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Zbigniew Chaj ę cki National Superconducting Cyclotron Laboratory Michigan State University

Probing the symmetry energy with heavy ions. Zbigniew Chaj ę cki National Superconducting Cyclotron Laboratory Michigan State University B. Lynch, B. Tsang, M. Kilburn, D. Coupland, M. Youngs. Outline. Symmetry energy Probing Symmetry Energy with heavy ions n/p , t/ 3 He spectrum

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Zbigniew Chaj ę cki National Superconducting Cyclotron Laboratory Michigan State University

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  1. Probing the symmetry energywith heavy ions Zbigniew Chajęcki National Superconducting Cyclotron Laboratory Michigan State University B. Lynch, B. Tsang, M. Kilburn, D. Coupland, M. Youngs

  2. Outline • Symmetry energy • Probing Symmetry Energy with heavy ions • n/p , t/3He spectrum • isospin diffusion • correlations • neutron and proton emission time and symmetry energy (particle emission chronology) • pion production • Summary Z. Ch. - WWND 2011, Feb 6-13, 2011

  3. Nuclear Equation of State Examples of possible research areas in NSCL/FRIB Astrophysics Nuclear structure Nuclear reactions • mass and size of neutron stars • nature of neutron stars and dense nuclear matter • origin of elements heavier than iron in the cosmos • nuclear reactions that drive stars and stellar explosions? • n/p ratios • t/³He ratios • Isospin diffusion • Isoscaling • proton-proton correlations • etc... • Neutron skin thickness • GMR • PDR • Isobaric Analog States • nature of the nuclear force that binds protons and neutrons into stable nuclei and rare isotopes • etc... E/A (,) = E/A (,0) + d2S() d = (n- p)/ (n+ p) = (N-Z)/A Z. Ch. - WWND 2011, Feb 6-13, 2011

  4. EOS: symmetric matter and neutron matter • Crucial to obtain • stellar radii • moments of interia • maximum masses • neutron star cooling rates • crustal vibration frequencies E/A (,) = E/A (,0) + d2S() d = (n- p)/ (n+ p) = (N-Z)/A   1 Brown, Phys. Rev. Lett. 85, 5296 (2001) stiff Neutron matter EOS E/A [MeV] soft The density dependence of symmetry energy is largely unconstrained. Z. Ch. - WWND 2011, Feb 6-13, 2011

  5. Probes of the symmetry energy 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 Correlations High densities (20) : Neutron/proton spectra and flows + vs. - production Correlations E/A (,) = E/A (,0) + d2S()d = (n- p)/ (n+ p) = (N-Z)/A stiff soft >0 <0 symmetry energy S()= 12.5·(ρ/ρ0)2/3 + Sint·(ρ/ρ0)  Z. Ch. - WWND 2011, Feb 6-13, 2011

  6. International Collaboration Symmetry Energy Project Collaboration Determination of the Equation of State of Asymmetric Nuclear MatterNSCL MSU, USA: B. Tsang & W. Lynch, Gary Westfall, Pawel Danielewicz, Edward Brown, Andrew Steiner Rutgers University: Jolie Cizewski Smith College : Malgorzata Pfabe University of Texas, El Paso: Jorge Lopez Texas A&M University : Sherry Yennello Western Michigan University : Michael Famiano RIKEN, JP: Hiroshi Sakurai, Shunji Nishimura, Yoichi Nakai, Atsushi Taketani Kyoto University: Tetsuya MurakamiRikkyo University, JP: Jiro Murata, Kazuo Ieki Tohoku University: Akira Ono GSI DE: Wolfgang Trautmann, Yvonne Leifels, Marcus Bleicher Daresbury Laboratory, UK: Roy Lemmon INFN LNS Catania, IT: Giuseppe Verde, Angelo Pagano, Paulo Russotto, Massimo di Toro, Maria Colonna, Aldo Bonasera, Vincenzo Greco SUBATECH FR: Christoph Hartnack GANIL FR: Abdou Chbihi, John Frankland, Jean-Pierre WieleczkoRuđer Bosković Institute, Zoran Basrak, China Institute of Atomic Energy: Yingxun Zhang, Zhuxia Li Brazil: Sergio Souza, Raul Donangelo, Brett Carlson E/A (,) = E/A (,0) + d2S() d = (n- p)/ (n+ p) = (N-Z)/A RIBF FRIB MSU GSI ? FAIR Z. Ch. - WWND 2011, Feb 6-13, 2011

  7. Modeling heavy-ion collisions : transport models Danielewicz, Bertsch, NPA533 (1991) 712 B. A. Li et al., PRL 78 (1997) 1644 • BUU - Boltzmann-Uehling-Uhlenbeck • Simulates two nuclei colliding Micha Kilburn • Parameter space • not only about the symmetry energy • also important to understand e.g. an effect of cross section (free x-section, in-medium x-section), reduced mass • Production of clusters: d,t, 3He (alphas) Z. Ch. - WWND 2011, Feb 6-13, 2011

  8. Probing Symmetry Energy:Experimental Observables Z. Ch. - WWND 2011, Feb 6-13, 2011

  9. n/p yield ratios F2 F1 stiff F3 gi soft S(r)=12.5(r/ro)2/3+17.6(r/ro) ImQMD F1=2u2/(1+u) F2=u F3=u soft Y(n)/Y(p) soft u = stiff stiff • n and p potentials have opposite sign • n and p energy spectra depend on the symmetry energy and softer density dependence emits more neutrons at low density =0.3 Uasy (MeV) • More n’s are emitted from the n-rich system and softer iso-EOS Z. Ch. - WWND 2011, Feb 6-13, 2011

  10. t/3He yield ratios L-W Chen et al., PRC 69 (2004) 054606 t/3He ratio sensitive to the symmetry energy (similarly as n/p) - advantage: easier to measure However, the magnitude of the ratio depends also on the details within the symmetry energy potential Z. Ch. - WWND 2011, Feb 6-13, 2011

  11. Probing Symmetry Energy with n’s and p’s Density dependence of the symmetry energy with emitted neutrons and protons & Investigation of transport model parameters. Famiano, Coupland, Youngs NSCL experiments 05049 & 09042 Z. Ch. - WWND 2011, Feb 6-13, 2011

  12. Measurement of n/p spectral ratios: probes the pressure due to asymmetry term at 0. Probe expulsion of neutrons from bound neutron-rich system by symmetry energy. Has been probed by direct measurements of neutrons vs. proton emission rates in central Sn+Sn collisions. gi Esym=12.7(r/ro)2/3+19(r/ro) Double Ratios 124Sn+124Sn;Y(n)/Y(p) 112Sn+112Sn;Y(n)/Y(p) soft stiff minimize systematic errors • Double ratio removes the sensitivity to neutron efficiency and energy calibration. Z. Ch. - WWND 2011, Feb 6-13, 2011

  13. Isospin diffusion is measured with fragments emitted from the neck region. Probe the symmetry energy at subsaturation densities in semi-peripheral collisions, e.g. 124Sn + 112Sn at b=6 fm Isospin “diffuse” through low-density neck region Symmetry energy drives system towards equilibrium. =(N-Z)/A stiff EOS  small diffusion; |Ri|>>0 soft EOS  fast equilibrium; Ri0 Experimental observable: Isospin dependence Projectile 124Sn Target 112Sn stiff soft Z. Ch. - WWND 2011, Feb 6-13, 2011

  14. Isospin diffusion is measured with fragments emitted from the neck region. Probe the symmetry energy at subsaturation densities in semi-peripheral collisions, e.g. 124Sn + 112Sn at b=6 fm Isospin “diffuse” through low-density neck region Symmetry energy drives system towards equilibrium. stiff EOS  small diffusion; |Ri|>>0 soft EOS  fast equilibrium; Ri0 Experimental observable: Isospin dependence S()= 12.5·(ρ/ρ0)2/3 + Sint·(ρ/ρ0)  Z. Ch. - WWND 2011, Feb 6-13, 2011

  15. Emission of p’s and n’s: Sensitivity to SymEn 52Ca 48Ca Stiff EoS L-W Chen et al., PRL90 (2003) 162701 Soft EoS Soft EoS (γ=0.5) Stiff EoS (γ=2) p’s emitted after n’s later emission times p’s and n’s emitted at similar time fasteremission times Z. Ch. - WWND 2011, Feb 6-13, 2011

  16. Sym.En. and correlations Soft EoS Stiff EoS L-W Chen et al., PRL90 (2003) 162701 Stiff EoS Soft EoS Soft Stiff n-n, p-p, n-p correlations sensitive to the symmetry energy Z. Ch. - WWND 2011, Feb 6-13, 2011

  17. proton-proton correlations Theoretical CF: Koonin-Pratt equation S.E. Koonin, PLB70 (1977) 43 S.Pratt et al., PRC42 (1990) 2646 … 2-particle wave function … source function (p,p) correlation function (p,p) correlation function S-wave interraction Coulomb uncorrelated |q| = 0.5 |p1 - p2| |q| = 0.5 |p1 - p2| p1 Experimental correlation function: x1 r x2 p2 few fm P(p1,p2) P(p1)P(p2) |q| = 0.5 |p1 - p2| Z. Ch. - WWND 2011, Feb 6-13, 2011

  18. NSCL experiments 05045: HiRA + 4 detector November 2006 = High Resolution Array beam • 4π detector => impact parameter + reaction plane • HiRA => light charge particle correlations (angular coverage 20-60º in LAB, • 63 cm from target (= ball center)) Reaction systems: 40Ca + 40Ca @ 80 MeV/u 48Ca + 48Ca @ 80 MeV/u Z. Ch. - WWND 2011, Feb 6-13, 2011

  19. Telescope 4x CsI(Tl) 4cm Si-E 1.5 mm Si-DE 65mm pixel 32 strips v.(front) 32 strips h. (back) 32 strips v. (front) Beam • ASIC readout • up to 20 Telescopes • 62.3 x 62.3 mm2 active area • strip pitch 2 mm • 1024 Pixels per telescope @ 63 cm from target => Δθ<0.2º Z. Ch. - WWND 2011, Feb 6-13, 2011

  20. Detector performance High resolution at low relative momentum good PID Z. Ch. - WWND 2011, Feb 6-13, 2011

  21. Initial size effect R=r0 A1/3 R(40Ca) = 4.3 fm R(48Ca) = 4.6 fm R 48Ca+ 48Ca > R 40Ca+ 40Ca Z. Ch. - WWND 2011, Feb 6-13, 2011

  22. Comparing data to pBUU Backward angle Forward angle BUU Pararameters No dependence on symmetry energy Rostock in-medium reduction Producing clusters BUU does reasonably well Except at forward angles - Spectator source Where evaporation and secondary decays are important! Micha Kilburn Z. Ch. - WWND 2011, Feb 6-13, 2011

  23. Emission of p’s and n’s: Sensitivity to SymEn 52Ca 48Ca Stiff EoS L-W Chen et al., PRL90 (2003) 162701 Soft EoS Soft EoS (γ=0.5) Stiff EoS (γ=2) p’s emitted after n’s later emission times p’s and n’s emitted at similar time fasteremission times Z. Ch. - WWND 2011, Feb 6-13, 2011

  24. n-p correlation function (n,p) correlation function (n,p) correlation function S(x) S(x) x x 0 0 Theoretical CF: Koonin-Pratt equation p1 S.E. Koonin, PLB70 (1977) 43 S.Pratt et al., PRC42 (1990) 2646 x1 r … 2-particle wave function … source function x2 p2 few fm q = 0.5(p1 - p2) Z. Ch. - WWND 2011, Feb 6-13, 2011

  25. Emission of p’s and n’s: Sensitivity to SymEn 52Ca 48Ca Stiff EoS L-W Chen et al., PRL90 (2003) 162701 Soft EoS Soft EoS (γ=0.5) Stiff EoS (γ=2) p’s emitted after n’s later emission times p’s and n’s emitted at similar time fasteremission times Z. Ch. - WWND 2011, Feb 6-13, 2011

  26. Possible emission configurations (stiff sym. pot.) n n n n p p p p Catching up Catching up qx<0 qx>0 Moving away Moving away qx<0 qx>0 (n,p) correlation function q=pp -pn =(qx, qy=0,qz=0); r=(x, y=0,z=0) qx<0 qx>0 S(x) x 0 q = 0.5(pp - pn) Z. Ch. - WWND 2011, Feb 6-13, 2011

  27. Emission of p’s and n’s: Sensitivity to SymEn 52Ca 48Ca Stiff EoS L-W Chen et al., PRL90 (2003) 162701 Soft EoS Soft EoS (γ=0.5) Stiff EoS (γ=2) p’s emitted after n’s later emission times p’s and n’s emitted at similar time fasteremission times Z. Ch. - WWND 2011, Feb 6-13, 2011

  28. Sensitivity to particle emission (soft sym. pot.) n n p p Experimentally, we measure the CF, not the source distribution! Moving away Catching up qx<0 qx>0 (n,p) correlation function qx<0 qx>0 S(x) x 0 q=pp -pn =(qx, qy=0,qz=0); r=(x, y=0,z=0) qx = 0.5(px,p - px,n) Z. Ch. - WWND 2011, Feb 6-13, 2011

  29. Relating asymmetry in the CF to space-time asymmetry Stiff EoS Soft EoS (n,p) correlation function qx<0 qx>0 S(x) <x> x 0 qx = 0.5(px,p - px,n) Clasically, average separation b/t protons and neutrons Not expected if n,p emitted from the same source (no n-p differential flow) =0 Protons emitted later Z. Ch. - WWND 2011, Feb 6-13, 2011

  30. High density probe: pion production 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. Yong et al., Phys. Rev. C 73, 034603 (2006) soft stiff Z. Ch. - WWND 2011, Feb 6-13, 2011

  31. 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 wide 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. • Need more guidance from theory regarding observables beyond normal nuclear matter density • The availability of intense fast rare isotope beams at a variety of energies at FRIB & FAIR allows increased precisions in probing the symmetry energy at a wide range of densities • Experimental programs are being developed to do such measurements at MSU/FRIB, RIKEN/RIBF and GSI/FAIR Z. Ch. - WWND 2011, Feb 6-13, 2011

  32. Acknowledgments • Brent Barker, Dan Brown, Zbigniew Chajecki, Dan Coupland, Pawel Danielewicz, Vlad Henzl, Daniela Henzlova, Clemens Herlitzius, Micha Kilburn, Jenny Lee, Sergei Lukyanov, Bill Lynch, Andy Rogers, Alisher Sanetullaev, Zhiyu Sun, Betty Tsang, Andrew Vander Molen, Gary Westfall, Mike Youngs • NSCL-MSU Bob Charity Jon ElsonLee Sobotka Washington University, St. Louis Abdou Chbihi GANIL, Caen, France Romualdo DesouzaSylvie Hudan Indiana University, Bloomington Mike Famiano Western Michigan University, Kalamazoo Giuseppe Verde INFN, Catania, Italy Mark Wallace LANL Z. Ch. - WWND 2011, Feb 6-13, 2011

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