1. 1 Skyrme Hartree-Fock 理论 对奇异性原子核性质的研究 周先荣 厦门大学物理系 2012.4.11-16 ，第十四届全国核结构大会，湖州

2. 2 奇异性原子核 超核： 核系统中束缚 Λ 、 Σ 或 Ξ 等超子 K- 核： 核系统中束缚一个 K - 介子 奇异性原子核是指带有奇异量子数（ s 夸克） 的核多体系统。

3. 3 Hypernuclei

4. 4 World of matter made of u, d, s quarks N Z N u ~ N d ~ N s Higher density ３ -D nuclear chart Strangeness in neutron stars (  > 3 - 4  0 ) Strange hadronic matter (A → ∞) ,  Hypernuclei ,  Hypernuclei Strangeness 0 -2 “Stable” Lower density n-rich nuclei

5. 5 Present Status of  Hypernuclear Spectroscopy O. Hashimoto and H. Tamura, Prog. Part. Nucl. Phys. 57 (2006) 564. (2006)

6. 6 Theoretical studies Studies based on spherical symmetry: 1. Relativistic mean-field model (RMF) 2. Skyrme Hartree-Fock model (SHF) 3. Woods-Saxon potential + YN interaction 4. Few-body theory

7. 7 Theoretical studies Deformed calculations: Deformed HF with nonrealistic interaction: T. H. Ho and A.Volkov, Phys. Lett. B30, 303, 1969. W. H. Bassichis, A. Gal, Phys. Rev. C1, 28, 1970. J. Zofka, Czech, J. Phys. B30, 95, 1980. Nilsson Model: assume the same deformation for core and hypernuclei: K. Hagino, Phys. Rev. C63, 044318, 2001 Deformed SHF with Microscopic YN int. (self-consistent) X.-R. Zhou, et al., Phys. Rev. C 76, 034312 (2007)

8. 8 Theoretical studies Relativistic mean-field model (RMF): Myaing Thi Win et al., Phys. Rev. C 78, 054311 (2008) Triaxial SHF with Skyrme-like YN interaction: Myaing Thi Win, et al., Phys. Rev. C 83, 014301 (2011) Antisymmetrized molecular dynamics (AMD): M. Isaka, et al., Phys. Rev. C 83, 044323 (2011) Triaxial RMF: Bing-Nan Lu ( 吕炳楠 ), Phys. Rev. C 84, 014328 (2011)

9. 9 Why to study deformations of hypernuclei Many p-shell and sd-shell nuclei are deformed. For example, experimentally, 10 B and 11 C have large quadrupole moments. F. Ajzenberg-Selove, Nucl. Phys. A490, 1 (1988); A506, 1(1990). Also, 8 Be is known to be strongly deformed due to its double-α structure.

10. 10 Microscopic hyperon-nucleon interaction for deformed hypernuclei B Y, Hypernuclear Structure Effective YN interaction BHF cal. for asymmetric matter Free YN interaction DSHF MF cal. YN: Nijmegen soft-core hyperon-nucleon potential NSC89 NN: Argonne v18 nucleon-nucleon interaction

11. 11 Extended DSHF including hyperon-nucleon interaction Total energy of a hypernucleus in extended DSHF where the energy density SHF Due to the NY force,

12. 12 Energy density due to hyperons where the last term corresponds to the kinetic energy contribution of the Λ’s. The hyperon effective mass extracted from the BHF single-particle potential, It can be constructed from BHF energy density,

13. 13 Finally, the energy density is written as The parameterizations of numerical results: Parameterizations

14. 14 Extended SHF equation Minimizing the total energy of the hypernucleus, one arrives with extended SHF equation

15. 15 For light nuclei, For medium-mass and heavy nuclei, Pairing interaction Nucl. Phys. A722, c183, 2003 Euro. Phys. J. A8, 59, 2000 The pairing interaction is taken to be a density- dependent delta force Nucl. Phys. A551, 434 (1993)

16. 16 Binding energies vs deformations 0.65 0.63 0.55 0.52 0.55 X.-R. Zhou, et.al, PRC76, 034312(2007)

17. 17 Binding energies vs deformations X.-R. Zhou, H.-J. Schulze, et.al, PRC76, 034312(2007)

18. 18 Binding energies vs deformations X.-R. Zhou, H.-J.Schulze, et.al, PRC76, 034312(2007)

19. 19 Other theoretical studies Relativistic mean-field model (RMF): Myaing Thi Win et al., Phys. Rev. C 78, 054311 (2008) Triaxial SHF with Skyrme-like YN interaction: Myaing Thi Win, et al., Phys. Rev. C 83, 014301 (2011) Antisymmetrized molecular dynamics (AMD): M. Isaka, et al., Phys. Rev. C 83, 044323 (2011) Triaxial RMF: Bing-Nan Lu ( 吕炳楠 ), Phys. Rev. C 84, 014328 (2011)

20. 20 Shrinking effect of hyperons B(E2) ∝ | | 2 ∝ R 4 or (  ) 2 R  similar to Q-moment Motoba, Bando, Ikeda Prog.Theor.Phys. 70 (1983) 189. 4He + d +  model ～ 20% shrinkage

21. 21 The effect of hyperon in neutron-rich nuclei X.-R. Zhou, H.-J. Schlze, et.al, PRC78, 054306(2008)

22. 22 The Oxygen isotopes X.-R. Zhou, et.al, PRC78, 054306(2008) exp.

23. 23 Kaonic nuclei

24. 24 K- 核的束缚态？ 1. 核物质中可能存在 K - 介子凝聚 D. B. Kaplan and A. E. Nelson, Phys. Lett. B 175, 57(1986). 2. 可能存在分立的 K - 介子的深束缚态 -K- 核 Y. Akaishi and T. Yamazaki, Nucl. Phys. A 684, 409 (2001). Y. Akaishi and T. Yamazaki, Phys. Rev. C 65, 044005 (2002).

25. 25 K- 核实验信息 2. FUNUDA 实验组宣称他们探测到了 K - pp 的 K - 介子束缚态 M. Agnello, G. Beer, L. Benussi, M. Bertani, S. Bianco, E. Botta, et al., [FUNUDA collaboration], "Evidence for a Kaon-Bound State K - pp Produced in K - Absorption Reactions at Rest", Phys. Rev. Lett.94, 212303 (2005). T. Kishimoto, T. Hayakawa, S. Ajimura, S. Minami, A. Sakaguchi, Y. Shimizu, et al., "Kaonic nuclei probed by the in-flight (K−,n) reaction", Nucl. Phys. A 754, 383-390 (2005). 1. T.Kishmoto 等人宣称他们探测到了 K- 核的深束缚信号 T. Hiraiwa, S. Ajimura, G. Beer, H. Bhang, M. Bragadireanu, P. Buehler, et. al.,"The search for deeply-bound kaonic nuclear states at J-PARC", Int. J. Mod. Phys. A 26, 561-563 (2011). 3. 实验上未放弃寻找

26. 26 Extended Skyrme Hartree-Fock including nucleon-kaon interaction Skyrme Hartree-Fock equation ：

27. 27 Kaonic nuclei DSHF + Nucleon-kaon interaction (meson-exchange chiral model) ： According to chiral model, the K - θ ： chiral angle f: meson decay constant (93MeV)

28. 28 Including NK Int.

29. 29 Including NK Int.

30. Mean field changed by kaons: Including NK Int. Local chemical potential : Where μ S is determined by

31. 31

32. 32 Summary 2. The main qualitative effect of added hyperons is demonstrated: the nuclei close to the drip line are stabilized and new isotopes are potentially made available. 1.The calculated core nuclei and the corresponding hypernuclei have similar deformations with the same sign when the core nuclei are well deformed.

33. 33 Prospect 2. The deformation of K-nuclei? 1. Properties of K-nuclei with SHF.

34. 34 Cooperators H.-J. Schulze, University of Catania, Italy

35. 35 Thank you! Welcome to Xiamen University! Furong Lake Xiamen Univ.