新学術

Dec. 3, 2011
素核宇融合による計算基礎物理学の進展–ミクロとマクロのかけ橋の構築–
2011 年 12 月 3 日 〜 5 日 於 合歓の郷

テンソル力に適した巨大次元殻模型による中性子過剰ハイパー核の構造研究の進捗状況(TOSM Calculation of Neutron-Rich Hypernuclei)
Atsushi UMEYA (NIT)
Takayuki MYO (OIT), Emiko HIYAMA (RIKEN)
Hiroshi TOKI (RCNP), Kiyomi IKEDA (RIKEN)

1

新学術

Dec. 3, 2011

Purpose of hypernuclear study
To get information on baryon-baryon interaction
from the structure of hypernuclei
940
n (udd)1197
Σ− (dds)938
p (uud)

I=1/2, S=01193
Σ0 (uds)1189
Σ+ (uus) I=1, S=−1

Λ (uds)1116

I=0, S=−1

Ξ− (dss)1322

Ξ0 (uss)1315

I=1/2, S=−22

新学術

Dec. 3, 2011

Purpose of hypernuclear study
To get information on baryon-baryon interaction
from the structure of hypernuclei
940 ΣN int.,
938 ΛN-ΣN coupling int.)
S = −1 sector (ΛN int.,n (udd)1197
Σ− (dds)p (uud)

I=1/2, S=01193
Σ0 (uds)1189
Σ+ (uus) I=1, S=−1

Λ (uds)1116

I=0, S=−1

Ξ− (dss)1322

Ξ0 (uss)1315

I=1/2, S=−22新学術

Dec. 3, 2011

Purpose of hypernuclear study
To get information on baryon-baryon interaction
from the structure of hypernuclei
940 ΣN int.,
938 ΛN-ΣN coupling int.)
S = −1 sector (ΛN int.,n (udd)p (uud)

I=1/2, S=0

Eﬀective ΛN interaction Hypernuclear γ-ray data since 1998
1197

1193

1189

eﬀ+0VΛN= V0 +VσσΣ−σ(dds)·σ+Vℓ·(s+sN(uus))+VI=1,ℓΛN ·(sΛ − sN )+VTensor S12Σ(uds)ΣNΛ
SLS ΛNΛ
ALSS=−1Λ (uds) Nucl. Phys.I=0,• Millener (p-shell model)
A S=−1804, 84 (2008).
1116• Hiyama (Few-body) Prog. Part. Nucl. Phys. 63, 339 (2009).
Ξ− (dss)1322

Ξ0 (uss)1315

I=1/2, S=−22

新学術

Dec. 3, 2011

Purpose of hypernuclear study
To get information on baryon-baryon interaction
from the structure of hypernuclei
940 ΣN int.,
938 ΛN-ΣN coupling int.)
S = −1 sector (ΛN int.,n (udd)p (uud)

I=1/2, S=0

Eﬀective ΛN interaction Hypernuclear γ-ray data since 1998
1197

1193

1189

eﬀ+0VΛN= V0 +VσσΣ−σ(dds)·σ+Vℓ·(s+sN(uus))+VI=1,ℓΛN ·(sΛ − sN )+VTensor S12
Σ(uds)ΣNΛ
SLS ΛNΛ
ALSS=−1Λ (uds) Nucl. Phys.I=0,• Millener (p-shell model)
A S=−1804, 84 (2008).
1116• Hiyama (Few-body) Prog. Part. Nucl. Phys. 63, 339 (2009).
I=1/2, S=−2
Ξ− (dss)Ξ0 (uss)1322
1315
One of the open questions
inS=−1 sector of YN interaction→ ΛN-ΣN coupling interaction

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新学術Dec. 3, 2011

Role of ΛN-ΣN coupling interaction
ΛN-ΣN coupling =⇒ Great contribution to study of neutron starΛ

NΣ

N

Λ

NΛ

=⇒

N

ΣEffectiveNΛN

Eﬀective 2-body ΛN interaction
NΛN=⇒

Σ
N

Λ

NN

Λ

NEffectiveΣNΛNEﬀective 3-body ΛNN interaction(Fujita-Miyazawa type)Strength of the ΛN-ΣN coupling interaction → still unknown

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Dec. 3, 2011

Studies for analysis of ΛN-ΣN couplings-shell hypernuclei• Y. Akaishi et al., Phys. Rev. Lett. 84, 3539 (2000).
• E. Hiyama et al., Phys. Rev. C 65, 011341(R) (2001).
• A. Nogga et al., Phys. Rev. Lett. 88, 172501 (2002).
• H. Nemura et al., Phys. Rev. Lett. 89, 142504 (2002).
p-shell hypernuclei (Shell-model study)• D. Halderson, Phys. Rev. C 77, 034304 (2008).
• D.J. Millener, Nucl. Phys. A 804, 84 (2008).
• A. Umeya, T. Harada, Phys. Rev. C 79, 024315 (2009).
• A. Umeya, T. Harada, Phys. Rev. C 83, 034310 (2011).

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Dec. 3, 2011

ΛN-ΣN coupling in neutron-rich hypernuclei
Neutron-rich hypernuclei are suited for investigating the ΛN-ΣN couplingΣ hyperon: Isospin I = 1
Neutron-rich nuclei: Large isospin⇒ Large Σ-mixing

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新学術Dec. 3, 2011

ΛN-ΣN coupling in neutron-rich hypernuclei
Neutron-rich hypernuclei are suited for investigating the ΛN-ΣN couplingΣ hyperon: Isospin I = 1
Neutron-rich nuclei: Large isospin⇒ Large Σ-mixing

Productions of neutron-rich Λ hypernuclei• J-PARC E10 (spokes person: A. Sakaguchi)
9→ Λ6 HnΛ He
Λnnpnn 5Hnp Λnp nn 8n
He• JLab Hall C E01-011 (spokes person: S.N. Nakamura)→ Λ7 HeΛn p
np nn 6Heanalysis is in progress

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新学術Dec. 3, 2011

Research plan

ab initio calculation for neutron-rich hypernuclei
with realistic interactions
taking into account ΛN-ΣN coupling explicitly
Nuclei: Λ He isotope ⇒Λ Li isotope⇒Λ Be isotope⇒ ···Method: (1) Tensor-Optimized Shell Model (TOSM)
T. Myo et al., Prog. Theor. Phys. 117, 257 (2007).

+Unitary Correlation Operator Method (UCOM)

H. Feldmeier et al., Nucl. Phys. A 632, 61 (1998).

(2) Gaussian Expansion Method (GEM)
E. Hiyama et al., Prog. Part. Nucl. Phys. 51, 223 (2003).

in collaboration with Myo, Hiyama, Toki, and Ikeda

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新学術Dec. 3, 2011

Research plan

ab initio calculation for neutron-rich hypernuclei
with realistic interactions
taking into account ΛN-ΣN coupling explicitly
Nuclei: Λ He isotope ⇒Λ Li isotope⇒Λ Be isotope⇒ ···Method: (1) Tensor-Optimized Shell Model (TOSM)
Myo etintoal., accountProg. Theor.
Phys. force
117, 257(2007).
• Shell model T.
takingatensor
explicitly+Unitary Correlation Operator Method (UCOM)
H. Feldmeier et al., Nucl. Phys. A 632, 61 (1998).

(2) Gaussian Expansion Method (GEM)
E. Hiyama et al., Prog. Part. Nucl. Phys. 51, 223 (2003).

in collaboration with Myo, Hiyama, Toki, and Ikeda

6

新学術

Dec. 3, 2011

Research plan

ab initio calculation for neutron-rich hypernuclei
with realistic interactions
taking into account ΛN-ΣN coupling explicitly
Nuclei: Λ He isotope ⇒Λ Li isotope⇒

Λ Be isotope⇒ ···Method: (1) Tensor-Optimized Shell Model (TOSM)
Myo etintoal., accountProg. Theor.
Phys. force
117, 257(2007).
• Shell model T.
takingatensorexplicitly+Unitary Correlation Operator Method (UCOM)
Feldmeier et al., Nucl. Phys. A 632, 61 (1998).
• To describe H.
short-range
correlations
whichExpansion
are includedin NN,(GEM)
YN interactions(2) Gaussian
MethodbyPart.
usingNucl.
correlation
E. Hiyama et al., Prog.
Phys. 51,functions
223 (2003).

in collaboration with Myo, Hiyama, Toki, and Ikeda

6

新学術Dec. 3, 2011

Research plan

ab initio
calculation for neutron-rich hypernuclei
Suited for a systematic investigation of nuclei with A = 3–10

with realistic without
interactions
supposing an α cluster
taking into account ΛN-ΣN coupling explicitlyNuclei: Λ He isotope ⇒Λ Li isotope⇒Λ Be isotope⇒ ···Method: (1) Tensor-Optimized Shell Model (TOSM)
Myo etintoal., accountProg. Theor.
Phys. force
117, 257(2007).
• Shell model T.
takingatensor
explicitly+Unitary Correlation Operator Method (UCOM)
Feldmeier et al., Nucl. Phys. A 632, 61 (1998).
• To describe H.
short-range
correlations
whichExpansion
are includedin NN,(GEM)
YN interactions(2) Gaussian
MethodbyPart.
usingNucl.
correlation
E. Hiyama et al., Prog.
Phys. 51,functions
223 (2003).

in collaboration with Myo, Hiyama, Toki, and Ikeda

6新学術

Dec. 3, 2011

Research plan

ab initio
calculation for neutron-rich hypernuclei
Suited for a systematic investigation of nuclei with A = 3–10

with realistic without
interactions
supposing an α cluster
taking into account ΛN-ΣN coupling explicitly

But, insuﬃcient accuracy of about a few MeV
extending to about a few hundred keV
Nuclei: Λ He isotope ⇒ →Λ Li isotope ⇒ Λ Be isotope ⇒ · · ·Method: (1) Tensor-Optimized Shell Model (TOSM)
Myo etintoal., accountProg. Theor.
Phys. force
117, 257(2007).
• Shell model T.
takingatensor
explicitly+Unitary Correlation Operator Method (UCOM)

Feldmeier et al., Nucl. Phys. A 632, 61 (1998).
• To describe H.
short-range
correlations
whichExpansion
are includedin NN,(GEM)
YN interactions(2) Gaussian
MethodbyPart.
usingNucl.
correlation
E. Hiyama et al., Prog.
Phys. 51,functions
223 (2003).

in collaboration with Myo, Hiyama, Toki, and Ikeda

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新学術
Example of TOSM calculation

Dec. 3, 2011
(4 He; 0+ )← Exact value
Benchmark testof ab initio calculations(Kamada et al.,Phys. Rev. C 64, 044001 (2001).)
Energy of 4 He
TOSM with AV8’
−22.3 MeV
Benchmark test calculation−25.9 MeV

Energy of 4 He in TOSM as a function of the maximum angular momentum

T. Myo et al., Prog. Theor. Phys. 121, 511 (2009).

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Dec. 3, 2011

Example of TOSM calculation(Energy spectra of He isotope)

T. Myo, AU, H. Toki, K. Ikeda, Phys. Rev. C 84, 034315 (2011).

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Dec. 3, 2011

In this talk...
• Λ4 H5Λ Hen

Λn p3HΛ
pnp n 4He

• Contributions of components of Y N interactions
to binding energies of Λ4 H and Λ5 He9

新学術

Dec. 3, 2011Interactions• NN interaction
AV8’ B.S. Pudliner et al., Phys. Rev. C 56, 1720 (1997).
• YN interaction
YN
YN
VYN = V0YN + σ · σ VσYN + ℓ · s Vℓs+ S12 Vtensor

made by S. Shinmura
simulated NSC97f(not original NSC97f)

used in few-body calculations
E. Hiyama et al., Phys. Rev. C 65, 011301(R).
H. Nemura et al., Phys. Rev. Lett. 89, 142504 (2002).

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Dec. 3, 2011

Numerical results of energy levels of Λ4 H, Λ5 He+1.0+1.28

t+Λ

BΛ (MeV)

0.0
−1.0

−0.59
−1.64

−2.0
−3.04
ΛH

This work+0.40

5ΛHeα+Λ

−1.05 1+

−2.33

−2.04 0+

[1]

Exp.

−2.10
−3.12 1/2+

Exp.
This work [2][1] E. Hiyama et al., Phys. Rev. C 65, 011301(R) (2001).
[2] H. Nemura et al., Phys. Rev. Lett. 89, 142504 (2002).
(G3RS potential is used in [2].)R. Tamagaki, Prog. Theor. Phys. 39, 91 (1968).

11新学術Dec. 3, 2011

Convergence of BΛ

BΛ (MeV)

4+H(0)
Λ4+H(1)
Λ5ΛHe22211

10 t+Λ

0 t+Λ

0 α+Λ

−1−1−1−2−2−2

6 8 10 12 14lmax

6 8 10 12 14lmax

6 8 10 12 14lmax

insuﬃcient convergence → in progress of calculations with lmax = 20

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新学術

Dec. 3, 2011

Role of ΛN-ΣN coupling⟨VYN ⟩ in Λ4 H; 0+Central

NΛ-NΛ
NΛ-NΣ
NΣ-NΣ

−5.46
−3.42
0.45(MeV)
Tensor

−1.11−8.75−2.04⟨VYN ⟩ in Λ5 He
CentralNΛ-NΛ
NΛ-NΣ
NΣ-NΣ

⟨VYN ⟩ in Λ4 H; 1+LS−0.16
0.30
−0.06

CentralNΛ-NΛ
NΛ-NΣ
NΣ-NΣ

−1.99
−1.38
0.64

(MeV)
Tensor

−0.60
−9.13
−0.30

LS−0.04
0.13
−0.09

(MeV)
Tensor

−3.86 −0.64−1.43 −10.52
0.70 −0.08

LS−0.03
0.12−0.12

These results are qualitative agreement with the few-body calculationby H. Nemura.
H. Nemura et al., Phys. Rev. Lett. 89, 142504 (2002).

13新学術Dec. 3, 2011

Future plan
• to get a suﬃcient energy convergence of a few hundred keV(in progress of calculations with lmax = 20)→ We can get the results which are close to ab initio calculation.
• quantitative discussion of role of the ΛN-ΣN coupling interaction

NΛ

N

Σ

N

Λ

NΛ

Λ

=⇒

Λ

ΣEffectiveN
Λ

NN

=⇒

Σ
NN

N

N
Λ

N

EffectiveΣNΛN• ab initio like calculations for p-shell hyper nuclei
without supposing an α cluster→ prediction of energy levels of Λ He isotope up to A = 914

新学術Dec. 3, 2011

Backup新学術

Dec. 3, 2011

Correlation functions in Λ4 He• The correlation function ofYN interaction is diﬀerent
from that of NN interaction.
⇓The UCOM parameters ofYN int. should be diﬀerent
from those of NN int.
• In the present calculation,
the same UCOM parameters
are used for NN and YN int.
E. Hiyama et al., Phys. Rev. C 65, 011301(R) (2001).

新学術

Dec. 3, 2011

Energy convergence of 3 H and 4 He
3Energy (MeV)

4HHe

50−5−10−15−20−250 1 2 3 4 5 6 7 8 9 10 11 12 13 14lmax

新学術Dec. 3, 2011

Matter radius of He isotopes in TOSM
Cluster ModelT. Myo, R. Ando, K. Kato,Phys. Lett. B 691, 150 (2010).

TOSM

T. Myo, AU, H. Toki, K. Ikeda, Phys. Rev. C 84, 034315 (2011).
Exp. data
I. Tanihata et al., Phys. Lett. B 289, 261 (1992). / G.D. Alkhazov et al., Phys. Rev. Lett. 78, 2313 (1997).
O.A. Kiselev et al., Eur. Phys. J. A 25, Suppl. 1, 215 (2005). / P. Mueller et al., Phys. Rev. Lett. 99, 252501 (2007).