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									Deformed hypernuclei with
the Skyrme-Hartree-Fock
approach


     Xian-Rong Zhou

   Department of physics,
    Xiamen University,
      Xiamen, China

      9th, Feb. 2012, Tokai
                              1
   Outline
Introduction
Extended deformed Skyrme-
 Hartree-Fock (DSHF)
Results
Summary

                             2
     Introduction

Why do we study hypernuclei?

Nucleon-nucleon interaction
Hyperon-nucleon interaction


Multistrange system
Neutron star

                               3
Present Status of  Hypernuclear Spectroscopy

        (2006)




  O. Hashimoto and H. Tamura, Prog. Part. Nucl. Phys. 57 (2006) 564.
                                                                       4
        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



                                            5
          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)
                                                     6
         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)


                                                         7
        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.

                                                                  8
         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)


                                           9
Microscopic hyperon-nucleon interaction
for deformed hypernuclei

          Free YN interaction

    BHF cal. for   YN: Nijmegen soft-core hyperon-nucleon
                       potential NSC89
    asymmetric
                   NN: Argonne v18 nucleon-nucleon interaction
    matter


       Effective YN interaction


    DSHF MF cal.


     BY, Hypernuclear Structure
                                                        10
        Extended DSHF including
        hyperon-nucleon interaction
Total energy of a hypernucleus in extended DSHF



where the energy density

 SHF


Due to the YN force,



                                                  11
     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
           Parameterizations

Finally, the energy density is written as



The parameterizations of numerical results:




                                              13
           Extended SHF equation

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




                                                          14
            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
          Results

Hypernuclei is deformed or not?


Self-consistent DSHF calculations for
experimentally studied hypernuclei
including light, medium-mass and
heavy hypernuclei.


                                        16
Binding energies vs deformations



                                   0.65

                                    0.63
                                   0.63
                                   0.52
                                   0.55
                                    0.55




                                          17
Binding energies vs deformations




                                                 18

                 X.-R. Zhou, et.al, PRC76, 034312(2007)
Deformations, Energies, and B Λ




                                  19
Binding energies vs deformations




                                                       20

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




                                                        21

          X.-R. Zhou, H.-J.Schulze, et.al, PRC76, 034312(2007)
          Shrinking effect of hyperons
    R       b<r2>


 B(E2) ∝|<f| e r2 Y2 |i>|2
        ∝R4 or (b<r2>)2
similar to Q-moment

Motoba, Bando, Ikeda
Prog.Theor.Phys. 70 (1983) 189.
4He + d +  model ~20%

shrinkage




                                         22
The effect of hyperon in neutron-rich nuclei




                                                           23

             X.-R. Zhou, H.-J. Schlze, et.al, PRC78, 054306 (2008)
The Oxygen isotopes X.-R. Zhou, et.al, PRC78, 054306 (2008)



    exp.




                                                     24
           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. 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.
                                                        25
         Prospect

1. Kaonic nuclei

  DSHF + Nucleon-kaon interaction


2. η nuclei?

  DSHF + η-nucleon interaction



                                    26
       Cooperators

         H. Sagawa
     University of Aizu, Japan

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


           En-Guang Zhao
Institute of Theoretical Physics, CAS, China


                                               27
     Thank you!


Welcome to Xiamen University, China!
                              Furong Lake
                                     28

                              Xiamen Univ.

								
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