fragments and residues  determine S(r) at r<2ro. 108Sn+112,124Sn – RI beam used to increase d.

  34. Detectors needed: ~ 1.2 M TPC ~ 0.78 M Travel: 0.37 M n detectors: NSCL/pre-FRIB; GSI; RIBF/Riken Pions/kaons & p, t, 3He detectors: TPC NSCL Dual purpose AT-TPC: proposal to be submitted to DOE RIBF TPC: SUMARAI magnet funded, TPC – Japan-US collaboration: proposal to be submitted to DOE. AT-TPC: FRIB

  35. Summary • The density dependence of the symmetry energy is of fundamental importance to nuclear physics and neutron star physics. • Observables in HI collisions provide unique opportunities to probe the symmetry energy over a range of density especially for dense asymmetric matter • Calculations suggest a number of promising observables that can probe the density dependence of the symmetry energy. • Isospin diffusion, isotope ratios, and n/p spectral ratios provide some constraints at 0, -- refinement in constraints foreseen in near future with improvement in calculations and experiments at MSU, GANIL & Riken • + vs. - production, n/p, t/3He spectra and differential flows may provide constraints at 20 and above, MSU, GSI, Riken • The availability of intense fast rare isotope beams at a variety of energies at RIKEN, FRIB & FAIR allows increased precisions in probing the symmetry energy at a range of densities.

  36. Acknowledgements Y.X. Zhang (ImQMD),P. Danielewicz, M. Famiano, W.A. Friedman,W.G. Lynch, L.J. Shi, Jenny Lee, Experimenters Michigan State University T.X. Liu (thesis), W.G. Lynch, Z.Y. Sun, W.P. Tan, G. Verde, A. Wagner, H.S. Xu L.G. Sobotka, R.J. Charity (WU) R. deSouza, V. E. Viola (IU) M. Famiano: (Westen Michigan U) NSCL Transport simulation group Brent Barker, Abby Bickley, Dan Coupland, Krista Cruse, Pawel Danielewicz, Micha Kilburn, Bill Lynch, Michelle Mosby, Scott Pratt, Andrew Steiner, Josh Vredevooqd, Mike Youngs, YingXun Zhang

  37. How to connect different symmetry energy representations • Expansion around r0: • Symmetry slope L & curvature Ksym • Symmetry pressure Psym Value of symmetry energy at saturation

  38. Density region sampled depends on collision observable & beam energy • r>r0 examples: – Pion energy spectra – Pion production ratios – Isotopic spectra – Isotopic flow – With NSCL beams, densities up to 1.7ρ0 are accessible – Beams: 50-150 MeV, 50,000pps 106Sn-126Sn, 37Ca-49Ca Riken Samurai TPC

  39. Density region sampled depends on collision observable & beam energy • r>r0 examples: – Pion energy spectra – Pion production ratios – Isotopic spectra – Isotopic flow – With NSCL beams, densities up to 1.7ρ0 are accessible – Beams: 50-150 MeV, 50,000pps 106Sn-126Sn, 37Ca-49Ca Riken Samurai TPC

  40. Projectile 124Sn No diffusion Target 112Sn Degree of Asymmetry from isoscaling from Y(7Li)/Y(7Be) Complete mixing Isospin Diffusion

  41. Laboratory experiments to study properties of neutron stars Extrapolate information from limited asymmetry and temperature to neutron stars!

  42. Laboratory experiments to study properties of neutron stars 208Pb extrapolation from 208Pb radius to n-star radius

  43. N/Z ratios from bound fragments (Z=3-8)  complementary to n/p ratios P T gi Esym=12.7(r/ro)2/3+19(r/ro) EC.M. Effects are small Hot fragments produced in calculations.

  44. N/Z ratios from bound fragments (Z=3-8)  complementary to n/p ratios P T gi Esym=12.7(r/ro)2/3+19(r/ro) Sequential decay effects are important Data consistent with soft EOS

  45. Experimental Observables to probe the symmetry energy E/A(,) = E/A(,0) + d2S() ; d = (n- p)/ (n+ p) = (N-Z)/A • Collision systems: 124Sn+124Sn, 124Sn+112Sn, 112Sn+124Sn, 112Sn+112Sn • E/A=50 MeV • Low densities (<0): • n/p spectra and flows; Y(n)/Y(p), Y(t)/Y(3He), • Fragment isotopic distributions, • Isoscaling: interpretation with statistical model is incorrect • <N>/<Z> of Z=3-8 fragments • Isospin diffusion • Correlation function, C(q) • Neutron, proton radii, E1 collective modes. • High densities (20) • Neutron/proton spectra and flows; C(q) • + vs. - production, k, hyperon production.

  46. Tsang, HW QF Li, Di Toro BA Li, HW Di Toro, Lukasic Tsang DiToro, Reisdorf, QF Li Di Toro Prassa, QF Li Aumann, Ducoin BA Li, Kubis Danielewicz Lehaut Exploring Bulk properties of Nuclear Matter with Heavy Ion Collisions asy-stiff asy-soft • Low density/energy • fragments, ratios • isospin diffusion • isoscaling • migration/fractionat. • collective excitations • surface phenomena • phase transitions • High density/energy • differential flow • n/p, LIF ratios • pions ratios • kaon ratios • neutron stars Hermann Wolter

  47. Constraints from Isospin Diffusion Data • IBUU04: • Collisions of Sn+Sn isotopes at E/A=50 MeV • b=6 fm • Projectile-like residue determined from density & • y/yb>0.5 • No clusters • Data: • Collisions of Sn+Sn isotopes at E/A=50 MeV • b/bmax>0.8 <b>~7.2 fm from multiplicity gates. • y/yb>0.7 • Results obtained with clusters x=-1 x=-2 124Sn+112Sn data x=0 x=1(soft)

  48. Isospin diffusion in the projectile-like region Basic ideas: • Peripheral reactions • Asymmetric collisions 124Sn+112Sn, 112Sn+124Sn -- diffusion • Symmetric Collisions 124Sn+124Sn, 112Sn+112Sn -- no diffusion • Relative change between target and projectile is the diffusion effect Projectile Target

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