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

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

3. Z. Ch. - WWND 2011, Feb 6-13, 2011 3 E/A ( ,  ) = E/A ( ,0) +  2  S(  )  = (  n -  p )/ (  n +  p ) = (N-Z)/A Nuclear Equation of State Examples of possible research areas in NSCL/FRIB AstrophysicsNuclear structureNuclear 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?  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...  n/p ratios  t/³He ratios  Isospin diffusion  Isoscaling  proton-proton correlations  etc...

4. Z. Ch. - WWND 2011, Feb 6-13, 2011 4 EOS: symmetric matter and neutron matter Brown, Phys. Rev. Lett. 85, 5296 (2001) Neutron matter EOS The density dependence of symmetry energy is largely unconstrained. E/A ( ,  ) = E/A ( ,0) +  2  S(  )  = (  n -  p )/ (  n +  p ) = (N-Z)/A   1 E/A [MeV] Crucial to obtain  stellar radii  moments of interia  maximum masses  neutron star cooling rates  crustal vibration frequencies stiff soft

5. 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 symmetry energy <0<0 >0>0 E/A ( ,  ) = E/A ( ,0) +  2  S(  )  = (  n -  p )/ (  n +  p ) = (N-Z)/A S(  ) = 12.5·(ρ/ρ 0 ) 2/3 + S int · (ρ/ρ 0 )  stiff soft

6. Z. Ch. - WWND 2011, Feb 6-13, 2011 6 International Collaboration RIBF FRIB MSU GSI FAIR ? FacilityProbeBeam En. [MeV] YearDensity MSUn,p,t, 3 He50-1402009 <  0 GSIn,p,t, 3 He4002010/2011 2.5  0 MSUiso-diffusion502010/2011 <  0 RIKENiso-diffusion502010 <  0 MSU     1402012-2014 1-1.5  0 RIKENn,p,t, 3 He,     200-3002014 2  0 GSIn,p,t, 3 He8002014 2-3  0 FRIBn,p,t, 3 He,     2002018- 2-2.5  0 FAIRK +,K - 800-10002018 3  0 E/A ( ,  ) = E/A ( ,0) +  2  S(  )  = (  n -  p )/ (  n +  p ) = (N-Z)/A Symmetry Energy Project Collaboration Determination of the Equation of State of Asymmetric Nuclear Matter NSCL 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 Murakami Rikkyo 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 Wieleczko Ruđer Bosković Institute, Zoran Basrak, China Institute of Atomic Energy: Yingxun Zhang, Zhuxia Li Brazil: Sergio Souza, Raul Donangelo, Brett Carlson

7. Z. Ch. - WWND 2011, Feb 6-13, 2011 7 Modeling heavy-ion collisions : transport models 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, 3 He (alphas) BUU - Boltzmann-Uehling-Uhlenbeck Simulates two nuclei colliding Danielewicz, Bertsch, NPA533 (1991) 712 B. A. Li et al., PRL 78 (1997) 1644 Micha Kilburn

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

9. Z. Ch. - WWND 2011, Feb 6-13, 2011 9 n/p yield ratios F 1 =2u 2 /(1+u) F 2 =u F 3 =  u F1F1 F2F2 F3F3 u = stiff soft U asy (MeV)  =0.3 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 More n’s are emitted from the n-rich system and softer iso-EOS ImQMD Y(n)/Y(p) S (  )=12.5(  /  o ) 2/3 +17.6(  /  o ) ii soft stiff soft stiff

10. Z. Ch. - WWND 2011, Feb 6-13, 2011 10 t/ 3 He yield ratios L-W Chen et al., PRC 69 (2004) 054606 t/ 3 He 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

11. 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. ProjTarget E/ARange 40Ca124Sn 140  >  0 40Ca112Sn 140 48Ca124Sn 140 48Ca112Sn 140 124Sn 50, 120  <  0  >  0 112Sn 50, 120 Famiano, Coupland, Youngs NSCL experiments 05049 & 09042

12. 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. E sym =12.7(  /  o ) 2/3 + 19(  /  o ) ii minimize systematic errors 124 Sn+ 124 Sn;Y(n)/Y(p) 112 Sn+ 112 Sn;Y(n)/Y(p) Double Ratios Double ratio removes the sensitivity to neutron efficiency and energy calibration. soft stiff

13. 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. 124 Sn + 112 Sn at b=6 fm  Isospin “diffuse” through low-density neck region  Symmetry energy drives system towards equilibrium.  =(N-Z)/A stiff EOS  small diffusion; |R i |>>0 soft EOS  fast equilibrium; R i  0 Projectile Target 124 Sn 112 Sn soft stiff Experimental observable: Isospin dependence

14. 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. 124 Sn + 112 Sn at b=6 fm  Isospin “diffuse” through low- density neck region  Symmetry energy drives system towards equilibrium. stiff EOS  small diffusion; |R i |>>0 soft EOS  fast equilibrium; R i  0 Experimental observable: Isospin dependence ProjectileTarget E/Alabrange 124,118,112Sn 50NSCL  <  0 124,112,108Sn124,112Sn 50RIKEN S(  ) = 12.5·(ρ/ρ 0 ) 2/3 + S int · (ρ/ρ 0 ) 

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

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

17. Z. Ch. - WWND 2011, Feb 6-13, 2011 17 proton-proton correlations few fm x1x1 x2x2 p1p1 p2p2 Experimental correlation function: r |q| = 0.5 |p 1 - p 2 | (p,p) correlation function P(p 1,p 2 ) P(p 1 )P(p 2 ) |q| = 0.5 |p 1 - p 2 | … 2-particle wave function … source function Theoretical CF: Koonin-Pratt equation S.E. Koonin, PLB70 (1977) 43 S.Pratt et al., PRC42 (1990) 2646 |q| = 0.5 |p 1 - p 2 | (p,p) correlation function uncorrelated Coulomb S-wave interraction

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

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

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

21. Z. Ch. - WWND 2011, Feb 6-13, 2011 21 Initial size effect R=r 0 A 1/3 R( 40 Ca) = 4.3 fm R( 48 Ca) = 4.6 fm R 48Ca+ 48Ca > R 40Ca+ 40Ca

22. Z. Ch. - WWND 2011, Feb 6-13, 2011 22 Comparing data to pBUU 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! Forward angle Backward angle Micha Kilburn

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

24. Z. Ch. - WWND 2011, Feb 6-13, 2011 24 n-p correlation function few fm x1x1 x2x2 p1p1 p2p2 … 2-particle wave function … source function Theoretical CF: Koonin-Pratt equation S.E. Koonin, PLB70 (1977) 43 S.Pratt et al., PRC42 (1990) 2646 r 0 x S(x) (n,p) correlation function 0 x S(x) (n,p) correlation function q = 0.5(p 1 - p 2 )

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

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

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

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

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

30. Z. Ch. - WWND 2011, Feb 6-13, 2011 30 High density probe: pion production Double ratio involves comparison between neutron rich 132 Sn+ 124 Sn and neutron deficient 112 Sn+ 112 Sn 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 FacilityProbeBeam En. [MeV] YearDensity MSU     1402012-2014 1-1.5  0

31. Z. Ch. - WWND 2011, Feb 6-13, 2011 31 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/FAIRSummary

32. 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 Abdou Chbihi GANIL, Caen, France Mike FamianoWestern Michigan University, Kalamazoo Giuseppe VerdeINFN, Catania, Italy Mark WallaceLANL Washington University, St. Louis Romualdo Desouza Sylvie Hudan Indiana University, Bloomington Bob Charity Jon Elson Lee Sobotka