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Properties of hypernuclei in the Skyrme Hartree-Fock method

Properties of hypernuclei in the Skyrme Hartree-Fock method. Xian-Rong Zhou Department of physics, Xiamen University, Xiamen, China. Present Status of the Nuclear Interaction Theory , 08/25 -09/19,2014, Beijing, China. Outline. Introduction

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Properties of hypernuclei in the Skyrme Hartree-Fock method

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  1. Properties of hypernuclei in the Skyrme Hartree-Fock method Xian-Rong Zhou Department of physics, Xiamen University, Xiamen, China Present Status of the Nuclear Interaction Theory , 08/25 -09/19,2014, Beijing, China

  2. Outline • Introduction • Extended Skyrme Hartree-Fock • Properties of hypernuclei • shapes of hypernuclei • effects of hyperon • enegery spetrum • Summary

  3. Strangeness LL, X Hypernuclei Z L, S Hypernuclei -2 N -1 0 3-D nuclear chart

  4. Why to study hypernuclei? Nucleon-nucleon interaction Hyperon-nucleon interaction Impurity of nuclear system Multistrange system: Neutron star, …

  5. Theoretical studies about hypernuclei Energy spectrum Decay properties Theeffect of hyperon(s) Shapes ……. 5

  6. Theoretical studies about the shapes of hypernuclei 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. Calculations considering deformation: Deformed HF with nonrealistic YN 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 7

  8. Considering deformation self-consistently: Deformed SHF with Microscopic YN int. X.-R. Zhou, H.-J. Schulze, H. Sagawa,et al., Phys. Rev. C76, 034312(2007) Relativistic mean-field model (RMF): Myaing Thi Win, H. Hagino, et al., Phys. Rev. C 78, 054311 (2008) Triaxial SHF with Skyrme-like YN interaction: Myaing Thi Win, H. Hagino, 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), S.-G.Zhou, Phys. Rev. C 84, 014328 (2011) 8

  9. Superdeformation in hypernuclei Bing-Nan Lu, E. Hiyama, H. Sagawa, and S.-G. Zhou, Phys. Rev. C 89, 044307 (2014) 9

  10. 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.

  11. Several models for deformed nuclei Alpha-model Projected shell model (PSM) Deformed Skyrme Hartree-Fock (DSHF) Relativistic mean-field model (RMF) Antisymmetrized molecular dynamics (AMD) ……

  12. Microscopic hyperon-nucleon interaction for deformed hypernuclei Free YNinteraction YN: Nijmegen soft-core hyperon-nucleon potential NSC89,NSC97a,NSC97f,ESC08 BHF cal. for asymmetric matter NN: Argonne v18 nucleon-nucleon interaction Effective YNinteraction MF cal. BY, Hypernuclear Structure

  13. Comparison of different hyperon-nucleon potential

  14. SHF Extended DSHF including hyperon-nucleon interaction DSHF + YN interaction: Total energy of a hypernucleus in extended DSHF: where the energy density Due to the YN force,

  15. The energy density functional εNΛis obtained from a fit to the binding energy per baryon, B/A(ρn, ρp, ρ), of asymmetrichypermatter, as generated by BHF calculations. Effective mass of hyperon

  16. In practice we use the following parametrizations:

  17. Extended SHF equation Minimizing the total energy of the hypernucleus, one arrives with extended SHF equation with the modified mean field by hyperon:

  18. Pairing interaction We take a density-dependent delta pairing 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 18

  19. 1. Hypernuclei is deformed or not? 19

  20. Binding energies vs deformations 0.65 0.63 0.63 0.52 0.55 0.55 20 X.-R. Zhou, H.-J. Schulze, H. sagawa et.al, PRC76, 034312(2007)

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

  22. 2. The effect of hyperon on nuclear structure? 22

  23. The effect of hyperon in neutron-rich nuclei X.-R. Zhou,A.Polls,H.-J.Schulze, et al.,PRC78,054306(2008)

  24. exp. The Oxygen isotopes

  25. 3. Energy spectrum of hypernulcei 25

  26. The SHF models can just give the single-particle energies and ground state of Λ hypernuclei in intrinsic frame of reference. The conservation of particle number is destroyed by BCS method. The study of the gamma spectra and electromagnetic transitions needs symmetry restoration. Limitations of extended SHF+BCS method: Angular momentum and particle-number projection (AMP&PNP)are needed !

  27. Projected SHF+BCS Model The projected mean-field state The projection operator Energies with angular momentum and E2 transitions

  28. Energy potential surface of 12C and Ji-Wei Cui, X.-R. Zhou, in preparation

  29. Energy potential surface of 20 Ne and

  30. Energy potential surface of 24Mg and

  31. Energy potential surface of 26Mg and

  32. Energy potential surface of 26Si and

  33. Energy potential surface of 28Si and

  34. Comparison of NSC89(upper) and Skyrme-type(lower) ΛN Interactions

  35. Comparison of different Skyrme parameters

  36. Energy spectrum of 12C and cal1 and cal2 label energy levels with or without the Λspin-orbit term.

  37. Energy spectrum of 20Ne and cal1 and cal2 label energy levels with or withoutthe Λspin-orbit term.

  38. Energy spectrum of 24Mg and cal1 and cal2label energy levels with or withoutthe Λ spin-orbit term.

  39. Energy spectrum of 28Si and cal1 and cal2 label energy levels with or withoutthe Λspin-orbit term.

  40. Exp data in W.u. from:http://www.nndc.bnl.gov The B(E2) transitions of hypernuclei become a little smaller due to the shrinkage of the quadruple shape. B(E2) transition probabilities

  41. Summary 1.The DSHF was extended to hypernuclei by including a microscopically derived hyperon- nucleon interaction. 2.The calculated core nuclei and the corresponding hypernuclei have similar deformations with the same sign when the core nuclei are well deformed. 3. Due to the effect of hyperons, the nuclei close to the drip line are stabilized and new isotopes are potentially made available. 4. The projected SHF+BCS model gives reasonable initial results of energy spectra and E2 transition rates for well-deformed sd-shell nuclei and hypernuclei .

  42. Cooperators H.-J. Schulze, University of Catania, Italy H. Sagawa University of Aizu, Japan En-Guang Zhao Institute of Theoretical Physics, CAS, China Ji-Wei Cui Xiamen University, China

  43. Thank you for your attention! Furong Lake Xiamen Univ.

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