1. Three- and four-body structure of S=-2 hypernuclei E. Hiyama (Nara Women’s Univ.)

2. nuclei + Hyperon(Λ 、 Σ 、・・ ) => Hypernuclei To study 3- and 4-body structure of light hypernuclei consisting of nucleus and hyperon

3. At Japan Proton Accelerator Research Complex (J-PARC), they are planning to produce (1) Many double Λ hypernuclei (2)Many Ξ hypernuclei Here, I shall discuss these subjects. I also discuss what is interesting and important to study double Λ hypernuclei and Ξ hypernuclei. nuclei Λ Λ Ξ

4. The purpose of my talk (1)To predict level structure of many double Λ hypernuclei α Λ Λ N α Λ Λ p α ΛΛ d α ΛΛ ｔ α ΛΛ ３ He αα ΛΛ ７ He ７ Li ８ Li ９ Li ９ Be １０ Be ΛΛ N N Ξ N NNNΞ (2)To predict level structure Ξ hypernucleus

5. Why is it important to produce many double Λ and Ξ hypernuclei? Answer Since there are NO hyperon(Y)-hyperon(Y) scattering data, YY interaction so far proposed have a large degree of ambiguity. In order to understand YY interaction, we need YY scattering data. However, even at J-PARC facility, it is very difficult to perform YY scattering experiment.

6. Therefore, it is very important to obtain information about YY interaction from the spectroscopy experiments of many double Λ and Ξ hypernuclei. My contribution To understand the hypernuclear structure by performing our three- and four-body calculations and to use this structure information to understand the YN and YY interactions

7. The purpose of my talk (1)To predict level structure of many double Λ hypernuclei α Λ Λ N α Λ Λ p α ΛΛ d α ΛΛ ｔ α ΛΛ ３ He αα ΛΛ ７ He ７ Li ８ Li ９ Li ９ Be １０ Be ΛΛ N N Ξ N NNNΞ (2)To predict level structure of Ξ hypernucleus

8. Up to now, there was NO experimental data about double Λhypernuclei with NO ambiguity. Two epoch-making data have been reported by the KEK-E373 experiment.

9. (1) Observation of 6 He Uniquely identified without ambiguity for the first time ΛΛ α+Λ+Λ 7.25 ±0.1 MeV 0+0+ α ΛΛ NAGARA Event

10. (2) Observation of 10 Be ΛΛ 12.33 +0.35 -0.21 MeV 8 Be+Λ+Λ αα ΛΛ Deamchi-Yanagi event ground state ? excited state?

11. Two important issues: (1)Does the ΛΛ interaction which is designed to reproduce the binding energy of 6 He reproduce the Demachi-Yanagi event for 10 Be consistently? (2) When we use the same ΛΛ interaction, how is theoretical prediction of level structure of other double Λ hypernuclei? ΛΛ

12. Two important issues: (1)Does the ΛΛ interaction which is designed to reproduce the binding energy of 6 He reproduce the Demachi-Yanagi event for 10 Be consistently? (2) When we use the same ΛΛ interaction, how is theoretical prediction of level structure of other double Λ hypernuclei? αα Λ Λ 10 Be ΛΛ

13. ←KEK-E373 Demachi- Yanagi event

14. Our 4-body calculation is predictive. Therefore, hoping to observe many doubleΛhypernuclei in the future experiment at J-PARC, I predict level structure of double Λ hypernuclei. α x Λ Λ x = Npd t 3 He == = = = 7 He 7 Li 8 Li ΛΛ 8 Li 9 Be ΛΛ 3N ΛΛ 5 H, 5 He ΛΛ np ΛΛ 4H4H

15. Two important issues: (1)Does the ΛΛ interaction which is designed to reproduce the binding energy of 6 He reproduce the Demachi-Yanagi event for 10 Be consistently? (2) When we use the same ΛΛ interaction, how is theoretical prediction of level structure of other double Λ hypernuclei? ΛΛ

16. Spectroscopy of ΛΛ-hypernuclei prediction -3.38 5 He 4H4H ΛΛ

17. In the s-shell hypernuclei, new component of interaction should be taken into account. A missing component is ΛΛ ー ΞN coupling.

18. A missing component is ΛΛ ー ΞN component. nuclei ΛΛ V ΛΛ ー ΞN => nuclei Ξ N convert into Double Λ hypernuclei

19. Non-strangeness nuclei N Δ N N N Δ 250MeV Probability of Δ in nuclei is not large. 25MeV ΛΛ ΞN There is significant probability of Ξ in double Λ hypernuclei.

20. In hypernuclear physis, it is fashionable subject to investigate ΛΛ ー ΞN coupling mechanism in double Λ hypernuclei.

21. 4 H is very suitable hypernucleus to get information on ΛΛ-ΞN coupling interaction. Up to now, there is NO experimental data about 4 H. ΛΛ n p Λ Λ 4H4H The important issue: Does the YY interaction which designed to reproduce the binding energy of 6 He make 4 H bound? And how does the effect of ΛΛ ー ΞN coupling play important role in the binding energy of 6 He and 4 H? ΛΛ

22. 1)I.N. Filikhin and A. Gal, Phys. Rev. Lett. 89, 172502 (2002) 2)H. Nemura, Y. Akaishi et al., Phys. Rev. C67, 051001 (2002) n p Λ Λ V ΛΛ α Λ Λ NOT BOUND ! 4H4H ΛΛ 6 He ΛΛ NAGARA event α+Λ+Λ 7.25±0.1 MeV 0+0+

23. Did not include ΛΛ-ΞN coupling ΛΛ-ΞN coupling => ・ significant in 4 H ΛΛ np ΛΛ 4H4H ・ Not so important in 6 He ΛΛ α ΛΛ 6 He ΛΛ

24. S 1/2 P 3/2 6 He ΛΛ nnpp ΛΛ Ξ０Ξ０ n Forbidden The effect of ΛΛ-ΞN coupling is small in 6 He and the p-shell double Λ hypernuclei ・ I.R. Afnan and B.F. Gibson, Phys. Rev. C67, 017001 (2003). ・ Khin Swe Myint, S. Shinmura and Y. Akaishi, nucl-th/029090. ・ T. Yamada and C. Nakamoto, Phys. Rev.C62, 034319 (2000). ΛΛ V ΛΛ ー ΞN

25. S 1/2 np ΛΛ Ξ０Ξ０ n 4H4H ΛΛ P 3/2 allowed (Ξ- p) There is NO Pauli blocking and the ΛΛ ー ΞN effect can be large.

26. np Λ Λ N N N Ξ + 4H4H ΛΛ One of the most numerically difficult 4-body problem E. Hiyama Dr. Nemura n n ΛΣ nn Σ Σ

27. E(MeV) 0 -3.12 -7.25 0+0+ Exp. (KEK-E373) CAL. 5 He+Λ Λ α+Λ+Λ 6 He ΛΛ with Pauli blocking E(MeV) n+p+Λ+Λ 3 H+Λ Λ No Exp. unbound NNΛΛ channel only NNΛΛ + NNNΞ P Ξ =1.6% 0.1MeV P Ξ =3.2% 4 H with no Pauli blocking ΛΛ α 0MeV

28. It is possible that ΛΛ ー ΞN coupling potential makes the lightest double Λ hypernucleus, 4 H bound. If the bound state of 4 H is observed at J-PARC, we can obtain useful information on ΛΛ ー ΞN coupling mechanism. ΛΛ

29. Outline of my talk (2) To predict level structure of Ξ hypernucleus N N Ξ N NNNΞ

30. n+p+Λ+Λ 3 H+Λ Λ 0.1MeV 0 28MeV NNNΞ ？？ 4H4H ΛΛ E(MeV)

31. So far, there was NO experimental data about Ξ hypernuclei. To produce Ξ hypernuclei is one of main experimental project at J-PARC. Therefore, it is requested to predict what kind of Ξ hypernuclei exist as bound states theoretically. And also it is requested to suggest what part of ΞN interaction we can determine from structure of Ξ hypernuclei.

32. N N Ξ N NNNΞ The strategy of this study (1)I should perform 4-body calculation using realistic force directly. (2) Although we cannot predict the level structure of NNNΞ hypernucleus due to the large degree of ambiguity of ΞN interaction, we can investigate what part of ΞN interaction contribute to the binding energy of this hypernucleus. (3)If this hypernucleus will be observed in the future at J-PARC, we can suggest how to improve the realistic force directly form the structure study side.

33. YY interaction: Extended soft core potential 04 (ESC04) proposed by Nijmegen group Nijmegen soft core ’97 e and f (NSC97e and f)

34. Results ESC04 (3N)+Ξ 0 MeV 0+0+ 1+1+ -2.3 -0.86 NN N Ξ NNNΞ NNΛΛ 1 + : [12V(1,1)+V(1,0)+10V(0,1)+3V(0,0)]/26 0 + :[V(1,0)+V(0,1)]/2 T,S == repulsive strongly attractive repulsive weakly repulsive strongly attractive

35. Results 3N+Ξ unbound NSC97e NSC97f N N N Ξ NNNΞ If the NNNΞ state is observed as a bound state in the future, we can extract information on ΞN interaction. Therefore, I hope to perform search-experiment of this hypernucleus.

36. Spectroscopy of ΛΛ-hypernuclei prediction

37. 28MeV 6 He 7 He 7 Li 8 Li 9 Li 9 Be 10 Be ΞΞΞΞΞ Ξ Ξ α +x+N+Ξ ? ?? ? ?? ? Spectroscopy of Ξ hypernuclei at J-PARC α Ξ x N =n,p,d,t, 3 He,α

38. My future study plan The study of structure of p-shell hypernuclei based on α+x+Ξ+N 4-body model. n,p,d,t, 3 He,α α Ｘ Ξ N

39. Conclusion (1)To predict level structure of many double Λ hypernuclei α Λ Λ N α Λ Λ p α ΛΛ d α ΛΛ ｔ α ΛΛ ３ He αα ΛΛ ７ He ７ Li ８ Li ９ Li ９ Be １０ Be ΛΛ N N Ξ N NNNΞ (2)To predict Ξ hypernucleus

40. 6 He ΛΛ 10 Be ΛΛ S=-2 S=0 N N I hope that J-PARC project will produce many doubleΛ hypernuclei. S=-1 Schematic illustration of the nuclear chart In this way, I hope that J-PARC project give an important contribution to extending the strangeness nuclear chart. They will observe Ξ hypernuclei for the first time at J-PARC.