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
奇异性原子核是指带有奇异量子数（s夸克）
的核多体系统。
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
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Hypernuclei
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World of matter made of u, d, s quarks
Nu ~ Nd ~ Ns
“Stable”
Strangeness in neutron stars ( r > 3 - 4 r0 )
Strangeness
Strange hadronic matter (A → ∞)
Higher
density
LL, X Hypernuclei
Z
-2
L, S Hypernuclei
n-rich nuclei
N
-1
Lower density
0
３-D nuclear chart
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Present Status of L 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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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 NY 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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Binding energies vs deformations
0.65
0.63
0.63
0.52
0.55
0.55
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X.-R. Zhou, et.al, PRC76, 034312(2007)
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)
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
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 + L 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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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
1. T.Kishmoto等人宣称他们探测到了K-核的深束缚信号
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).
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).
3. 实验上未放弃寻找
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).
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Extended Skyrme Hartree-Fock
including 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 angle
f: meson decay constant (93MeV)
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Including NK Int.
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Including NK Int.
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Including NK Int.
Mean field changed by kaons:
Local chemical potential :
Where μS is determined by
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Summary
1.The calculated core nuclei and the corresponding
hypernuclei have similar deformations with the same
sign when the core nuclei are well deformed.
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.
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Prospect
1. Properties of K-nuclei with SHF.
2. The deformation of K-nuclei?
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Cooperators
H.-J. Schulze,
University of Catania, Italy
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Thank you!
Welcome to Xiamen University!
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Furong Lake
Xiamen Univ.