非对称核物质性质

1. 非对称核物质性质 • 左维 • 中国科学院近代物理研究所 Outline: 1. Introduction (Motivation) 2. Theoretical approaches 3. Results 4. Summary and conclusion 北京，2010年6月

2. 非对称核物质性质 原子核多体理论与核子-核子有效相互作用

3. 低密非对称核物质性质 Isospin diffusion 关键性进展 Experiments at the NSCL/MSU：Sn+Sn， Ebeam/A=50 MeV Iso-scaling 结论：

4. 高密区对称能的密度依赖性 Z. G. Xiao etal, Phys. Rev. Lett. 102(2009)062502 Z.-Q. Feng, G.-M. Jin, Phys. Lett. B 683 (2010) 140

5. HIRFL-CSR in IMP, Lanzhou SFC: several to 10 AMeV SSC: tens to 100 AMeV North Building 2# SSC External Target SFC CSRe Internal Target CSRe Cancer Therapy Building 6# • Nuclear Physics • Reaction reduced by RIB • Effective strong interaction in dense matter • EOS under extreme conditions (density, isospin,temperature) • Isospin Physics and related subjects in astrophysics • Structure of nuclei far from stable line CSRm High Energy Density CSRm:520AMeV(238U72+), 1.1 AGeV(12C6+), 2.88 GeV(p) CSRe: 520AMeV(238U72 ), 0.76 AGeV (12C6+) CSRm Internal Target

6. 与CSR相关的核物质相图 弱束缚核性质 核子核子有效相互作用 ………. 高密区非对称核物质性质 中子星性质 中子星冷却 核子-核子相互作用 核微观多体理论 …….. 同位旋非对称度β

7. CSR能区高密非对称核物质的形成 Soft Esym Stiff Esym Bao-An Li, Gao-Chan Yong, Wei Zuo, Phys. Rev. C71，014608(2005)

8. CSR能区高密非对称核物质状态方程的灵敏观测量CSR能区高密非对称核物质状态方程的灵敏观测量 Soft Esym Stiff Esym

9. High-density behavior of symmetry energy G.C.Yong, B.A.Li, W. Zuo, PRC71(2006)014608; 044604

10. Double n/p ratio B.A.Li, L.W.Chen,G.C.Yong, W. Zuo, PLB634(2006)378

11. Theoretical Approaches • Skyrme-Hartree-Fock • Relativistic Mean Field Theory, Relativistic Hartree-Fock • Variational Approach • Green’s Function Theory • Brueckner Theory • Dirac-Brueckner Approach • Effective Field Theory

12. 研究现状 唯像多体理论： SHF和RMF理论 B. A. Li， L. W. Chen， C. M. Ko，Phys. Rep. 464（2008）113

13. 微观多体理论： 非相对论BHF理论 Z.H. Li, U. Lombardo, H.-J. Schulze, Zuo et al., PRC74(2006)047304

14. 微观多体理论： 相对论Dirac-BHF理论 Klahn et al. Nucl-th/0602038 Krastev and Sammarruca Nucl-th/0601065

15. Brueckner-Hartree-Fock (BHF) 理论 Brueckner, Bethe, Goldstone et al., 1954--1967 重要进展： BHF理论方法的扩展(EBHF)：在单粒子性质中考虑基态关联效应，改善其内在自洽性（Lejeune,Mahaux,Baldo,Bombaci,Lombardo,Zuo,…，1970--2005) 同位旋相关的BHF与EBHF方法（Bombaci,Lombardo,Zuo,…) 空穴线展开收敛性的证实(Song,Baldo,Lombardo,…,1998）√ 引入微观三体核力（Lejeune,Lombardo,Zuo…，1989-2002) √ 微观三体核力重排项的提出和实现（Zuo,Lombardo,…，2006)

16. Bethe-Goldstone Theory • Bethe-Goldstone equation and effective G-matrix → Nucleon-nucleon interaction: ★ Two-body interaction : AV18 (isospin dependent) ★ Effective three-body force →Pauli operator : →Single particle energy : →“Auxiliary” potential : continuous choice Confirmation of the hole-line expansion of the EOS under the contineous chioce (Song,Baldo,Lombardo,et al,PRL(1998))

17. Brueckner Theory of Nuclear Matter

18. Microscopic Three-body Forces • Based on meson exchange approach • Be constructed in a consistent way with the adopted two-body force---------microscopic TBF ! • Grange et.al PRC40(1989)1040 Z-diagram

19. Effective Microscopic Three-body Force • Effective three-body force • →Defect function: (r12)= (r12) – (r12) • ★Short-range nucleon correlations (Ladder correlations) • ★Evaluated self-consistently at each iteration • Effective TBF ---- Density dependent • Effective TBF ---- Isospin dependent for asymmetric nuclear matter

20. EOS of Nuclear Matter

21. EOS of SNM & saturation properties TBF is necessary for reproducing the empirical saturation property of nuclear matter in a non-relativistic microscopic framework. Saturation properties: W. Zuo, A. Lejeune, U.Lombardo, J.F.Mothiot, NPA706(2002)418

22. Isospin dependence of the EOS W. Zuo, A. Lejeune, U.Lombardo, J.F.Mothiot, Nucl.Phys.A706(2002)418 W. Zuo et al., Phys. Rev. C69 (2004) 064001

23. Density dependence of symmetry energy Symmetry energy from different approaches Thermal effect TBF effect ？ W. Zuo et al. PRC 69(2004)064001 W. Zuo, A. Lejeune, U.Lombardo, J.F.Mothiot, EPJA 14(2002)469 C. Fuchs and H. H. Wolter, EPJA30(2006)5

24. Critical temperature for liquid-gas phase transition in warm nuclear matter SHF : 14-20 MeV RMT : 14 MeV DBHF: 10 MeV BHF(2BF): 16 MeV BHF(TBF): 13 MeV BHF(Z-d): 11 MeV Z-diagram Full TBF A possible explanation of the discrepancy between the DBHF and BHF predictions W. Zuo, Z.H.Li,A. Li, U.lombardo, NPA745(2004)34.

25. Single Particle Properties • Neutron and proton s.p. potential • Isovector part : Symmetry potential • Isosping splitting of effective mass • TBF rearrangement cobtribution

26. Single Particle Potential beyond the mean field approximation: 1. Single particle potential at lowest BHF level 2. Ground state correlations 3. TBF rearrangement Full s.p. potential：

27. Single particle potential at the BHF level In neutron rich matter : Up<Un at low momenta Up>Un at high enough momenta W. Zuo, L.G. Gao, B.A. Li et al., Phys. Rev. C72 (2005)014005 .

28. Symmetry Potential: The isovector Part

29. Pauli rearrangement contribution: Ground state correlation 1. The Pauli rearrangement is repulsive 2. It affects maily the s.p. potential at low momenta and vanishes repaidly above Fermi momentum 3. It distories the linear beta-dependence of the s.p. potential W. Zuo, I. Bombaci, U. Lombardo, PRC 60 (1999) 024605

30. Neutron-proton effective mass splitting in neutron-rich matter neutrons M*n > M*p protons Comparison to other predictions: DBHF: mn* > mp* Dalen et al., PRL95(2005)022302 Z. Y. Ma et al., PLB 604 (2004)170 F. Sammarruca et al., nucl-th/0411053 Skyrme-like interactions: mp* < mn* or mn* < mp* B. A. Li et al., PRC69(2004)064602

31. TBF rearrangment contribution in symmetric nuclear matter Effective mass 1. The TBF induces a strongly repulsive rearrangement modification of the s. p. potential at high densities and momenta. 2. The TBF rearrangement contribution is strongly momentum dependent at high densities and momenta. Zuo, Lombardo, Schulze, Li, Phys. Rev. C74 (2006) 017304

32. Isospin dependence of the TBF rearrangment effect Symmetry potential Effective masses 1. Negligible at low densities around and below the Fermi momentum. 2. Enhancement of the repulsion for neutrons and the attraction for protons at high densities 1. Remarkable reduction of the neutron and proton effective masses. 2. Suppression of the isospin splitting in neutron-rich matter at high densities.

33. S.P. Potential：Ground state correlation and TBF rearrangement effect

34. Proton fraction in β-stable neutron star matter A. Lejeune, U.Lombardo, W. Zuo, Phys.Lett. B477(2000)45

35. Neutron Star Structure Kaon condensation in neutron stars Variational RMT BHF + 3BF W. Zuo. A. Li, Z.H.Li, U. Lombardo, PRC70(2004)055802. X.R.Zhou et al., PRC69(2004)018801

36. W. Zuo et al., PLB 595(2004)44 1S0 neutron and proton gap in -stable neutron star matter : TBF effect pp nn TBF suppresses strongly the 1S0 proton superfluidity in neutron stars 1. It reduces the energy gap from ~1 to ~0.5 2. It suppresses largely the density region of the superfluidity no significant effect since nn pairs are embedded inlow density neutron background: Vnn (3) ~ 0

37. 3PF2 neutron pairing gap in a neutron star : TBF effect W. Zuo et al., Phys. Rev. C78(2008)015805

38. 总结: 1）发展和改进了微观三体核力模型和BHF理论方法，改善了BHF理论的内在热力学自洽性及其对于核物质饱和点性质的描述 2）提出并在扩展的微观多体BHF理论框架内中实现了微观三体核力重排贡献的计算，解决了非相对论BHF理论预言的光学势在高密度和高动量区域吸引性过强和动量依赖性过弱的问题 3）在扩展的微观多体BHF理论框架内预言了非对称核物质中质子和中子单粒子势和有效质量的同位旋劈裂性质，提出了有效质量同位旋劈裂的微观机制。 4）系统研究了非对称核物质的性质，预言了非对称核物质的状态方程对于非对称度的依赖性满足平方规律并预言了对称能在低密度区域和高密度区域具有的不同密度依赖关系 5）利用微观多体理论预言了微观三体核力对中子星物质中质子超流性具有强烈的抑制作用，并预言了新的质子1S0态超流性强度参量。

39. 谢谢!THANK YOU!