ハイパー核構造の今後の展望 -- 少数粒子系理論物理的観点から --

ハイパー核構造の今後の展望 -- 少数粒子系理論物理的観点から --

肥山詠美子（理研）

精密少数多体系計算

“Gaussian Expansion Method for Few-Body Systems”E. Hiyama, Y. Kino, M. Kamimura,

Prog. Part. Nucl. Phys. 51 (2003) 223 - 307.

ガウス展開法

　　量子力学的３体系、４体系のシュレディンガー方程式を　　　厳密に（近似的ではなく）解く方法（束縛状態に対して）

３体問題

３体問題シュレーディンガー方程式　：　６変数２階偏微分方程式

４体問題

・構成粒子は何でもよい、　質量、電荷を問わない。　

少数多体系のシュレーディンガー方程式を精密に解く

「ガウス展開法」の利点

３体問題４体問題５体問題現在は、さらに

クーロン３体問題は１０桁の精度　

0R・粒子間に強い相関がある場合

にも精密に適用できる。

強い相関 ( 核力など）

（電子、陽子、中性子、クオーク、・・・・・）

V(R ）

私が創った研究法「無限小変位ガウス・ローブ法」　（量子力学的３体・４体問題を　　精密に解く方法）

ハイパー核物理

不安定核物理

少数粒子系物理

ハドロン物理

ミュオン触媒核融合

適用・貢献宇宙・天体核物

理私の研究法の発展

私の研究の進め方の特徴

フィードバック：

特に重点をおいてこれまで研究を行ってきた。

QCD

ハドロンLattice QCD

中間子理論クオーク模型

ハイペロンー核子（ YN) 、ハイペロンーハイペロン（ YY) 間力

多体系のダイナミクス

YN 散乱実験

　現在のS= -1, -2 の世界　　　　

X

極端に少ない

Shell 模型Few-body 計算

Cluster 模型

私の役割（ Few-body 計算法を用いて）

よく分かっていない

まずは、構造の研究から、相互作用を決めるのが、先決なのが現状

中性子星の内部の研究まだまだ発展途上

相互作用を決めるストラテジー

ハイペロン (Y)- 核子 (N) 、ハイペロン (Y)- ハイペロン (Y) 相互作用　　中間子理論　　クオーク理論

ハイパー核構造の精密計算

ハイパー核の高分解能の分光実験　Ｇｅ検出器を用いたガンマ線分光技術の発展

ハイパー核の励起準位からのガンマ線を数 keV の精度で測定可能

① 使用

② 比較XNo directinformation

③ 改良点を指摘私の少数粒子系精密計算法



ハイパー核構造の精密計算



① 使用


③ 改良点を指摘

実際にどのようにして構造研究から相互作用を決めていくのか？

2. S= -1 ハイパー核と

YN 相互作用

ΛN interaction 　 (effectively including ΛN -ΣN coupling)

Almost determined since 1998

----- SLS (Symmetric LS)

----- ALS (Anti symmetric LS)

One of the important issue

9Be 13CΛ

0 < VALS (meson theory) << VALS (constituent quark model)

In the ALS part :

YN LS force and energy-splitting in 9Be and 13CΛ Λ

----- SLS (Symmetric LS)

----- ALS (Antisymmetric LS)

Λ

12C8Be

Λ

Λ

Nijgemen model D, F , soft core ’97a-f Kyoto-NiijataFSS potential

[vanishes in S=0 nuclei, Pauli][breaks charge symmetry]

BNL-E930 BNL-E929

ΔE 　LS splitting

0+

2+

8Be

Λ

1/2+

5/2+

3/2+

γ

γ

9BeΛ

(0s)

12C 13CΛ

γγ

1/2+

3/2-

1/2-

ΔEΛ

0+

(0p)

α

Λ α

α

3- and 4-body calculations:E. Hiyama, M. Kamimura, T. Motoba, T. Yamada and Y. YamamotoE. Hiyama, M. Kamimura, T. Motoba, T. Yamada and Y. YamamotoPhys. Rev. Lett. 85 (2000) 270.Phys. Rev. Lett. 85 (2000) 270.

YN LS force

　　　 1) Meson theory : Nijmegen Model D, F, soft core’97 a – f.

　　　 2) Qurak model : Kyoto-Niigata, FSS 　　　　

αΛ

α13CΛ

9BeΛ

5/2+

3/2+ 80

200keV

～

Meson

3/2-

1/2- 360

960keV

～

Meson

5/2+

3/2+35

40keV

Quark

～

150

200keV

Quark

～1/2-

3/2-

Exp.

5/2+

3/2+

Exp. keV

BNL-E930

H. Akikawa et al.Phys. Rev. Lett. 88 (2002)082501; H. Tamura et al.Nucl. Phys. A754 (2005) 58c

152

1/2-

3/2-

BNL-E929

± 54 ± 36 keVS.Ajimura et al.Phys. Rev. Lett. 86,(2001) 4255

43±5

ΛN LS force and 9Be and 13CΛ Λ

9BeΛ

13CΛ

Nijmegen model D,FSoft core ’97a-f

140 ～ 250 keV

9BeΛ

SLS

5/2+

3/2+

SLS + 　 ALS

80 ～ 200 keV

Meson Theory

5/2+

3/2+

35 ～ 40keV3/2+

5/2+

SLS + ALS

Quark-based

We suggested there are 2 paths to improve theMeson models :reduce the SLS strengthor enhance the ALS strength so as to reproduce theobserved LS splittings in 9Be and 13C.

Λ

Λ

(Large) (Small)

(Large) - (Large)

LS splitting in 9BeΛ

α

Λ

α

5/2+

3/2+

Exp. keV43±5

Recently, a new YN interaction based on meson theory,

extended soft core potential 06 (ESC06) by Th. A Rijken

5/2+

3/2+

39 keV

ESC06

5/2+

3/2+

Exp. keV

BNL-E930

H. Akikawa et al.Phys. Rev. Lett. 88,(2002)82501;H. Tamura et al.Nucl. Phys. A754,58c(2005)

43±5

98 keV

SLSSLS + ALS

(reduced)(small)

LS splitting in 9Be Λ

9BeΛ

Good agreement

Hiyama (2007)



9Be と 13C のハイパー核構造の精密計算



① 使用


Λ Λ

④ new version potential (ESC06)③ 改良点を指摘

⑤ 実験と一致

Hypernuclear -ray data since 1998

・ Millener (p-shell model), 　・ Hiyama (few-body)

Picture by Tamura

In S=-1 セクターにおいて、残されている重要課題

(1)Charge symmetry breaking

(2) ΛN － ΣN coupling

・ E13 “γ-ray spectroscopy of light hypernuclei” by Tamura and his collaborators Day-1 experiment

11B 4HeΛ Λ

・ E10 “Study on Λ-hypernuclei with the doubleCharge-Exchange reaction” by Sakaguchi , Fukuda and his collaboratiors

9HeΛ6HΛ

(1) Charge Symmetry breaking

N+N+N

1/2+- 8.48 MeV

0 MeV

- 7.72 MeV1/2+

3H

3He

n n

p

n

p

p

0.76

MeV

Energy difference comes from

dominantly Coulomb force

between 2 protons.

Charge symmetry breaking

effect is small.

In S=0 sector Exp.

3He+Λ0 MeV

-1.24

-2.39

1+

0+

3H+Λ0 MeV

-1.00

-2.04

1+

0+

0.35 MeV

n n

p Λ

4HΛ

n

p Λ

4HeΛ

p

Exp.

0.24 MeV

Charge Symmetry breaking

3He+Λ0 MeV

-1.24

-2.39

1+

0+

3H+Λ0 MeV

-1.00

-2.04

1+

0+

n n

p Λ

4HΛ

n

p Λ

4HeΛ

p

・ A. Nogga, H. Kamada and W. Gloeckle, Phys. Rev. Lett. 88, 172501 (2002)

(Exp: 0.24 MeV)

(Exp: 0.35 MeV)(cal. 0.07 MeV(NSC97e))

(cal: -0.01 MeV(NSC97e))

・ E. Hiyama, M. Kamimura, T. Motoba, T. Yamada and Y. Yamamoto,

Phys. Rev. C65, 011301(R) (2001).

・ H. Nemura. Y. Akaishi and Y. Suzuki,

Phys. Rev. Lett.89, 142504 (2002).

N

Λ

N

N N

N N

Σ+

3He+Λ0 MeV

-1.15

-2.39

1+

0+

n

p Λ

4HeΛ

p

Exp.

Recently, Tamura et al. pointed out that

it is necessary to perform γ-ray experiment

about this hypernucleus again .

“Because the measurement of this data

was once reported in 1970’s.

At that time, the statistical quality of the 4He γ- ray spectrum was extremely poor ”Λ

・ E13 “γ-ray spectroscopy of light hypernuclei” by Tamura and his collaborators

We should wait for their data at J-PARC.

J-PARC: Day-1 experiment

γ

But, we needBΛ in 4He.Λ

It is interesting to investigate the charge symmetry breaking effectin p-shell Λ hypernuclei as well as s-shell Λ hypernuclei.

For this purpose, to study structure of A=7 Λ hypernuclei is suited.

Because, core nuclei with A=6 are iso-triplet states.

α

n

α

n pn

α

pp

6He6Li(T=1)

6Be

α

n

α

n pn

α

pp

7He 7Li(T=1)7Be

ΛΛ Λ

ΛΛ Λ

Then, A=7 　 Λ hypernuclei are also iso-triplet states.It is possible that CSB interaction between Λ and valence nucleons contribute to the Λ-binding energies in these hypernuclei.

Exp.1.54

-3.79

BΛ=

5.16

MeV

BΛ=

5.26

MeV

Pre

limin

ary

data

: 5.7

±0.2

±0.2

Reported by Hashimoto at HYP-X

7BeΛ

(T=1)7LiΛ

7HeΛ

6He

6Li(T=1)

6Be

JLA

B:E

01-0

11 e

xper

imen

t

Important issue: To predict the Λ binding energy of 7He whose analysis is in progress at JLAB using 　 ΛN 　 interaction to reproduce the Λ binding energies of 7Li (T=1) and 7BeTo study the effect of CSB in iso-triplet A=7 hypernuclei. Λ Λ

Λ

α

n

α

n pn

α

pp

7He 7Li(T=1)7Be

ΛΛ Λ

ΛΛ Λ

For this purpose, we study structure of A=7 hypernuclei within the framework of α+Λ+N+N 4-body model.

E. Hiyama, Y. Yamamoto, T. Motoba and M. Kamimura,PRC80, 054321 (2009)

Now, it is interesting to see as follows:

(1)What is the level structure of A=7 hypernuclei without CSB interaction?

(2) What is the level structure of A=7 hypernuclei with CSB interaction?

BΛ

：C

AL=

5.21

BΛ

：C

AL=

5.28

6Be6Li

7BeΛ

(T=1)

(T=1)7LiΛ

6He

7HeΛ

EX

P=

5.2

6

EX

P=

5.1

6

CA

L= 5

.36

BΛ

： E

XP

= 5

.7±0

.2±0

.2pr

elim

inar

y

(Exp: 1.54)

(Exp: -0.14)(exp:-0.98)

Re

por

ted

by

Has

him

oto

by

HY

P-X

JLA

B:E

01-0

11 e

xper

imen

t

Next we introduce a phenomenological CSB potential with the central force component only.

3He+Λ0 MeV

-1.24

-2.39

1+

0+

3H+Λ0 MeV

-1.00

-2.04

1+

0+

0.35 MeV

n n

p Λ

4HΛ

n

p Λ

4HeΛ

p

Exp.

0.24 MeV

Strength, rangeare determinedao as to reproduce the data.

BΛ

： E

XP

= 5

.7±0

.2±0

.2

α

p n

5.36

(with

out C

SB

)

5.21

(w

ithou

t CS

B)

5.16

(with

CS

B)

5.44

(with

CS

B)

With CSB

Without CSB With CSB

α

Λ

pp

7BeΛ

The experimental BΛ 　 valueis found to be reproducedresults without the CSB effect and to be inconsistent withthe results with CSB.

In order to reproduce the bindingenergy of 7Be, the CSB interactionseems to be vanishing or opposite sign from that in the A=4 systems.

Λ

For the study of CSB interaction, we need BΛ within 100keV

accuracy.For this purpose, (e,e’K+) reaction might be powerful tool.

For the study of CSB interaction,

(1) 4He (e,e’K+) 4H

(2) 4He(π+,K+) 4HeΛ

Λ

We want to know BΛ accurately in s-shell Λ hypernuclei.

Maintz?

Where? Possible? or emulsion experiment again?

10B (e, e’K+) 10Be

10B(π+,K+) 10B

Λ

Λ

Analysis is in progress.

Where?

ハイペロンー核子間相互作用が分かるとその先には？

陽子＋中性子＋第３の粒子（ハイペロン）で構成される多体系の新しい特徴を正確に捉えることができる。

通常の原子核では考えられなかった新しい現象を予言し、発見、解明することができる。

物理的興味深い現象は、 sd-shell にあるのではないか？

Λ

原子核

Λ

ハイパー核

原子核全体が縮む！従来の原子核の常識を超えた新しい現象十数年前に元場、池田、山田によって指摘

Theoretical calculationE. Hiyama et al. Phys. Rev. C59 (1999), 2351.

p n

n

n

p

p

Λ

p

nnn

p

p

Λ

２２％原子核が縮むと予言6Li

KEK-E419 実験K.Tanida et al., Phys. Rev. Lett. 86, 1982(2001).

１９％縮むことが検証

予言とほぼ一致

このような原子核が縮むという従来の原子核の常識を破るような現象を予言できたのは、 Λ と核子の間の相互作用がほぼ確立してきたから

もう少し重い原子核に Λ 粒子を投入するとその構造はどのように変化するのか？

For example

α

α α

+ Λ

α

α αΛ

12C13CΛ

Shell structure Cluster structure 共存

Example :13C

0 MeV

0+2

0+1

-7.27

+0.86

3α threshold

Shell-like compact state

Loosely coupled α clustering state

Λ

Λ

Λ

How is the structure change when a Λ particle is injectedinto 2 kinds of 0+ states in 12C ?

12C

α

α

α

Λ

α

ααDrastic

shrinkage

No change

O

O

The density of α―α relative motion as a function of α―α distance.

This difference comes from the state dependence of nucleon density distribution in core nucleus.

excitate-state

ground-state

CC

CC

C

　　　　

0+1

2+1

0+2

2+2

2+1

0+2

2+2

shell-like states

cluster-likestates

3αthreshold

B(E2):Reduced

B(E2):Enhanced

B(E2):No change

B(E2)

12C

α

αα

α

αα

Λ

13CΛ

0+1

13C のＢ（Ｅ２）の測定をして欲しいΛ

01+

0+2

shell-likestates

α-clusteringstates

A≥10 core nucleus

2+1

2+2

01+

0+2

2+1

2+2

Does energy gain goin parallel way for all the states?

No !

Λ

A≥11 Λ hypernucleus

Schematic illustration

Energy gain by Λ-particle addition

ΔE(shell-like) > ΔE(clustering)

shell-likestate

clusteringstate

shell-likestate

A≥10 corenucleus

A≥11 Λ hypernucleus

Level crossing

For example of level crossing : 12C and 13CΛ

α

α α

α

αα

Λ

12C13CΛ

Level crossing between shell-like state and clustering state

shell-like states

clustering states

shell-likestates

B =7.83MeV

B (EXP,C

AL)=11.69M

eVLevel crossing

3. S=-2 ハイパー核と

YY 相互作用

Λ+ ・・・・

It is conjectured that extreme limit, which includes many Λs in nuclear matter, is the core of a neutron star.

In this meaning, the sector of S=-2 nuclei ,

double Λ hypernuclei and Ξ hypernuclei is just the entrance to the multi-strangeness world.

　 However, we have hardly any knowledge of the YY interaction

　 because there exist no YY scattering data.Then, in order to understand the YY interaction, it is crucial to study the structure of double Λ hypernuclei and Ξ hypernuclei.

What is the structure when one or more Λs are added to a nucleus?

nucleus

ΛΛΛΛ

+ + +

Talked by Ohnishi

Uniquely 　 identified 　 without 　 ambiguity

for 　 the first time

α+Λ+Λ

7.25 ±0.1 MeV

0+

　　　 Recently, the epoch-making data

　　 has been reported by the 　　　 KEK-E373 experiment.

Observation of 　 6HeΛΛ

α

ΛΛ

使用 spin-independent force の強さを半分にするように提案

比較

①

②

③

YY 相互作用 Nijmegen model D　

Λ Λ

αダブルラムダハイパー核の構造計算

Spectroscopic experiments Emulsion experiment (KEK-E373) by Nakazawa and his collaborators

6HeΛΛ

④

YY 相互作用を決めるストラテジー

未発見ダブルラムダハイパー核を予言

比較

少数粒子系計算法を使用した私の役割

・ E07 “Systematic Study of double strangness systems at J-PARC” by Nakazawa and his collaborators

Approved proposal at J-PARC

エマルジョン実験理論計算インプット : ΛΛ interaction to reproduce the observed binding energy of 　 6HeΛΛ

the identification of the state

(1) スピン・パリティ

(2) 発見された状態は基底状態？励起状態？実験で決めるのは困難

Successful example to determine spin-parity ofdouble Λ hypernucleus --- Demachi-Yanagi event for 10Be

Demachi-Yanagi event

12.33+0.35

-0.21 MeV

8Be+Λ+Λ

ground state ?excited state ?

Observation of 　 10Be --- KEK-E373 experiment

ΛΛ

ΛΛ

αα

Λ Λ

10BeΛΛ

10BeΛΛ

4-body calculation of 10Be (Deamchi-Yanagi event)ΛΛ

VΛΛ To reproduce the 　 observed binding energy of 6He

ΛΛα+Λ+Λ

7.25 ±0.1 MeV

E. Hiyama, M. Kamimura, T. Motoba, T.Yamada and Y. YamamotoPhys. Rev. C66, 024007 (2002)

The binding energies of all the subsystems in 10Be are reproduced .

ΛΛ

α

ΛΛ

αα

Λ Λ

αα

Λ Λαα

Λ Λ

In this way, we succeeded ininterpreting the spin-parityby comparing the experimental dataand our theoretical calculation.

Successful interplitation of spin-parity of

E. Hiyama, M. Kamimura,T.Motoba, T. Yamada and Y. YamamotoPhys. Rev. 66 (2002) , 024007

Demachi-Yanagi event

αα

Λ Λ

α

x

Λ Λ

x = n p d t3He

= = = = =

7He 7Li 8LiΛΛ ΛΛ ΛΛ

8Li 9BeΛΛ ΛΛ

Therefore, the 4-body calculation has predictive power. Hoping to observe new 　 double Λ hypernuclei in future experiments, I have predicted level structures of these 　 double Λ hypernuclei within the framework of the α+x+Λ+Λ 4-body model.

E. Hiyama, M. Kamimura, T. Motoba, T.Yamada and Y. YamamotoPhys. Rev. C66, 024007 (2002)

Spectroscopy of ΛΛ-hypernuclei E. Hiyama, M. Kamimura,T.Motoba, T. Yamada and Y. YamamotoPhys. Rev. 66 (2002) , 024007

By comparing this theoretical prediction and future experimental data, we can interpret the spectroscopy of those double Λ hypernuclei.

Spectroscopy of ΛΛ-hypernuclei E. Hiyama, M. Kamimura,T.Motoba, T. Yamada and Y. YamamotoPhys. Rev. 66 (2002) , 024007

A 11ΛΛ hypernuclei >

I have been looking forward to having

new data in this mass-number region.

new data

(2009)

αα

Λ Λ

n

11BeΛΛ

BΛΛ= 20.83±1.27 MeV

Important issues: Is the Hida event the observation of 11Be or 12Be ?

Observation of 　 Hida eve

nt

αα

Λ Λ

n n

12BeΛΛ

BΛΛ= 22.48±1.21 MeV

ΛΛ

ΛΛ

α

Λ Λ

n

11BeΛΛ

α

Core nucleus, 9Be is well described as

α+α+ n three-cluster model.

Then, 11Be is considered to be suited for

studying with α+α+ n +Λ+Λ 5-body model.

ΛΛ

Difficult 5-body calculation:

1) 3 kinds of particles (α, Λ, n)

2) 5 different kinds of interactionsΛ Λ

Λ n

αΛ

αn

αα

3) Pauli principle between α and α,

and between α and n

But, I have succeeded in performing this calculation.

Two αparticles are symmetrized.

Two Λparticles are antisymmetrized.

Some of important Jacobi corrdinates of the α+ α+ n + Λ+ Λ system.

120 sets of Jacobi corrdinates are employed.

Before doing full 5-body calculation,

it is important and necessary to reproduce the observed

binding energies of all the sets of subsystems in 11Be.

In our calculation, this was successfully done using the same interactions for the following 9 subsystems:

CAL : +0.80 MeV

EXP : +0.80 MeV

5He (3/2-)

ΛΛ

8Be (0+)

CAL : +0.09 MeV

EXP : +0.09 MeV

9Be (3/2-)

CAL : -1.57 MeV

EXP : -1.57 MeV

αα

Λ Λn

αα

Λ Λn

αα

Λ Λ

n

αα

Λ Λn

CAL : -0.32 MeV

EXP : -0.32 MeV

5He (1/2-)6He (1-)Λ

CAL : -3.29 MeV

EXP : -3.29 MeV

αα

Λ Λn

Λ

αα

Λ Λn

9Be (1/2+)Λ

CAL : -6.64 MeV

EXP : -6.62 MeV

(The energy is measured from the full-breakup threshold

of each subsystem)

ΛΛαα

Λ Λ

n

10Be (0+, 2+ )Λ Λ

CAL (2+): -10.96 MeV

EXP (2+): -10.98 MeV

CAL (0+): -14.74 MeV

EXP (0+): -14.69 MeV

ΛΛαα

Λ Λ

n

6He (0+ )Λ Λ

CAL (0+): -6.93 MeV

EXP (0+): -6.93 MeV

ΛΛαα

Λ

Λ

n

10Be (1-)

CAL : -10.64 MeV

EXP : -10.64 MeV

Λ

All the potential parameters have been adjusted in the 2- and 3-body subsystems.

Therefore, energies of these 4-body susbsystems and the 5-body system are predicted with no adjustable pameters.11Be

Λ Λ

adjusted predicted

Convergence of the ground-state energy of the α+α+ n +Λ+Λ 5-body system ( ) 11Be

ΛΛ

J=3/2-

0α+α+ n +Λ+Λ

Exp.-22.42±1.27

-19.81

Exp =

20.83±1.27C

al = 18.24

BΛ

Λ

11BeΛΛ

-22.0

CAL

This event has another possibility, namely, observation of 12Be.ΛΛ

αα

Λ Λ

n n12BeΛΛ

BΛΛ= 22.48±1.21 MeV

For this study, it is necessary to calculate 6-body problem.At present, it is difficult for me to perform 6-body calculation.Next year, I will try to do it.

For the confirmation 　 of Hida event, we expect to have moreprecise data at J-PARC.

Spectroscopy of ΛΛ-hypernuclei

11Be ,ΛΛ

At J-PARC

A=12, 13, ……

For the study of this mass region,

we need to perform more of5-body cluster-model calculation.

Therefore, we intend to calculate the following 5-body systems.

αα

Λ Λ

α

14CΛΛ

To study 5-body structure of these hypernuclei is interesting and important as few-body problem.

αα

Λ Λp

11BΛΛ

αα

Λ Λd

12BΛΛ

αα

Λ Λt

αα

Λ Λ3He

13BΛΛ

13CΛΛ

4. Future subjects

Ξhypernuclei

11B

pK-

Ξ-

11B

12C Ξ hypernucleus

・ E05 “Spectroscopic study of Ξ-Hypernucleus, 12Be,

via the 12C(K-,K+) Reaction”

by Nagae 　 and his collaborators

Day-1 experiment

This will be the first observation of Ξ hypernucleus

K+

Approved proposal at J-PARC :

Ξ-

For the study of ΞN interaction, it is important to study

the structure of Ξ hypernuclei.

12C(K-, K+) 12BeΞ-

Day-1 experiment at J-PARC

What part’s information of the ΞN interaction do we extract?

(T=1, J=1-)

VΞN = V0 + σ ・ σ Vσ ・ σ ＋ τ ・ τ Vτ ・ τ ＋ (σ ・ σ)(τ ・ τ) Vσ ・ σ 　

τ ・ τ

All of the terms contribute to binding energy of

12Be ( 11B is not spin-, isospin- saturated).Ξ-

Then, even if we observe 　 this system

as a bound state, we shall get only information

that VΞN 　 itself is attractive.

Therefore, after the Day-1 experiment, next,

we want to know desirable strength of V0, the spi

n-,isospin-independent term.

12BeΞ-

Ξ- t

α α

Ξ-

α α

Ξ-

α

In order to obtain useful information about V0,

the following systems are suited, because

the (σ ・ σ), (τ ・ τ) and

(σ ・ σ) (τ ・ τ) terms ofVΞN 　 vanish

by folding them

into the α-cluster

wave function that are

spin-, isospin-satulated.

VΞN = V0 + σ ・ σ Vσ ・ σ ＋ τ ・ τ Vτ ・ τ ＋ (σ ・ σ)(τ ・ τ) Vσ ・ σ 　

τ ・ τ

problem : there is NO target to produce them by the (K-, K+) experiment .

Because, ・・・

To produce αΞ- and ααΞ- systems by (K-, K+) reaction,

K-

5Li

K+

5HΞ-

K-

K+

9B 9LiΞ-

These systems

are unbound.

Then, we

cannot use them

as targets.

α

Ξ-

α

α

p

α

Ξ-

α α

p

target

As the second best candidates to extract information about the

spin-, isospin-independent term V0, we propose to perform…

K- K+

7HΞ-

K-

K+

10B (T=0) 10Li (T=1)Ξ-

α

p n

n α

Ξ-

α α

p

α

Ξ-

α

n

n

7Li (T=1/2) (T=3/2)

n n

Why they are suited

for investigating V0?

7HΞ-

αΞ-

n n

(T=3/2)

Valence neutrons are located in p-orbit,

whereas Ξparticle is located in 0s-orbit.

Then, distance between Ξ and nis much larger than the interaction range of

Ξ and n.

10Li (T=1)Ξ-

α α

n

Ξ-

n

Then, αΞ potential, in which only V0 term

works, plays a dominant role in the binding

energies of these system.

(more realistic illustration)

Ξ-

Core nucleus 6He is known to be halonucleus. Then, valence neutrons are locatedfar away from α particle.

7HΞ-

α

Ξ- n

n

(T=3/2)

10Li (T=1)Ξ-

α

Ξ-

α

n

Before the experiments will be done,

we should predict whether these

hypernuclei will be observed as

bound states or not.

Namely, we calculate the binding energies of these hypernuclei.

Ξ-

ΞN interaction

Only one experimental information about ΞN interaction

Y. Yamamoto, Gensikaku kenkyu 39, 23 (1996),

T. Fukuda et al. Phys. Rev. C58, 1306, (1998);

P.Khaustov et al., Phys. Rev. C61, 054603 (2000).

Well-depth of the potential between Ξ and 11B: -14 MeV

Among all of the Nijmegen model,

ESC04 (Nijmegen soft core) and ND (Nijmegen Model D)

reproduce the experimental value.

OtherΞN interaction are repulsive or weak attractive.

We employ ESC04 and ND.

The properties of ESC04 and ND are quite different from each other.

T=0, S=1 　　 strongly attractive

T=0, S=0 weakly attractiveT=1, S=1

T=1, S=0

V(T,S)

V0 = [ V(0,0) + 3V(0,1) + 3V(1,0) + 9V(1,1) ] / 16,

Property of the spin- and isospin-components of ESC04 and ND

ESC04 ND

Although the spin- and isospin-components of these two models are

very different between them (due to the different meson contributions),

we find that the spin- and isospin-averaged property,

namely, strength of the V0- term is similar to each other.

weakly attractive

weakly repulsive

(a bound state)

weakly repulsive

As mentioned before,

αΞ potential, in which only V0 term works,

plays a dominant role in the binding

energies of these system.

7HΞ-

α

Ξ- n

n

(T=3/2)

10Li (T=1)Ξ-

α

Ξ-

α

n

Therefore, interestingly,

we may expect to have similar binding ener

gies between ESC04 and ND,

although the spin- and isospin-components

are very different between the two.

α+ n + n + Ξ-

(αΞ- ) + n + n

6He + Ξ-

0.0

-1.35 1/2+

ESC04ND

0.75

1.71α+ n + n + Ξ-

(αΞ- ) + n + n

6He + Ξ-0.0

-1.56 1/2+

0.39

0.96

MeV

MeV

7HΞ-

7HΞ-

n

Ξ- n

α

E. Hiyama et al.,

PRC78 (2008) 054316

In experiments, we can expect a bound state.

4-body calculation of 7HΞ-

Similar bindingenergies using ND and ESC04.

Independent on employed ΞN potential

α+ α+ n +Ξ-

(ααΞ- ) + n

9Be + Ξ-

0.0

-3.18 2-

ESC04d ND

3.60

5.17α+ α + n +Ξ-

0.0

-2.96 2-

1.32

2.86

MeV

MeV

10LiΞ-

Ξ- n

α

E. Hiyama et al.,

PRC78 (2008) 054316 4-body calculation of

α

10LiΞ-

9Be + Ξ-

(ααΞ- ) + n

10Li-Ξ

In experiments, we can expect a bound state.

Similar bindingenergies using ND and ESC04d.

Independent on employed ΞN potential

In this way, the binding energies of Ξ hypernuclei with A=7 and 10 are dominated by αΞ potential, namely, spin-, and 　 iso-spin independent ΞN interaction （Ｖ 0 ） .

Then, to get information about this part, we propose to perform the (K-,K+) experiment by using 7Li and 10B targets at J-PARC after the Day-1 experiment with 12C target.

QCD



ハイペロンー核子（ YN) 、ハイペロンーハイペロン（ YY) 間力


YN 散乱実験

現在のS= -1, -2 の世界の研究方針　　　　

X

極端に少ない

Shell 模型Few-body 計算

Cluster 模型

私の役割（ Few-body 計算法を用いて）

よく分かっていない

まずは、構造の研究から、相互作用を決めるのが、先決なのが現状

中性子星の内部の研究まだまだ発展途上

QCD

ハドロン

Lattice QCD


核子ー核子間力（ NN ）ハイペロンー核子 (YN) 間力

まだまだ荒削りではあるが、QCD から、バリオン多体系の構造を理解できる日が近い？

N. Ishii, S. Aoki and T. Hatsuda,Phys. Rev. Lett. 99, 022001(2007)

最新の研究動向

5 年後、１０年後のハドロン物理研究の考えられる将来像

QCD


現実的相互作用（ YN 、 YY 、メソンーバリオン）


Shell 模型 Few-body 計算Cluster 模型

J-PARCYN 散乱実験

ペタコンの導入でさらに発展

J-PARC高分解能ガンマ線実験ペタコン

有限温度における高密度状態の物理（中性子星内部の研究）

（ personal view)

新しくこの矢印が生まれる！

今は予想もできない現象を予言可能チャーム核、オメガハイペロンを原子核に入

れたハイパー核、いろいろなメソンを原子核に入

れたエキゾチックな原子核を予言

Multi-strangeness systemsuch as Neutron star

J-PARC

Concluding remark

おわり

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ハイパー核構造の今後の展望 -- 少数粒子系理論物理的観点から --