少数粒子系理論物理的観点から〜 - J-PARC

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
ガウス展開法
“Gaussian Expansion Method for Few-Body Systems”
E. Hiyama, Y. Kino, M. Kamimura,
Prog. Part. Nucl. Phys. 51 (2003) 223 - 307.
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体問題シュレーディンガー方程式：６変数２階偏微分方程式
３体問題
４体問題
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
クーロン３体問題は
１０桁の精度
V(R）
・構成粒子は何でもよい、
質量、電荷を問わない。
強い相関 (核力など）
（電子、陽子、中性子、クオーク、・・・・・）
・粒子間に強い相関がある場合
にも精密に適用できる。
３体問題
４体問題
0
R
現在は、
さらに
５体問題
特に重点をおいて
これまで研究を行ってきた。
私の研究の
進め方の特徴
ハイパー核物理
フィードバック：
不安定核物理
適用・貢献
私の研究法の発展
宇宙・天体核物理
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）
ミュオン触媒核融合
少数粒子系物理
ハドロン物理
QCD
現在の
S= -1, -2 の世界
Lattice QCD
ハドロン
中間子理論
クオーク模型
YN散乱実験
極端に少ない
ハイペロンー核子（YN)、
ハイペロンーハイペロン（YY)間力
私の役割
（Few-body計算法
を用いて）
X
よく分かっていない
多体系のダイナミクス
Few-body計算
Shell 模型
Cluster模型
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
③改良点を指摘
①使用
ハイパー核構造の精密計算
No direct
informationX
私の少数粒子系
精密計算法
② 比較
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
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
①使用
③改良点を指摘
ハイパー核構造の精密計算
No direct
X
information
② 比較
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？
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
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
One of the important issue
----- SLS (Symmetric LS)
----- ALS (Anti symmetric LS)
YN LS force and energy-splitting in 9Be and
Λ
----- SLS (Symmetric LS)
----- ALS (Antisymmetric LS)
13C
Λ
Λ
Λ
8Be
12C
9Be
Λ
13C
Λ
[vanishes in S=0 nuclei, Pauli]
[breaks charge symmetry]
In the ALS part :
0 < VALS (meson theory) << VALS (constituent quark model)
Nijgemen model D, F , soft core ’97a-f
Kyoto-Niijata
FSS potential
BNL-E929
BNL-E930
Λ (0s)
3/2+
γ
2+
γ
5/2+
0+
ΔE
3/2-
ΔE
LS
splitting
γ
γ
0+
1/2+
8Be
1/2-
Λ (0p)
1/2+
12C
9Be
13C
Λ
Λ
3- and 4-body calculations:
E. Hiyama, M. Kamimura, T. Motoba, T. Yamada and Y. Yamamoto
Phys. Rev. Lett. 85 (2000) 270.
Λ
α α
9Be
Λ
α
α α
Λ
13C
Λ
YN LS force
1) Meson theory : Nijmegen Model D, F, soft core’97 a – f.
2) Qurak model : Kyoto-Niigata, FSS
ΛN LS force and
9Be
Λ
and
13C
Λ
9Be
Λ
BNL-E930
80
5/2+
200
keV
～
3/2+
3/2+
5/2+
Quark
Meson
13C
Λ
H. Akikawa et al.
Phys. Rev. Lett. 88 (2002)
082501; H. Tamura et al.
Nucl. Phys. A754 (2005) 58c
35
～
40
keV
Nijmegen model D,F
Soft core ’97a-f
360
3/2-
960
keV
～
1/2-
Meson
3/2+
5/2+
Exp. 43±5 keV
BNL-E929
1/23/2Quark
150
～
200
keV
1/23/2Exp. 152 ± 54
±36
keV
S.Ajimura et al.
Phys. Rev. Lett. 86,(2001) 4255
LS splitting in Λ9Be
Meson Theory
SLS
5/2+
140～250 keV
(Large) (Small)
SLS + ALS
5/2+
We suggested there are 2
paths to improve the
Meson models :
reduce the SLS strength
or enhance the ALS
strength
so as to reproduce the
observed LS splittings
in 9Be and Λ13C.
Λ
80～200 keV
3/2+
3/2+
Exp. 43±5 keV
(Large) - (Large)
SLS + ALS
Λ
α
35～40keV
α
9Be
Λ
Quark-based
3/2+
5/2+
5/2+
3/2+
LS splitting in 9Be
Λ
Recently, a new YN interaction based on meson theory,
extended soft core potential 06 (ESC06) by Th. A Rijken
9Be
Λ
(reduced)
(small)
SLS
SLS + ALS
3/2+
98 keV
5/2+
ESC06
Hiyama (2007)
39 keV
Good agreement
BNL-E930
3/2+
5/2+
Exp. 43±5 keV
H. Akikawa et al.
Phys. Rev. Lett. 88,(2002)82501;
H. Tamura et al.
Nucl. Phys. A754,58c(2005)
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
①使用
No direct
informationX
③改良点を指摘
④ new version
potential (ESC06)
9Beと13Cのハイパー核構造の精密計算
Λ
Λ
② 比較
⑤実験と一致
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
Hypernuclear g-ray data since 1998
・Millener (p-shell model),
Picture by Tamura
・ Hiyama (few-body)
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
Λ
4He
Λ
・E10 “Study on Λ-hypernuclei with the doubleCharge-Exchange reaction”
by Sakaguchi , Fukuda and his collaboratiors
9He
Λ
6H
Λ
(1) Charge Symmetry breaking
In S=0 sector
Energy difference comes from
dominantly Coulomb force
between 2 protons.
Exp.
N+N+N
0 MeV
Charge symmetry breaking
effect is small.
- 7.72 MeV
1/2+
1/2+
- 8.48 MeV
3H
n
n
n
p
3He
p
p
Charge Symmetry breaking
Exp.
3He+Λ
0 MeV
-1.00
1+
-1.24
3H+Λ
0 MeV
0.24 MeV
-2.39
1+
-2.04
0+
0+ 0.35 MeV
n
p
p
4He
Λ
Λ
n
n
p
Λ
4H
Λ
3He+Λ
0 MeV
1+
-1.00
-1.24
(cal: -0.01 MeV(NSC97e))
0+
(cal. 0.07 MeV(NSC97e))
-2.04
Λ
n
n
Λ
p
Λ
4He
0+
(Exp: 0.35 MeV)
p
p
1+
(Exp: 0.24 MeV)
-2.39
n
3H+Λ
0 MeV
・A. Nogga, H. Kamada and W. Gloeckle,
Phys. Rev. Lett. 88, 172501 (2002)
4H
Λ
・E. Hiyama, M. Kamimura, T. Motoba, T. Yamada and Y. Yamamoto,
Phys. Rev. C65, 011301(R) (2001).
N
・H. Nemura. Y. Akaishi and Y. Suzuki,
Phys. Rev. Lett.89, 142504 (2002).
N
N
Λ
+
N
N
N
Σ
Exp.
3He+Λ
0 MeV
-1.15
1+
γ
-2.39
0+
n
p
p
4He
Λ
But, we need
BΛ in Λ4He.
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
Λ
J-PARC: Day-1 experiment
・E13 “γ-ray spectroscopy of light hypernuclei”
by Tamura and his collaborators
We should wait for their data at J-PARC.
It is interesting to investigate the charge symmetry breaking effect
in 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.
n
n
α
6He
n
p
α
6Li(T=1)
p
p
α
6Be
n
n
n
α
7He
Λ
p
Λ
Λ
Λ
p
p
α
7Li(T=1)
Λ
α
7Be
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.
Reported by Hashimoto at HYP-X
Exp.
1.54
6He
6Be
6Li
(T=1)
-3.79
7Li (T=1)
Λ
Λ
7He
7Be
Λ
Important issue:
To predict the Λ binding energy of 7ΛHe whose analysis is in progress at JLAB
using ΛN interaction to reproduce the Λ binding energies of
7Li (T=1) and 7Be
Λ
Λ
To study the effect of CSB in iso-triplet A=7 hypernuclei.
n
n
n
α
7He
Λ
p
Λ
Λ
Λ
p
p
α
7Li(T=1)
Λ
α
7Be
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?
Reported by Hashimoto by HYP-X
(Exp: 1.54)
6Be
(Exp: -0.14)
(exp:-0.98)
6Li
6He
(T=1)
7Be
Λ
7Li (T=1)
Λ
7He
Λ
Next we introduce a phenomenological CSB potential
with the central force component only.
Strength, range
are determined
ao as to reproduce
the data.
3He+Λ
0 MeV
-1.00
1+
-1.24
3H+Λ
0 MeV
0.24 MeV
-2.39
1+
-2.04
0+
0+ 0.35 MeV
n
p
p
4He
Λ
Λ
Exp.
n
n
p
Λ
4H
Λ
With CSB
p
α
n
p
p
Λ
α
7Be
Λ
The experimental BΛ value
is found to be reproduced
results without the CSB effect
and to be inconsistent with
the results with CSB.
Without CSB
With CSB In order to reproduce the binding
energy of Λ7Be, the CSB interaction
seems to be vanishing or
opposite sign from that in the
A=4 systems.
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+) Λ4H
(2) 4He(π+,K+) 4ΛHe
Maintz?
Where? Possible?
or emulsion experiment again?
We want to know BΛ accurately in s-shell Λ hypernuclei.
10B
(e, e’K+)
10Be
Λ
10B(π+,K+) 10B
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
Λ
原子核
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 calculation
E. Hiyama et al. Phys. Rev. C59 (1999), 2351.
p
n
n
Λ
n
Λ
n
p
p
n
6Li
n
p
p
p
２２％原子核が縮むと予言
予言とほぼ
一致
KEK-E419実験
K.Tanida et al., Phys. Rev. Lett. 86, 1982(2001).
１９％縮むことが検証
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
Λ
13C
Λ
12C
Shell structure
Cluster structure
α
共存
Example :13Λ C
Λ
α
α
12C
0+2
Λ
Loosely coupled α clustering state
+0.86
0 MeV
α
3α threshold
Λ
0+1
Shell-like compact state
-7.27
How is the structure change when a Λ particle is injected
into 2 kinds of 0+ states in 12C ?
The density of α―α relative motion as a function of α―α distance.
α
excitate-state
C
C
α
O
Drastic
shrinkage
O
ground-state
C
C
α
C
No change
This difference comes from the
state dependence of nucleon
density distribution in core nucleus.
2+2
cluster-like
states
0+2
13CのＢ（Ｅ２）の測定をして欲しい
Λ
3αthreshold
2+2
2+1
B(E2):Reduced
shell-like
states
B(E2)
0 +1
0+ 2
B(E2):Enhanced
12C
2+ 1
α
B(E2):No change
0+1
α
α
13C
Λ
α
α
α
Λ
Schematic illustration
shell-like
states
α-clustering
states
Does energy gain go
in parallel way for all the states?
No !
2+ 2
0+ 2
2+ 1
2+ 2
0+2
01 +
2+ 1
A≥10 core nucleus
Λ
01 +
A≥11 Λ hypernucleus
Energy gain by Λ-particle addition
ΔE(shell-like) > ΔE(clustering)
shell-like
state
clustering
state
shell-like
state
Level crossing
A≥10 core
nucleus
A≥11 Λ hypernucleus
For example of level crossing : 12C and 13
C
Λ
α
α
α
α
α
12C
α
Λ
13C
Λ
Level crossing between shell-like state and clustering state
shell-like
states
clustering
states
shell-like
states
Level crossing
3. S=-2 ハイパー核
と
YY 相互作用
What is the structure when one or more Λs are
added to a nucleus?
Λ
nucleus
Λ
+
Λ
+
Λ
+
Λ
+ ・・・・
It is conjectured that extreme limit, which includes
many Λs in nuclear matter, is the core of a neutron star.
Talked by Ohnishi
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.
Recently, the epoch-making data
has been reported by the
KEK-E373 experiment.
Observation of
6He
ΛΛ
Uniquely identified without ambiguity
for the first time
α+Λ+Λ
7.25 ±0.1 MeV
0+
Λ
Λ
α
YY相互作用を決めるストラテジー
YY 相互作用
Nijmegen model D
① 使用
③
比較
Spectroscopic experiments
Emulsion experiment (KEK-E373)
by Nakazawa and his collaborators
ΛΛ
Λ
ダブルラムダハイパー核の構造計算
②
6He
spin-independent force の
強さを半分にするように提案
Λ
α
④
未発見ダブル
ラムダハイパー核
を予言
Approved proposal at J-PARC
・E07
“Systematic Study of double strangness systems at J-PARC”
by Nakazawa and his collaborators
(1)スピン・パリティ
実験で決めるのは困難
(2)発見された状態は基底状態？励起状態？
少数粒子系計算法を使用した
私の役割
比較
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 ΛΛ6He
the identification of the state
Successful example to determine spin-parity of
double Λ hypernucleus --- Demachi-Yanagi event for 10Be
Observation of
10Be
8Be+Λ+Λ
--- KEK-E373 experiment
Λ
Λ
α
α
+0.35
12.33 -0.21 MeV
ground state ?
excited state ?
10Be
10Be
Demachi-Yanagi event
4-body calculation of
10Be
ΛΛ
(Deamchi-Yanagi event)
E. Hiyama, M. Kamimura, T. Motoba, T.Yamada and Y. Yamamoto
Phys. Rev. C66, 024007 (2002)
VΛΛ
Λ
Λ
α
α
To reproduce the observed binding
energy of ΛΛ 6He
α+Λ+Λ
7.25 ±0.1 MeV
The binding energies of all the subsystems in ΛΛ10Be
are reproduced .
Λ
Λ
α
α
Λ
Λ
α
Λ
Λ
α
α
Successful interplitation of spin-parity of
Λ
Λ
α
α
E. Hiyama, M. Kamimura,T.Motoba,
T. Yamada and Y. Yamamoto
Phys. Rev. 66 (2002) , 024007
In this way, we succeeded in
interpreting the spin-parity
by comparing the experimental data
and our theoretical calculation.
Demachi-Yanagi
event
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. Yamamoto
Phys. Rev. C66, 024007 (2002)
Λ
Λ
x
t
=
7He 7Li
8Li
8Li
ΛΛ
ΛΛ
ΛΛ
ΛΛ
3He
=
d
=
=
p
=
x
n
=
α
9Be
ΛΛ
Spectroscopy of ΛΛ-hypernuclei
E. Hiyama, M. Kamimura,T.Motoba,
T. Yamada and Y. Yamamoto
Phys. 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. Yamamoto
Phys. Rev. 66 (2002) , 024007
A > 11
ΛΛ hypernuclei
new data
(2009)
I have been looking forward to having
new data in this mass-number region.
Observation of Hida event
Λ
Λ
Λ
Λ
n
n
α
α
n
α
α
11Be
ΛΛ
12Be
ΛΛ
BΛΛ= 20.83±1.27 MeV
BΛΛ= 22.48±1.21 MeV
Important issues:
Is the Hida event the observation of 11
Be
ΛΛ
12Be ?
or ΛΛ
Core nucleus, 9Be is well described as
α+α+ n three-cluster model.
11Be
ΛΛ
Λ
Λ
n
α
Then,ΛΛ 11Be is considered to be suited for
studying with α+α+ n +Λ+Λ 5-body model.
α
Difficult 5-body calculation:
1) 3 kinds of particles (α, Λ, n)
Λ
Λ
Λ
n
Λ
α
n
α
α
α
2) 5 different kinds of interactions
3) Pauli principle between α and α,
and between α and n
But, I have succeeded in performing this calculation.
Some of important Jacobi corrdinates of the α+ α+ n + Λ+ Λ system.
Two αparticles are
symmetrized.
Two Λparticles are
antisymmetrized.
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 ΛΛ11Be.
In our calculation, this was successfully done using the same
interactions for the following 9 subsystems:
Λ
Λ
Λ
α
5He (3/2-)
Λ
n
n
α
Λ
Λ
n
α
α
8Be
(0+)
α
9Be
α
(3/2-)
CAL : +0.80 MeV
CAL : +0.09 MeV
CAL : -1.57 MeV
EXP : +0.80 MeV
EXP : +0.09 MeV
EXP : -1.57 MeV
Λ
Λ
n
α
5He
Λ
α
(1/2-)
Λ
n
Λ
α
α
6He
Λ
(1-)
Λ
n
Λ
α
9Be
Λ
α
(1/2+)
CAL : -0.32 MeV
CAL : -3.29 MeV
CAL : -6.64 MeV
EXP : -0.32 MeV
EXP : -3.29 MeV
EXP : -6.62 MeV
(The energy is measured from the full-breakup threshold
of each subsystem)
adjusted predicted
Λ
n
Λ Λ
α
6He
ΛΛ
ΛΛ
n
Λ n
α ΛΛ α
α
(0+ )
CAL (0+): -6.93 MeV
EXP (0+): -6.93 MeV
Λ Λ
10Be
Λ
(1-)
CAL : -10.64 MeV
EXP : -10.64 MeV
α
ΛΛ
10Be
ΛΛ
α
(0+, 2+ )
CAL (2+): -10.96 MeV
EXP (2+): -10.98 MeV
CAL (0+): -14.74 MeV
All the potential parameters have been
adjusted in the 2- and 3-body subsystems.
EXP (0+): -14.69 MeV
Therefore, energies of these 4-body susbsystems and
the 5-body systemΛ Λ11Be are predicted with no adjustable pameters.
Convergence of the ground-state energy of
11Be
the α+α+ n +Λ+Λ 5-body system (
)
ΛΛ
0
α+α+ n +Λ+Λ
J=3/2-
11Be
ΛΛ
-19.81
-22.0
Exp.-22.42±1.27
CAL
This event has another
possibility, namely, observation of
Λ
n
12Be
ΛΛ
α
12Be.
ΛΛ
Λ
n
BΛΛ= 22.48±1.21 MeV
α
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 more
precise data at J-PARC.
Spectroscopy of ΛΛ-hypernuclei
At J-PARC
11Be
ΛΛ
, A=12, 13, ……
For the study of this mass region,
we need to perform more of
5-body cluster-model calculation.
Therefore, we intend to calculate the following 5-body systems.
Λ
Λ
Λ
p
α
α
11B
ΛΛ
Λ
α
α
α
14C
Λ
α
α
Λ
Λ
t
d
12B
ΛΛ
Λ
ΛΛ
Λ
α
13B
ΛΛ
Λ
3He
α
α
α
13C
ΛΛ
To study 5-body structure of these hypernuclei
is interesting and important as few-body problem.
4. Future subjects
Ξhypernuclei
For the study of ΞN interaction, it is important to study
the structure of Ξ hypernuclei.
Approved proposal at J-PARC : Day-1 experiment
・E05 “Spectroscopic study of Ξ-Hypernucleus, 12Be,
via the
12C(K-,K+)
Ξ
Reaction”
by Nagae and his collaborators
K+
K-
Ξ-
p
11B
12C
11B
Ξ
hypernucleus
This will be the first observation of Ξ hypernucleus
12C(K-,
K+) 12Be
Day-1 experiment at J-PARC
Ξ-
What part’s information of the ΞN interaction do we extract?
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-
Ξ-
t
α
α
12Be
Ξ-
(T=1, J=1-)
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
spin-,isospin-independent term.
VΞN = V0 + σ・σ Vσ・σ ＋ τ・τ Vτ・τ＋ (σ・σ)(τ・τ) Vσ・σ
τ・τ
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 of
VΞN vanish
by folding them
into the α-cluster
wave function that are
Ξ-
α
Ξ-
α
spin-, isospin-satulated.
problem : there is NO target to produce them
by the (K-, K+) experiment .
Because, ・・・
α
To produce αΞ- and ααΞ- systems by (K-, K+) reaction,
K-
These systems
are unbound.
Then, we
cannot use them
as targets.
K+
target
p
Ξ-
α
α
5Li
Ξ-
5H
K+
K-
Ξ-
p
α
α
9B
α
Ξ-
α
9Li
As the second best candidates to extract information about the
spin-, isospin-independent term V0, we propose to perform…
K+
K-
p
n
Ξ-
n
α
n
α
n
7Li
(T=1/2)
7H
(T=3/2)
Why they are suited
Ξ-
K+
K
-
p
α
10B
n
α
(T=0)
Ξ-
α
n
α
10Li
Ξ-
(T=1)
for investigating V0?
(more realistic
illustration)
n
n
Ξ-
α
7H
Core nucleus 6He is known to be halo
nucleus. Then, valence neutrons are located
far away from α particle.
Valence neutrons n are located in p-orbit,
whereas Ξparticle Ξ- is located in 0s-orbit.
(T=3/2)
Ξ-
n
Then, distance between Ξ and n
is much larger than the interaction range of
Ξ and n.
α Ξ- α
10Li
Ξ-
(T=1)
Then, αΞ potential, in which only V0 term
works, plays a dominant role in the binding
energies of these system.
Before the experiments will be done,
we should predict whether these Ξhypernuclei will be observed as
bound states or not.
Ξ-
n
α
n
7H
(T=3/2)
Ξ-
Ξ-
n
α
α
10Li
Ξ-
(T=1)
Namely, we calculate the binding energies
of these hypernuclei.
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.
Property of the spin- and isospin-components of ESC04 and ND
V(T,S)
T=0, S=1
ESC04
ND
strongly attractive
(a bound state)
T=0, S=0
weakly repulsive
T=1, S=1
weakly attractive
T=1, S=0
weakly attractive
weakly repulsive
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,
V0 = [ V(0,0) + 3V(0,1) + 3V(1,0) + 9V(1,1) ] / 16,
namely, strength of the V0- term is similar to each other.
As mentioned before,
αΞ potential, in which only V0 term works,
Ξ-
n
α
n
7H
plays a dominant role in the binding
energies of these system.
(T=3/2)
Ξ-
Ξ-
α
n
α
10Li
Ξ-
(T=1)
Therefore, interestingly,
we may expect to have similar binding
energies between ESC04 and ND,
although the spin- and isospin-components
are very different between the two.
4-body calculation of
E. Hiyama et al.,
7H
Ξ-
PRC78 (2008) 054316
ESC04
MeV
1.71
ND
α+ n + n + Ξ6He
0.75
0.0
MeV
0.96
0.39
+ Ξ-
1/2+
6He
7H
+ Ξ-
1/2+
-1.56
7H
Ξ-
Ξ-
In experiments,
we can expect
a bound state.
(αΞ- ) + n + n
0.0
(αΞ- ) + n + n
-1.35
α+ n + n + Ξ-
α
Ξ-
n
n
Similar binding
energies using ND and
ESC04.
Independent on employed
ΞN potential
MeV
5.17
3.60
0.0
ESC04d
10Li
-Ξ
4-body calculation of
E. Hiyama et al.,
PRC78 (2008) 054316
ND
α+ α+ n +Ξ9Be
+ Ξ-
(ααΞ- ) + n
MeV
2.86
1.32
0.0
α+ α + n +Ξ9Be
+ Ξ-
(ααΞ- ) + n
2
-2.96
-3.18
2
In this way,10the binding energies of Ξ hypernuclei
with
10
Li
Li
Ξ- are dominated by αΞ potential, namely,
ΞA=7 and 10
nΞN interaction（Ｖ
ΞSimilar binding
spin-, and iso-spin independent
0）.
energies using ND and
Then, to get information about this part,ESC04d.
we propose to perform
+) experiment byα
10B targets
experiments,
the (KIn-,K
using 7α
Li andIndependent
on employed
we can expect
12C target.
ΞN potential
at J-PARC
after the Day-1 experiment with
a bound state.
QCD
現在の
S= -1, -2 の世界の
研究方針
Lattice QCD
ハドロン
中間子理論
クオーク模型
YN散乱実験
極端に少ない
ハイペロンー核子（YN)、
ハイペロンーハイペロン（YY)間力
私の役割
（Few-body計算法
を用いて）
X
よく分かっていない
多体系のダイナミクス
Few-body計算
Shell 模型
Cluster模型
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
最新の研究動向
QCD
Lattice QCD
ハドロン
中間子理論
クオーク模型
N. Ishii, S. Aoki and T. Hatsuda,
Phys. Rev. Lett. 99, 022001(2007)
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？
5年後、１０年後のハドロン物理研究の考えられる将来像
（personal view)
QCD
ペタコンの導入でさらに
発展
Lattice QCD
ハドロン
現実的相互作用（YN、YY、メソンーバリオン）
新しくこの矢印が生まれる！
有限温度における
多体系のダイナミクス
高密度状態の物理
（中性子星内部の研究）
Shell 模型
J-PARC
YN散乱実験
Few-body計算
Cluster模型
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
J-PARC
高分解能ガンマ線実験
ペタコン
Concluding remark
Multi-strangeness system
such as Neutron star
J-PARC
おわり

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