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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

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Outline

Introduction

Extended deformed Skyrme-

Hartree-Fock (DSHF)

Results

Summary

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Why do we study hypernuclei?

Multistrange systemNeutron star

IntroductionIntroduction

Nucleon-nucleon interaction

Hyperon-nucleon interaction

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Present Status of Hypernuclear Spectroscopy

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

(2006)

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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 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.

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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

BY, 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

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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

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,

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Finally, the energy density is written as

The parameterizations of numerical results:

Parameterizations

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Extended SHF equation

Minimizing the total energy of the hypernucleus, one arriveswith extended SHF equation

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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)

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Results

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

Hypernuclei is deformed or not?

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Binding energies vs deformations

0.65

0.63

0.63

0.55

0.52

0.55

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X.-R. Zhou, et.al, PRC76, 034312(2007)

Binding energies vs deformations

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Deformations, Energies, and B Λ

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Binding energies vs deformations

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

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Binding energies vs deformations

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

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Shrinking effect of hyperons

B(E2) |<f| e r∝ 2 Y2 |i>|2

∝R4 or (<r2>)2

R <r2>

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

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

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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 hyperon- nucleon interaction.

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.

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

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Prospect

DSHF + Nucleon-kaon interaction

1. Kaonic nuclei

2. η nuclei？

DSHF + η-nucleon interaction

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Cooperators

H. SagawaUniversity of Aizu, Japan

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

En-Guang ZhaoInstitute of Theoretical Physics, CAS, China

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