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  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 • 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? E/A (,) = E/A (,0) + d2S() d = (n- p)/ (n+ p) = (N-Z)/A

  3. How does E/A depend on  and ? Symmetry energy at =1 E/A (,) = E/A (,0) + d2S() d = (n- p)/ (n+ p) = (N-Z)/A Brown, Phys. Rev. Lett. 85, 5296 (2001) 0 • Symmetry energy calculations with effective interactions constrained by Sn masses • This does not adequately constrain the symmetry energy at higher or lower densities

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

  5. Overview of the experimental symmetry energy constraints 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) Introduction • 208Pb skin measurements • PREX • antiprotonic atom systematics • 208Pb(p,p) • 208Pb(p,p’) –dipole polarizability • Dipole Pygmy Resonance (DPR) Summary and Outlook

  6. Strategies used to study the symmetry energy with Heavy Ion collisions below E/A=100 MeV Proton Number Z Crab Pulsar Neutron Number N Hubble ST 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 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. B.A. Li et al., Phys. Rep. 464, 113 (2008)

  7. Projectile 124Sn stiff Target soft 112Sn u = E/A (,) = E/A (,0) + d2S() d = (n- p)/ (n+ p) = (N-Z)/A Two HIC observables: n/p ratios and isospin diffusion Tsang et al., PRL 92 (2004) 062701 Y(n)/Y(p); t/3He, p+/p- Isospin Diffusion; low r, Ebeam

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

  9. minimize systematic errors Double Ratio stiff soft u = gi Esym=12.7(r/ro)2/3+19(r/ro) E/A (,) = E/A (,0) + d2S() d = (n- p)/ (n+ p) = (N-Z)/A Two observables: n/p ratios and isospin diffusion 124Sn+124Sn;Y(n)/Y(p) 112Sn+112Sn;Y(n)/Y(p)

  10. minimize systematic errors Double Ratio gi Esym=12.7(r/ro)2/3+19(r/ro) E/A (,) = E/A (,0) + d2S() d = (n- p)/ (n+ p) = (N-Z)/A Two observables: n/p ratios and isospin diffusion • S() 12.3·(ρ/ρ0)2/3 + 17.6·(ρ/ρ0) γi • IQMD calculations were performed for i=0.35-2.0. • Momentum dependent mean fields with mn*/mn =mp*/mp =0.7 were used. Zhang et.al.,Phys. Lett. B 664 (2008) 145 124Sn+124Sn;Y(n)/Y(p) 112Sn+112Sn;Y(n)/Y(p)

  11. minimize systematic errors Double Ratio 0.4gi 1.05 E/A (,) = E/A (,0) + d2S() d = (n- p)/ (n+ p) = (N-Z)/A Two observables: n/p ratios and isospin diffusion • S() 12.3·(ρ/ρ0)2/3 + 17.6·(ρ/ρ0) γi • IQMD calculations were performed for i=0.35-2.0. • Momentum dependent mean fields with mn*/mn =mp*/mp =0.7 were used. Zhang et.al.,Phys. Lett. B 664 (2008) 145 124Sn+124Sn;Y(n)/Y(p) 112Sn+112Sn;Y(n)/Y(p)

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

  13. Consistent constraints from the 2analysis of isospin diffusion data S(r)=12.5(r/ro)2/3+17.6(r/ro) Projectile 0.4gi 1 124Sn gi Target 112Sn 0.45gi 0.95 Degree of isospin diffusion

  14. gi S(r)=12.5(r/ro)2/3+17.6(r/ro) Symmetry energy constraints from HIC arXiv:1204.0466 0.4gi 1 Consistent with previous isospin diffusion constraints Chen, Li et al., Phys. Rev. Lett. 94 (2005) 032701

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

  16. Extrapolation from 208Pb radius to pressure in n-star Typel & Brown, PRC 64, 027302 (2001) Steiner et al., Phys. Rep. 411, 325 (2005) P(r=0.1 fm) (MeV/fm3) =L/3r0

  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) Introduction • 208Pb skin measurements • PREX • antiprotonic atom systematics • 208Pb(p,p) • 208Pb(p,p’) –dipole polarizability • Dipole Pygmy Resonance (DPR) Summary and Outlook

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

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

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

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

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

  23. Challenge II: Constraints at very low density J.B. Natowitz et al, PRL 104 (2010) 202501 Esym(n)/Esym(n0) Symmetry energy at r<0.05ro, T<10 MeV is dominated by correlations and cluster formation

  24. Challenge III: Constraints at supra-normal densitieswith Heavy Ion Collisions • Isospin Observables: • Neutron/proton and t/3He and light isotopes energy spectra • • flow • – px vs. y (v1) • – Elliptic flow (v2) • – Disappearance of flow (balance energy) • • π+/π-spectra • • π+/π-flow RIBF, FRIB, KoRIA International Collaboration

  25. ASY-EOS experiment @GSI, May 2011 Au+Au @ 400 AMeV 96Zr+96Zr @ 400 AMeV 96Ru+96Ru@ 400 AMeV ~ 5x107 Events for each system TofWall Beam Line Krakow array Chimera target Shadow Bar MicroBall Land (notsplitted) Russotto & Lemmon

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

  27. arXiv:1204.0466 Acknowledgement: NSCL/HiRA group

  28. 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: TadaAkiIsobe, 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: AbdouChbihi CIAE, PU, CAS, China: Yingxun Zhang, Zhuxia Li, Fei Lu, Y.G. Ma, W. Tian Korea University, Korea: Byungsik Hong A Time projection chamber is being built in the US to measure p+/p- & light charge particles in RIKEN

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

  30. 0.16-0.27 fm Extracting the 208Pb skin thickness from HIC arXiv:1204.0466 Typel & Brown, PRC 64, 027302 (2001) Steiner et al., Phys. Rep. 411, 325 (2005)

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

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

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

  34. Symmetry coefficient from Isobaric Analog States aa(A) Charge invariance: invariance of nuclear interactions under rotations in n-p space Corrections for microscopic effects + deformation So = 31.5 MeV; L = 75.6 – 107.1 MeV So = 33.5 MeV; L = 80.4 – 113.9 MeV Danielewicz & Lee, NPA818, 36 (2009)

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

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

  37. Skin thickness from Pygmy Dipole Resonance Collective oscillation of neutron skin against the Core  dRnp dRnp(208Pb)= 0.20±0.02 fm L=65.1±15.5 MeV So=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)

  38. Systematics of anti-protonic atoms 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) Antiproton probe the extreme tail of nuclei. Data from 26 nuclei: 40Ca to 238U Strong correlation between dRnp and asymmetry d. dRnp d=(N-Z)/A dRnp= 0.16±(0.02)stat±(0.04)syst±(0.05)theo Large experimental and theoretical uncertainties Need better quality data & theory

  39. Constraining the EoS using Heavy Ion collisions E/A (,) = E/A (,0) + d2S(); d= (n- p)/ (n+ p) = (N-Z)/A Au+Au collisions E/A = 1 GeV) 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. pressure contours density contours

  40. in plane • out of plane Determination of symmetric matter EOS from nucleus-nucleus collisions Danielewicz et al., Science 298,1592 (2002). The curves represent calculations with parameterized Skyrme mean fields They are adjusted to find the pressure that replicates the observed flow. • Sideward Flow 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.

  41. NSCL experiments 05049 & 09042Density dependence of the symmetry energy with emitted neutrons and protons& Investigation of transport model parameters (May & October, 2009 ) GSI S394, May 2011 NSCL experiment 07038 Precision Measurements of Isospin Diffusion, June 2011)

  42. arXiv:1204.0466

  43. Definition of Symmetry Energy E/A (,) = E/A (,0) + d2S(); d= (n- p)/ (n+ p) = (N-Z)/A

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

  45. 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

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

  47. Laboratory experiments to measure the 208Pb neutron skin PREX (Parity Radius experiment) measures Rnp of 208Pb Why 208Pb? It has excess of neutrons dRnp=<rn2>1/2 -<rp2>1/2 It is doubly-magic Its first excited state is 2.6 MeV Expected uncertainty: APV (Parity-violating Asymmetry )~3% dRn ~1% Ran in Jefferson Lab in Spring 2010. 208Pb Phys Rev Let. 108, 112502 (2012)

  48. ?? Danielewicz, Lacey, Lynch, Science 298,1592 (2002) Pressure (MeV/fm3) Density dependence of Symmetry Energy E/A (,) = E/A (,0) + d2S(); d= (n- p)/ (n+ p) = (N-Z)/A