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 SkyrmeHartree-Fock (DSHF)
Results
Summary
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Introduction
Why do we study hypernuclei?
Nucleon-nucleon interaction
Hyperon-nucleon interaction
Multistrange system
Neutron star
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Present Status of  Hypernuclear Spectroscopy
(2006)
O. Hashimoto and H. Tamura, Prog. Part. Nucl. Phys. 57 (2006) 564.
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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
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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)
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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)
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Why to study deformations
of hypernuclei
Many p-shell and sd-shell nuclei are
deformed.
For example, experimentally, 10B and
have large quadrupole moments.
11C
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.
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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)
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Microscopic hyperon-nucleon interaction
for deformed hypernuclei
Free YN interaction
BHF cal. for
asymmetric
matter
YN: Nijmegen soft-core hyperon-nucleon
potential NSC89
NN: Argonne v18 nucleon-nucleon interaction
Effective YN interaction
DSHF MF cal.
BY, Hypernuclear Structure
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Extended DSHF including
hyperon-nucleon interaction
Total energy of a hypernucleus in extended DSHF
where the energy density
SHF
Due to the YN force,
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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,
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Parameterizations
Finally, the energy density is written as
The parameterizations of numerical results:
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Extended SHF equation
Minimizing the total energy of the hypernucleus, one arrives
with extended SHF equation
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Pairing interaction
The pairing interaction is taken to be a densitydependent 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
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Results
Hypernuclei is deformed or not?
Self-consistent DSHF calculations for
experimentally studied hypernuclei
including light, medium-mass and
heavy hypernuclei.
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Binding energies vs deformations
0.65
0.63
0.63
0.52
0.55
0.55
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Binding energies vs deformations
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X.-R. Zhou, et.al, PRC76, 034312(2007)
Deformations, Energies, and B Λ
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Binding energies vs deformations
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X.-R. Zhou, H.-J. Schulze, et.al, PRC76, 034312(2007)
Binding energies vs deformations
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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
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The effect of hyperon in neutron-rich nuclei
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X.-R. Zhou, H.-J. Schlze, et.al, PRC78, 054306 (2008)
The Oxygen isotopes X.-R. Zhou, et.al, PRC78, 054306 (2008)
exp.
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Summary
1.The DSHF was extended to hypernuclei by
including a microscopically derived hyperonnucleon 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.
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Prospect
1. Kaonic nuclei
DSHF + Nucleon-kaon interaction
2. η nuclei？
DSHF + η-nucleon interaction
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Cooperators
H. Sagawa
University of Aizu, Japan
H.-J. Schulze,
University of Catania, Italy
En-Guang Zhao
Institute of Theoretical Physics, CAS, China
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Thank you!
Welcome to Xiamen University, China!
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Furong Lake
Xiamen Univ.