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The Nuclear Symmetry Energy and Neutron Skin Thickness of Finite Nuclei

The Nuclear Symmetry Energy and Neutron Skin Thickness of Finite Nuclei. Collaborators ： Che Ming Ko and Jun Xu (TAMU) Bao-An Li (TAMU-Commerce) Xin Wang (SJTU) Bao-Jun Cai , Rong Chen, Peng-Cheng Chu, Zhen Zhang (SJTU). Lie-Wen Chen ( 陈列文 )

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The Nuclear Symmetry Energy and Neutron Skin Thickness of Finite Nuclei

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  1. The Nuclear Symmetry Energy and Neutron Skin Thickness of Finite Nuclei Collaborators： Che Ming Ko and Jun Xu (TAMU) Bao-An Li (TAMU-Commerce) Xin Wang(SJTU) Bao-Jun Cai, Rong Chen, Peng-Cheng Chu, Zhen Zhang(SJTU) Lie-Wen Chen (陈列文) (INPAC and Department of Physics, Shanghai Jiao Tong University. lwchen@sjtu.edu.cn) 第十三届全国核结构研讨会暨第九次全国“核结构与量子力学”专题讨论会,2010年7月24-30日,赤峰,内蒙古

  2. Outline • EOS of asymmetric nuclear matter and the symmetry energy • Constraints on density dependence of symmetry energy from nuclear structure and reactions – Present status • Constraining the symmetry energy with the neutron skin thickness of heavy nuclei in a novel correlation analysis • Symmetry energy and nuclear effective interactions • Summary and outlook Main References: B.A. Li, L.W. Chen, and C.M. Ko, Phys. Rep. 464, 113-281 (2008) L.W. Chen, B.J. Cai, C.M. Ko, B.A. Li, C. Shen, and J. Xu, PRC80, 014322 (2009) L.W. Chen, C.M. Ko, B.A. Li and J. Xu, arXiv:1004.4672, 2010

  3. On Earth!!! Transport Theory In Heaven!!! General Relativity EOS for Asymmetric Nuclear Matter Isospin Effects in HIC’s … Neutron Stars … Many-Body Theory Nuclear Force Many-Body Theory Structures of Neutron-rich Nuclei, … EOS of asymmetric nuclear matter and the symmetry energy Isospin in Nuclear Physics Reactions & Structures of Neutron-Rich Nuclei (CSR/Lanzhou, FRIB, GSI, RIKEN……) Most uncertain property of an asymmetric nuclear matter Density Dependence of the Nuclear Symmetry Energy Isospin Nuclear Physics What is the isospin dependence of the in-medium nuclear effective interactions???

  4. EOS of Nuclear Matter

  5. (Isospin) Symmetry energy term Symmetry energy including surface diffusion effects (ys=Sv/Ss) The Nuclear Symmetry Energy Liquid-drop model W. D. Myers, W.J. Swiatecki, P. Danielewicz, P. Van Isacker, A. E. L. Dieperink,……

  6. The Nuclear Symmetry Energy Symmetric Nuclear Matter (relatively well-determined) Symmetry energy term (poorly known) The Nuclear Matter Symmetry Energy (Parabolic law) EOS of Isospin Asymmetric Nuclear Matter

  7. The Symmetry Energy The multifaceted influence of the nuclear symmetry energyA.W. Steiner, M. Prakash, J.M. Lattimer and P.J. Ellis, Phys. Rep. 411, 325 (2005). The symmetry energy is also related to some issues of fundamental physics: 1. The precision tests of the SM through atomic parity violation observables (Sil et al., PRC05) 2. Possible time variation of the gravitational constant (Jofre etal. PRL06; Krastev/Li, PRC07) 3. Non-Newtonian gravity proposed in grand unification theories (Wen/Li/Chen, PRL10)

  8. Nuclear Matter EOS: Many-Body Approaches • Microscopic Many-Body Approaches Non-relativistic Brueckner-Bethe-Goldstone (BBG) Theory Relativistic Dirac-Brueckner-Hartree-Fock (DBHF) approach Self-consistent Green’s Function (SCGF) Theory Variational Many-Body (VMB) approach …… • Effective Field Theory Density Functional Theory (DFT) Chiral Perturbation Theory (ChPT) …… • Phenomenological Approaches Relativistic mean-field (RMF) theory • Relativistic Hartree-Fock (RHF) • Non-relativistic Hartree-Fock (Skyrme-Hartree-Fock) Thomas-Fermi (TF) approximations • Phenomenological potential models ……

  9. Z.H. Li et al., PRC74, 047304(2006) Dieperink et al., PRC68, 064307(2003) Chen/Ko/Li, PRC72, 064309(2005) Chen/Ko/Li, PRC76, 054316(2007) BHF Esym: Many-Body Approaches

  10. Symmetry energy around saturation density Promising Probes of the Esym(ρ)(an incomplete list !)

  11. Esym: Isospin Diffusion in HIC’s Symmetry energy, isospin diffusion, in-medium cross section Chen/Ko/Li, PRL94,032701 (2005) Isospin dependent BUU transport model Li/ Chen, PRC72, 064611(2005) Chen/Ko/Li, PRC72,064309 (2005) Isospin Diffusion Data  Esym(ρ0)=31.6 MeV L=88±25 MeV

  12. Esym: Isoscaling in HIC’s Constraining Symmetry Energy by Isocaling: TAMU Data Shetty/Yennello/ Souliotis, PRC75,034602(2007); PRC76, 024606 (2007) Isoscaling Data  Esym(ρ0)=31.6 MeV L=65 MeV Consistent with isospin diffusion data!

  13. Esym: Isospin diffusion and double n/p ratio in HIC’s ImQMD: n/p ratios and two isospin diffusion measurements Tsang/Zhang/Danielewicz/Famiano/Li/Lynch/Steiner, PRL 102, 122701 (2009) ImQMD: Isospin Diffusion and double n/p ratio  Esym(ρ0)=28 - 34 MeV L=38 - 103 MeV

  14. Esym: Nuclear Mass in Thomas-Fermi Model Myers/Swiatecki, NPA 601, 141 (1996) Thomas-Fermi Model analysis of 1654 ground state mass of nuclei with N,Z≥8 Thomas-Fermi Model + Nuclear Mass  Esym(ρ0)=32 .65 MeV L=49.9 MeV

  15. Esym: Pygmy Dipole Resonances Pygmy Dipole Resonances of 130,132Sn  Esym(ρ0)=32 ± 1.8 MeV L=43.125 ± 15 MeV Pygmy Dipole Resonances of 68Ni and 132Sn Esym(ρ0)=32.3 ± 1.3 MeV, L=64.8 ± 15.7 MeV

  16. Esym: IAS+LDM Danielewicz/Lee, NPA 818, 36 (2009) Esym from Isobaric Analog States + Liquid Drop model with surface symmetry energy IAS+Liquid Drop Model with Surface Esym  Esym(ρ0)=32.5 ± 1 MeV L=94.5 ± 16.5 MeV

  17. Esym: Droplet Model Analysis on Neutron Skin Droplet Model + N-skin  Esym(ρ0)=31.6 MeV, L=66.5 ± 36.5 MeV

  18. Esym: Droplet Model Analysis on Neutron Skin Droplet Model + N-skin  Esym(ρ0)=28 - 35 MeV, L=55 ± 25 MeV

  19. Esym around normal density 9 constraints on Esym (ρ0) and L from nuclear reactions and structures Esym(ρ0)=28 - 35 MeV L=28 - 111 MeV Still within large uncertain region !!

  20. The Nuclear Neutron Skin Bodmer, Nucl. Phys. 17, 388 (1960) Sprung/Vallieres/Campi/Ko, NPA253, 1 (1975) Shlomo/Friedman, PRL39, 1180 (1977) …… For heavier stable nuclei: N>Z Neutron Skin Thickness:

  21. The Esym vs. Nuclear Neutron Skin Chen/Ko/Li, PRC72,064309(2005) Good linear Correlation: S-L

  22. The Esym vs. Nuclear Neutron Skin Chen/Ko/Li, PRC72,064309(2005) For heavier nuclei: Still good linear correlation between S-L B.A. Brown, PRL85,5296(2000)

  23. _________ The Skyrme HF Energy Density Functional Standard Skyrme Interaction: There are more than 120 sets of Skyrme- like Interactions in the literature Agrawal/Shlomo/Kim Au PRC72, 014310 (2005) Yoshida/Sagawa PRC73, 044320 (2006) Chen/Ko/Li/Xu arXiv:1004.4672 9 Skyrme parameters: 9 macroscopic nuclear properties:

  24. The Skyrme HF Energy Density Functional Chen/Cai/Ko/Li/Shen/Xu, PRC80, 014322 (2009): Modified Skyrme-Like (MSL) Model Chen/Ko/Li/Xu, arXiv:1004.4672

  25. The Skyrme HF with MSL0 Chen/Ko/Li/Xu, arXiv:1004.4672

  26. Important Terms For heavy nuclei 208Pb and 120Sn: Δrnp is strongly correlated with L, moderately with Esym(ρ0), a little bit with m*s,0 For medium-heavy nucleus 48Ca: Δrnp correlation with Esym is much weaker; It further depends on GV and W0 Correlations between Nuetron-Skin thickness and macroscopic Nuclear Properties

  27. Constraining Esym with Neutron Skin Data Neutron skin constraints on L and Esym(ρ0) are insensitive to the variations of other macroscopic quantities.

  28. Constraining Esym with Neutron Skin Data and Heavy-Ion Reactions N-Skin + HIC (~independent of Esym(ρ0)) A quite stringent constraint on Δrnp of 208Pb: Core-Crust transition density in Neutron stars:

  29. Esym: Global nucleon optical potential Xu/Li/Chen, arXiv:1006.4321v1, 2010 Global nucleon optical potential  Esym(ρ0)=31.3 ± 4.5MeV, L=52.7 ± 22.5 MeV Consistent with Sn neutron skin data!

  30. Symmetry energy and Nuclear Effective Interaction Chen/Ko/Li, PRC72,064309 (2005) Chen/Ko/Li, PRC76, 054316(2007) L=58 ± 18 MeV: only 32/118 L=58 ± 18 MeV: only 8/23

  31. IV. Summary and Outlook • We have proposed a novel method to explore transparently the correlation between observables of finite nuclei and nuclear matter properties. • The neutron skin thickness of heavy nuclei provides reliable information on the symmetry energy. The existing neutron skin data of Sn isotopes give important constraints on the symmetry energy and the neutron skin of 208Pb • Combining the constraints on Esym from neutron skin with that from isospin diffusion and double n/p ratios in HIC’s impose quite accurate constraint of L=58±18 MeV approximately independent of Esym • Our correlation analysis method can be generalized to other mean- fieldmodels (e.g., RMF) or density functional theories and a number of other correlation analyses are being performed (giant resonance, shell structure,,…… )

  32. 谢 谢！

  33. Giant Monopole Resonance EOS of Symmetric Nuclear Matter (1) EOS of symmetric matter around the saturation density ρ0 K0=231±5 MeV PRL82, 691 (1999) Recent results: K0=240±10 MeV G. Colo et al. U. Garg et al. S. Shlomo et al. __

  34. EOS of Symmetric Nuclear Matter (2) EOS of symmetric matter for 1ρ0< ρ < 3ρ0 from K+ production in HIC’s J. Aichelin and C.M. Ko, PRL55, (1985) 2661 C. Fuchs, Prog. Part. Nucl. Phys. 56, (2006) 1 C. Fuchs et al, PRL86, (2001) 1974 Transport calculations indicate that “results for the K+ excitation function in Au + Au over C + C reactions as measured by the KaoS Collaboration strongly support the scenario with a soft EOS.” See also: C. Hartnack, H. Oeschler, and J. Aichelin, PRL96, 012302 (2006)

  35. Use constrained mean fields to predict the EOS for symmetric matter Width of pressure domain reflects uncertainties in comparison and of assumed momentum dependence. The highest pressure recorded under laboratory controlled conditions in nucleus-nucleus collisions High density nuclear matter 2 to 5ρ0 (3) Present constraints on the EOS of symmetric nuclear matter for 2ρ0< ρ < 5ρ0 using flow data from BEVALAC, SIS/GSI and AGS EOS of Symmetric Nuclear Matter P. Danielewicz, R. Lacey and W.G. Lynch, Science 298, 1592 (2002)

  36. Transport model for HIC’s Isospin-dependent BUU (IBUU) model • Solve the Boltzmann equation using test particle method • Isospin-dependent initialization • Isospin- (momentum-) dependent mean field potential • Isospin-dependent N-N cross sections • a. Experimental free space N-N cross section σexp • b. In-medium N-N cross section from the Dirac-Brueckner • approach based on Bonn A potential σin-medium • c. Mean-field consistent cross section due to m* • Isospin-dependent Pauli Blocking EOS

  37. Transport model: IBUU04 Isospin- and momentum-dependent potential (MDI) Das/Das Gupta/Gale/Li, PRC67,034611 (2003) Chen/Ko/Li, PRL94,032701(2005) Li/Chen, PRC72, 064611 (2005)

  38. Esym: Isospin Diffusion in HIC’s Isospin Diffusion/Transport ______________________________________ How to measure Isospin Diffusion? PRL84, 1120 (2000) A+A,B+B,A+B X: isospin tracer

  39. Esym: Isoscaling in HIC’s Isoscaling in HIC’s Isoscaling observed in many reactions M.B. Tsang et al. PRL86, 5023 (2001)

  40. High density behaviors of Esym Heavy-Ion Collisions at Higher Energies n/p ratio of the high density region Isospin fractionation! Li/Yong/Zuo, PRC 71, 014608 (2005)

  41. High density behaviors of Esym: kaon ratio Aichelin/Ko, PRL55, 2661 (1985):Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities Theory: Ferini et al., PRL97, 202301 (2006) Exp.: Lopez et al. FOPI, PRC75, 011901(R) (2007) K0/K+ yield is not so sensitive to the symmetry energy! Lower energy and more neutron-rich system??? Subthreshold K0/K+ yield may be a sensitive probe of the symmetry energy at high densities

  42. High density behaviors of Esym: pion ratio A Quite Soft Esym at supra-saturation densities ??? Zhang et al.,PRC80,034616(2009) IBUU04, Xiao/Li/Chen/Yong/Zhang, PRL102,062502(2009) Pion Medium Effects? Xu/Ko/Oh PRC81, 024910(2010) Threshold effects? …… IDQMD, Feng/Jin, PLB683, 140(2010)

  43. High density behaviors of Esym: n/p v2 A Stiff Esym at supra-saturation densities ??? W. Trauntmann et al., arXiv:1001.3867

  44. Horowitz and Schwenk, Nucl. Phys. A 776 (2006) 55 S. Kowalski, et al., PRC 75 (2007) 014601. Esym at very low densities: Clustering effects

  45. Esym at very low densities: Clustering effects J. B. Natowitz et al., arXiv:1001.1102 PRL, 2010

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