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

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.

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

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.

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).

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

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

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.

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

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.

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.

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+

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

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

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.