Skyrme Hartree-Fock 理论对奇异性原子核性质的研究

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. 奇异性原子核 奇异性原子核是指带有奇异量子数（s夸克） 的核多体系统。 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 2

3. Hypernuclei

4. Nu ~ Nd ~ Ns Strangeness in neutron stars ( r > 3 - 4 r0 ) Strange hadronic matter (A → ∞) Strangeness LL, X Hypernuclei Z L, S Hypernuclei -2 N n-rich nuclei -1 Lower density 0 World of matter made of u, d, s quarks “Stable” Higher density ３-D nuclear chart

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

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 6

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) 7

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) 8

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

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

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

12. Energy density due to hyperons It can be constructed from BHF energy density, 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, 12

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

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

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

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

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

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

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) 19

20. Shrinking effect of hyperons b<r2> R B(E2) ∝|<f| e r2 Y2 |i>|2 ∝R4 or (b<r2>)2 similar to Q-moment Motoba, Bando, IkedaProg.Theor.Phys. 70 (1983) 189. 4He + d +  model ～20% shrinkage

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

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

23. Kaonic nuclei

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. K-核实验信息 1. T.Kishmoto等人宣称他们探测到了K-核的深束缚信号 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). 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). 3. 实验上未放弃寻找 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). 25

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

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) 27

28. Including NK Int. 28

29. Including NK Int. 29

30. Including NK Int. Mean field changed by kaons: Local chemical potential : Where μS isdetermined by

32. Summary 1.The calculated core nuclei and the corresponding hypernuclei have similar deformations with the same sign when the core nuclei are well deformed. 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.

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

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

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