1. Overview of the experimental constraints on symmetry energy Betty Tsang, NSCL/MSU

2. Nuclear Equation of State Relationship between energy, temperature pressure, density in nuclear matter E/A ( ,  ) = E/A ( ,0) +  2  S(  )  = (  n -  p )/ (  n +  p ) = (N-Z)/A Nuclear Structure – What is the nature of the nuclear force that binds protons and neutrons into stable nuclei and rare isotopes? Nuclear Astrophysics – What is the nature of neutron stars and dense nuclear matter?

3. Symmetry energy calculations with effective interactions constrained by Sn masses This does not adequately constrain the symmetry energy at higher or lower densities E/A ( ,  ) = E/A ( ,0) +  2  S(  )  = (  n -  p )/ (  n +  p ) = (N-Z)/A Brown, Phys. Rev. Lett. 85, 5296 (2001) Symmetry energy at 00  =1 How does E/A depend on  and  ?

4. Symmetry energy calculations with effective interactions constrained by Sn masses This does not adequately constrain the symmetry energy at higher or lower densities Brown, Phys. Rev. Lett. 85, 5296 (2001) Symmetry energy at 00  =1 Overview of the experimental constraints on symmetry energy around saturation density

5. Experimental Observables: Heavy Ion Collisions  n/p ratios  Isospin diffusions Mass model (FRDM) Isobaric Analog States (IAS) Giant dipole Resonance (GDR) 208 Pb skin measurements PREX antiprotonic atom systematics 208 Pb(p,p) 208 Pb(p,p’) –dipole polarizability Dipole Pygmy Resonance (DPR) Summary and Outlook Introduction Overview of the experimental symmetry energy constraints around nuclear matter density

6. Strategies used to study the symmetry energy with Heavy Ion collisions below E/A=100 MeV  Vary the N/Z compositions of projectile and targets 124 Sn+ 124 Sn, 124 Sn+ 112 Sn, 112 Sn+ 124 Sn, 112 Sn+ 112 Sn  Measure N/Z compositions of emitted particles n & p yields isotopes yields: isospin diffusion  Simulate collisions with transport theory Find the symmetry energy density dependence that describes the data. Constrain the relevant input transport variables. Neutron Number N Proton Number Z Isospin degree of freedom Hubble ST Crab Pulsar B.A. Li et al., Phys. Rep. 464, 113 (2008)

7. Two HIC observables: n/p ratios and isospin diffusion E/A ( ,  ) = E/A ( ,0) +  2  S(  )  = (  n -  p )/ (  n +  p ) = (N-Z)/A u = stiff soft Y(n)/Y(p); t/ 3 He,  + /  - Projectile Target 124 Sn 112 Sn Isospin Diffusion; low , E beam Tsang et al., PRL 92 (2004) 062701

8. Experimental Layout Courtesy Mike Famiano Wall A Wall B LASSA – charged particles Miniball – impact parameter Neutron walls – neutrons Forward Array – time start Proton Veto scintillators

9. E/A ( ,  ) = E/A ( ,0) +  2  S(  )  = (  n -  p )/ (  n +  p ) = (N-Z)/A u = stiff soft E sym =12.7(  /  o ) 2/3 + 19(  /  o ) ii 124 Sn+ 124 Sn;Y(n)/Y(p) 112 Sn+ 112 Sn;Y(n)/Y(p) Double Ratio minimize systematic errors Two observables: n/p ratios and isospin diffusion

10. E/A ( ,  ) = E/A ( ,0) +  2  S(  )  = (  n -  p )/ (  n +  p ) = (N-Z)/A E sym =12.7(  /  o ) 2/3 + 19(  /  o ) ii 124 Sn+ 124 Sn;Y(n)/Y(p) 112 Sn+ 112 Sn;Y(n)/Y(p) Double Ratio minimize systematic errors Two observables: n/p ratios and isospin diffusion S(  )  12.3·(ρ/ρ 0 ) 2/3 + 17.6· (ρ/ρ 0 ) γ i IQMD calculations were performed for  i =0.35-2.0. Momentum dependent mean fields with m n */m n =m p */m p =0.7 were used. Zhang et.al.,Phys. Lett. B 664 (2008) 145

11. E/A ( ,  ) = E/A ( ,0) +  2  S(  )  = (  n -  p )/ (  n +  p ) = (N-Z)/A 124 Sn+ 124 Sn;Y(n)/Y(p) 112 Sn+ 112 Sn;Y(n)/Y(p) Double Ratio minimize systematic errors Two observables: n/p ratios and isospin diffusion  i  S(  )  12.3·(ρ/ρ 0 ) 2/3 + 17.6· (ρ/ρ 0 ) γ i IQMD calculations were performed for  i =0.35-2.0. Momentum dependent mean fields with m n */m n =m p */m p =0.7 were used. Zhang et.al.,Phys. Lett. B 664 (2008) 145

12. Isospin Diffusion Projectile Target 124 Sn 112 Sn mixed 124 Sn+ 112 Sn n-rich 124 Sn+ 124 Sn p-rich 112 Sn+ 112 Sn mixed 124 Sn+ 112 Sn n-rich 124 Sn+ 124 Sn p-rich 112 Sn+ 112 Sn R i =  1 no diffusion; R i = 0 equilibration Extent of diffuseness reflects strength of SE

13.  i   i  Consistent constraints from the  2 analysis of isospin diffusion data S (  )=12.5(  /  o ) 2/3 +17.6 (  /  o ) ii Projectile Target 124 Sn 112 Sn Degree of isospin diffusion

14. Symmetry energy constraints from HIC arXiv:1204.0466 S (  )=12.5(  /  o ) 2/3 +17.6 (  /  o ) ii  i  Consistent with previous isospin diffusion constraints Chen, Li et al., Phys. Rev. Lett. 94 (2005) 032701

15. Giant Dipole Resonance Collective oscillation of neutrons against protons Consistency in Symmetry Energy Constraints Trippa et al., PRC 77, 061304(R) (2008) Tsang et al, PRL 102,122701 (2009) Danielewicz & Lee, NPA818, 36 (2009) Isobaric Analog States a a (A) P. Moller et al, PRL 108,052501 (2012) FRDM-2011a.  ~0.57 MeV

16. Extrapolation from 208 Pb radius to pressure in n-star Typel & Brown, PRC 64, 027302 (2001) Steiner et al., Phys. Rep. 411, 325 (2005) =L/3  0 P(  fm  (MeV/fm 3 )

17. An experimental overview of the symmetry energy around nuclear matter density Experimental Observables: Heavy Ion Collisions  n/p ratios  Isospin diffusions Mass model (FRDM) Isobaric Analog States (IAS) Giant dipole Resonance (GDR) 208 Pb skin measurements PREX antiprotonic atom systematics 208 Pb(p,p) 208 Pb(p,p’) –dipole polarizability Dipole Pygmy Resonance (DPR) Summary and Outlook Introduction

18. 18  R np = 0.21±0.06 fm L=67±12.1 MeV S o =33±1.1 MeV Laboratory experiments to measure the 208 Pb neutron skin Pb(p,p) Zenihiro et al., PRC82, 044611 (2010)

19. Pb skin thickness from dipole polarizability Pb(p,p’) E beam =295 MeV  R np = 0.156+0.025-0.021 fm Theoretical uncertainties underpredicted ? Tamii et al., PRL107, 062502 (2011) p+p+ n polarizability p+p+ p+p+ p+p+ J.Piekarewicz et al., arXiv:1201.3807 Reinhard & Nazarewicz,PRC81, 051303 (R) (2010 )

20. Summary of Pb skin thickness and symmetry energy constraints Diverse experiments but consistent results arXiv:1204.0466

21. See references in arXiv:1204.0466 Importance of 3n force in the EoS of pure n-matter

22. Challenge I: constraints from neutron star observations arXiv:1204.0466 Steiner PRL108, 081102 (2012)

23. Challenge II: Constraints at very low density Symmetry energy at  <0.05  o, T<10 MeV is dominated by correlations and cluster formation J.B. Natowitz et al, PRL 104 (2010) 202501 Esym(n)/Esym(n 0 )

24. Isospin Observables: Neutron/proton and t/ 3 He and light isotopes energy spectra flow – p x vs. y (v 1 ) – Elliptic flow (v 2 ) – Disappearance of flow (balance energy) π + /π - spectra π + /π - flow Challenge III: Constraints at supra-normal densities with Heavy Ion Collisions RIBF, FRIB, KoRIA International Collaboration

25. ASY-EOS experiment @GSI, May 2011 Au+Au @ 400 AMeV 96 Zr+ 96 Zr @ 400 AMeV 96 Ru+ 96 Ru @ 400 AMeV ~ 5x10 7 Events for each system Beam Line Shadow Bar TofWall Land (not splitted) target Chimera Krakow array MicroBall Russotto & Lemmon

26. SAMURAI-TPC will be installed inside the SAMURAI dipole magnet in RIKEN TPC chamber Field Cage Electronics and pad plane Voltage step down Outer enclosure AT/TPC @ MSU

27. arXiv:1204.0466 NSCL/HiRA group Acknowledgement:

28. A Time projection chamber is being built in the US to measure p+/p- & light charge particles in RIKEN Nuclear Symmetry Energy (NuSym) collaboration http://groups.nscl.msu.edu/hira/sep.htm Determination of the Equation of State of Asymmetric Nuclear Matter MSU: B. Tsang & W. Lynch, G. Westfall, P. Danielewicz, E. Brown, A. Steiner Texas A&M University : Sherry Yennello, Alan McIntosh Western Michigan University : Michael Famiano RIKEN, JP: TadaAki Isobe, Atsushi Taketani, Hiroshi Sakurai Kyoto University: Tetsuya Murakami Tohoku University: Akira Ono GSI, Germany: Wolfgang Trautmann, Yvonne Leifels Daresbury Laboratory, UK: Roy Lemmon INFN LNS, Italy: Giuseppe Verde, Paulo Russotto GANIL, France: Abdou Chbihi CIAE, PU, CAS, China: Yingxun Zhang, Zhuxia Li, Fei Lu, Y.G. Ma, W. Tian Korea University, Korea: Byungsik Hong

29. Summary Consistent Symmetry Energy constraints for 0.3<  /  o <1 using different experimental techniques and theories. Importance of 3n force in the EoS of pure n-matter at high density. arXiv:1204.0466

31. Extracting the 208 Pb skin thickness from HIC Typel & Brown, PRC 64, 027302 (2001) Steiner et al., Phys. Rep. 411, 325 (2005) 0.16-0.27 fm arXiv:1204.0466

32. Laboratory experiments to measure the 208 Pb neutron skin 208 Pb Existence of a neutron skin 3%  1% measurement PREXII approved (2013-2014) Phys Rev Let. 108, 112502 (2012)

33. Neutron Number N Proton Number Z Symmetry Energy in Nuclei Inclusion of surface terms in symmetry Hubble ST Crab Pulsar

34. C sym =22.4 MeV Fitting of Empirical Binding Energies Ambiquities in the volume and surface terms of a sym Finite nuclei  infinite nuclear matter Souza et al., PRC 78, 014605 (2008)

35. Symmetry coefficient from Isobaric Analog States a a (A) Charge invariance: invariance of nuclear interactions under rotations in n-p space Corrections for microscopic effects + deformation S o = 31.5 MeV; L = 75.6 – 107.1 MeV S o = 33.5 MeV; L = 80.4 – 113.9 MeV Danielewicz & Lee, NP A818, 36 (2009)

36. Finite Range Droplet Model (FRDM) – Peter Moller S o = 32.5 ± 0.5 MeV; L = 70 ± 15 MeV Sophisticated mass model by adding improvements FRDM-2011a includes symmetry energy in the fit P. Moller et al, PRL 108,052501 (2012)

37. Correlation analysis of Pb skin thickness Reinhard & Nazarewicz,PRC81, 051303 (R) (2010)

38.  R np ( 208 Pb)= 0.20±0.02 fm L=65.1±15.5 MeV S o =32.3±1.3 MeV Klimkiewicz et al., PRC 76, 051603(R) (2007) Wieland et al., PRL102, 092502 (2009) Carbonne et al., PRC 81, 041301 (2010) Skin thickness from Pygmy Dipole Resonance Collective oscillation of neutron skin against the Core   R np

39.  R np = 0.16±(0.02) stat ±(0.04) syst ±(0.05) theo Systematics of anti-protonic atoms Large experimental and theoretical uncertainties Need better quality data & theory Antiproton probe the extreme tail of nuclei. Data from 26 nuclei: 40 Ca to 238 U Strong correlation between  R np and asymmetry . A. Trzcinska et al, PRL 87, 082501 (2001); M. Centelles et al, PRL 102, 122502 (2009); B.A. Brown et al., PRC 76, 034305 (2007); B. Klos et al., PRC76, 014311 (2007)  R np 

40. Constraining the EoS using Heavy Ion collisions pressure contours density contours Au+Au collisions E/A = 1 GeV) E/A ( ,  ) = E/A ( ,0) +  2  S(  );  = (  n -  p )/ (  n +  p ) = (N-Z)/A Two observable due to the high pressures formed in the overlap region: –Nucleons are “squeezed out” above and below the reaction plane. –Nucleons deflected sideways in the reaction plane. –

41. Sideward Flow in plane out of plane Determination of symmetric matter EOS from nucleus-nucleus collisions The curves represent calculations with parameterized Skyrme mean fields They are adjusted to find the pressure that replicates the observed flow. Danielewicz et al., Science 298,1592 (2002). The boundaries represent the range of pressures obtained for the mean fields that reproduce the data. They also reflect the uncertainties from the input parameters in the model.

43. NSCL experiments 05049 & 09042 Density dependence of the symmetry energy with emitted neutrons and protons & Investigation of transport model parameters (May & October, 2009 ) facilityProbe Beam Energy Travel (k) $ yeardensity MSUn, p,t,3He50-14002009 <o<o GSIn, p, t, 3He400252010/2011 2.5  o MSUiso-diffusion5002011 <o<o RIKENiso-diffusion50252012 <o<o MSU +,-+,- 14002014-2015 1-1.5  o RIKEN n,p,t, 3 He,  +,  - 200-300852013-2014 2o2o GSIn, p, t, 3He800252014 2-3  o FRIB n, p,t, 3 He,  +,  - 20002018- 2-2.5  o FAIRK + /K - 800-1000?20183o3o GSI S394, May 2011 NSCL experiment 07038 Precision Measurements of Isospin Diffusion, June 2011)

44. arXiv:1204.0466

45. Definition of Symmetry Energy E/A ( ,  ) = E/A ( ,0) +  2  S(  );  = (  n -  p )/ (  n +  p ) = (N-Z)/A

46. Challenges: Constraints on the density dependence of symmetry energy at supra normal density Fourpi experiments are not optimized to measure symmetry energy Need better experiments (ASYEOS & SAMURAI/TPC collaborations) Xiao et al., PRL102, 062502 (2009) Russotto et al., PL B697 (2011) 471

47. How to obtain the information about EoS using heavy ion collisions? Experiments: Accelerator: Projectile, target, energy Detectors: Information of emitted particles – identity, spatial info, energy, yields  construct observables Models Input: Projectile, target, energy. Simulate the collisions with the appropriate physics Success depends on the comparisons of observables. Theory must predict how reaction evolves from initial contact to final observables Transport models (BUU, QMD, AMD) Describe dynamical evolution of the collision process

48. Summary of Pb skin thickness and symmetry energy constraints arXiv:1204.0466 Hebeler et al., PRL 105, 161102 (2010)

49. Laboratory experiments to measure the 208 Pb neutron skin 208 Pb PREX (Parity Radius experiment) measures R np of 208 Pb Why 208 Pb? It has excess of neutrons  R np = 1/2 - 1/2 It is doubly-magic Its first excited state is 2.6 MeV Expected uncertainty: A PV (Parity-violating Asymmetry )~3%  R n ~1% Ran in Jefferson Lab in Spring 2010. Phys Rev Let. 108, 112502 (2012)

50. Density dependence of Symmetry Energy E/A ( ,  ) = E/A ( ,0) +  2  S(  );  = (  n -  p )/ (  n +  p ) = (N-Z)/A Danielewicz, Lacey, Lynch, Science 298,1592 (2002) Pressure (MeV/fm 3 ) ??

51. symmetry energy constraints from IAS Tsang et al, PRL 102,122701 (2009)

52. Equation of State (EoS) Ideal gas: PV=nRT

53. Definition of Symmetry Energy E/A ( ,  ) = E/A ( ,0) +  2  S(  );  = (  n -  p )/ (  n +  p ) = (N-Z)/A B.A. Brown, PRL 85 (2000) 5296 FRDM IAS Reactions nuclear structure

54. U.S. effort at NSCL Active Target Time Projection Chamber (MRI) Two alternate modes of operation Fixed Target Mode with target wheel inside chamber: –4  tracking of charged particles allows full event characterization –Scientific Program » Constrain Symmetry Energy at  >  0 Active Target Mode: –Chamber gas acts as both detector and thick target ( H 2, D 2, 3 He, Ne, etc.) while retaining high resolution and efficiency –Scientific Program » Transfer & Resonance measurements, Astrophysically relevant cross sections, Fusion, Fission Barriers, Giant Resonances U.S. collaboration on AT-TPC, U.S. – French GET collaboration on electronics.

55. S (  )=12.5(  /  o ) 2/3 +C (  /  o ) ii Symmetry Energy from phenomenological interactions B.A. Brown, PRL 85 (2000) 5296 arXiv:1204.0466

56. Acknowledgement: NSCL/HiRA group

57. Giant Dipole Resonance Collective oscillation of neutrons against protons Symmetry Energy from Giant dipole Resonsnce Trippa et al., PRC 77, 061304(R) (2008) Tsang et al, PRL 102,122701 (2009) Danielewicz & Lee, NPA818, 36 (2009) Isobaric Analog States a a (A) P. Moller et al, PRL 108,052501 (2012) FRDM-2011a.  ~0.57 MeV

58. Mini-summary of symmetry energy constraints from FRDM and IAS

59. An experimental overview of the symmetry energy around nuclear matter density Experimental Observables: Heavy Ion Collisions  n/p ratios  Isospin diffusions Giant dipole Resonance (GDR) Mass model (FRDM) Isobaric Analog States (IAS) 208 Pb skin measurements PREX antiprotonic atom systematics 208 Pb(p,p) 208 Pb(p,p’) –dipole polarizability Dipole Pygmy Resonance (DPR) Summary and Outlook Introduction

60. symmetry energy constraints from nuclear masses Tsang et al, PRL 102,122701 (2009) Danielewicz & Lee, NPA818, 36 (2009) Isobaric Analog States a a (A) relates the asymmetry term to isospin and energy differences of two IAS P. Moller et al, PRL 108,052501 (2012) Sophisticated mass model by adding improvements FRDM-2011a includes symmetry energy in the fit.  ~0.57 MeV