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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

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奇异性原子核

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

奇异性原子核是指带有奇异量子数（ s 夸克）的核多体系统。

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Hypernuclei

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World of matter made of u, d, s quarks

N

Z

Nu ~ Nd ~ Ns

Higherdensity

３ -D nuclear chart

Strangeness in neutron stars ( > 3 - 4 0 )

Strange hadronic matter (A → ∞)

, Hypernuclei

, Hypernuclei

Str

ang

enes

s

0

-1

-2

“Stable”

Lower density

n-rich nuclei

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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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Microscopic hyperon-nucleon interactionfor 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 NY 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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Binding energies vs deformations

0.65

0.63

0.63

0.55

0.52

0.55

X.-R. Zhou, 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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Binding energies vs deformations

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

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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)

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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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Kaonic nuclei

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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).

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K- 核实验信息

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).

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).

1. T.Kishmoto 等人宣称他们探测到了 K- 核的深束缚信号

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).

3. 实验上未放弃寻找

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Extended Skyrme Hartree-Fockincluding nucleon-kaon interaction

Skyrme Hartree-Fock equation ：

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Kaonic nuclei

DSHF + Nucleon-kaon interaction (meson-exchange chiral model) ：

According to chiral model, the K-

θ ： chiral anglef: meson decay constant (93MeV)

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Including NK Int.

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Including NK Int.

Mean field changed by kaons:

Including NK Int.

Local chemical potential :

Where μS is determined by

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Summary

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.

1.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

2. The deformation of K-nuclei?

1. Properties of K-nuclei with SHF.

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Cooperators

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

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