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

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

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

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

HIRFL-CSR in IMP, Lanzhou Building 2# Building 6# CSRm CSRe SFC SSC SFC: several to 10 AMeV SSC: tens to 100 AMeV CSRm:520AMeV( 238 U 72+ ), 1.1 AGeV( 12 C 6+ ), 2.88 GeV(p) CSRe: 520AMeV( 238 U 72 ), 0.76 AGeV ( 12 C 6+ ) North External Target High Energy Density Cancer Therapy CSRe Internal Target CSRm Internal Target 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

与 CSR 相关的核物质相图 同位旋非对称度 β 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 …….. 弱束缚核性质 核子核子有效相互作用 ……….

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

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

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

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

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

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

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

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

Brueckner-Hartree-Fock (BHF) 理论 Brueckner, Bethe, Goldstone et al., 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, … ， )  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 … ， ) √  微观三体核力重排项的提出和实现（ Zuo,Lombardo, … ， 2006)

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))

Brueckner Theory of Nuclear Matter

Microscopic Three-body Forces Z-diagram 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

Effective Microscopic Three-body Force Effective three-body force → Defect function:  (r 12 )=  (r 12 ) –  (r 12 ) ★ Short-range nucleon correlations (Ladder correlations) ★ Evaluated self-consistently at each iteration  Effective TBF ---- Density dependent  Effective TBF ---- Isospin dependent for asymmetric nuclear matter

EOS of Nuclear Matter

W. Zuo, A. Lejeune, U.Lombardo, J.F.Mothiot, NPA706(2002)418 EOS of SNM & saturation properties  (fm -3 ) E A (MeV) K (MeV) 0.19– – Saturation properties: TBF is necessary for reproducing the empirical saturation property of nuclear matter in a non-relativistic microscopic framework.

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

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

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

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

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

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

Symmetry Potential: The isovector Part

W. Zuo, I. Bombaci, U. Lombardo, PRC 60 (1999) 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

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

TBF rearrangment contribution in symmetric nuclear matter 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) Effective mass

Isospin dependence of the TBF rearrangment effect 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 Symmetry potential Effective masses 1. Remarkable reduction of the neutron and proton effective masses. 2. Suppression of the isospin splitting in neutron-rich matter at high densities.

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

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

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

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

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

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。 总结 :

谢谢 ! THANK YOU!