1. Calculations on ΞNN and ΞNNN systems
Emiko Hiyama(Kyushu Univ./RIKEN)

2. The major goal of hypernuclear physics
To understand baryon-baryon interactions
Fundamental and important for the study
of nuclear physics
For this purpose, we have a lot of effort to extract
information on ΛN interaction.
Currently, in S=-1 sector, it is important on study of
three-body effect and CSB effect from ΛN-ΣN coupling.
(Cf. Tuesday afternoon session)
Next step: S=-2 sector, especially, ΞN interaction
First, we wanted to know ΞN interaction should be
attractive or repulsive.

3. Ξ-
core
nucleus
For the study of ΞN interaction, it is important to study the structure of Ξ hypernuclei.

4. Kiso event Ξ- we observed bound Ξ hypernucleus, for the first time.
0 MeV
-4.38 ± 0.25 ～-1.10 ± 0.25 MeV Ξ-
14N
Kiso event
we observed bound Ξ hypernucleus, for the first time.
Now, we understood that ΞN interaction should be attractive.

5. 11B 11B 12C K+ K- p Ξ- “Spectroscopic study of Ξ-Hypernucleus, 12Be,
via the 12C(K-,K+) Reaction”
by Nagae　and his collaborators Ξ- K+ K- p Ξ-
11B
11B
12C
Ξ hypernucleus
This experiment has been done, also.
The observed data will be reported by Prof. Nagae (Wednesday).

6. 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 and 15ΞC ( 11B and 14N is not spin-, isospin- saturated).
15ΞC α α Ξ- α d
Then, even if we observe　this system
as a bound state, we shall get information that VΞN　itself is attractive.
This is very important information.
But we have a question:
Which partial contribution makes attractive for VΞN ? Ξ-
12Be Ξ- t Ξ- α α

7. We want to know which partial wave is attractive or repulsive.
ΞN interaction: T=0, S=0
T=0, S=1
T=1, S=0
T=1, S=1 Ξ N
We want to know which partial wave is attractive or repulsive.
The suited systems to study are s-shell Ξ hypernuclei such as
NNΞ and NNNΞ systems. N N N N
Talked by
Prof. Garcilazo Ξ Ξ N

8. I show my new results of these light systems.Ξ Ξ N
I show my new results of these light systems.
NN interaction: AV8 potential
ΞN interaction :
Nijimegen extended soft core potential (ESC08c)
Realistic potential (only ΞN　channel)
ΞN interaction by HAL collaboration (Lattice QCD calculation)
The potential was made by K. Sasaki and Miyamoto.

9. HAL potential
In HAL potential , the statistical errors are NOT included.
Talked by Prof. Inoue in this morning session

10. Property of the spin- and isospin-components of ESC08 and HAL
V(T,S)
ESC08c
HAL
T=0, S=1 strongly attractive
T=0, S=0
T=1, S=1
T=1, S=0
Weakly attractive
weakly repulsive
Strongly attractive
strong attractive
Weakly attractive
weakly repulsive
Weakly repulsive
Although the spin- and isospin-components of these two models are very different between them.
It is interesting to see the difference in the energy spectra in s-shell Ξ hypernuclei.

11. ESC08c d+ Ξ d+ Ξ -2.07 MeV -2.57 MeV J=3/2+ T=1/2, J=1/2+ and J=3/2+ Ξ
I used the different version of ESC08c (realistic force).
There is possibility to have different results.
However, I also have two bound states in three-body system.

12. No bound state HAL potential d+ Ξ d+ Ξ J=3/2+ T=1/2, J=1/2+ and J=3/2+
0 MeV
d+ Ξ
d+ Ξ
0 MeV
No bound state
J=1/2+
J=3/2+

13. 3N+Ξ 3N+Ξ No bound state ESC08c T=1 state 0 MeV 0 MeV -2.25MeV 0+
HAL potential
ESC08c

14. 3N+Ξ 3N+Ξ 0.01 MeV～0.3 MeV No bound state Preliminary result ESC08c
In HAL potential , the statistical errors are NOT included.
T=0 state
3N+Ξ
0 MeV
3N+Ξ
0 MeV 1+
0.01 MeV～0.3 MeV
No bound state
Preliminary result
HAL potential
ESC08c

15. Summary
To extract information on ΞN interaction, that is, to investigate
spin- isospin dependence on NNΞ and NNNΞ system,
we calculated these systems using two types ΞN interactions,
ESC08c and HAL potential.
For NNΞ system, T=1/2, J=1/2+ and 3/2+, we have bound states
using ESC08c which is consistent with the results by Prof. Galcilazo.
For NNNΞ system, ESC08c potential provides bound state for T=1,J=0+
state.
HAL potential provides bound state for T=0, J=1+ state.
We found that ΞN spin-isospin dependence is seen in the binding
energies of s-shell Ξ hypernuclei.
To investigate this fact, I suggest to produce these Ξ hypernuclei
Using 3He and 4He target by (K+,K-) reaction.