Three- and four-body structure of S=-2 hypernuclei

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

2. Hyperon(Λ、Σ、・・) nuclei => + 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. Λ Λ nuclei Ξ nuclei

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

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 ７He ７Li ９Li ８Li ９Be １０Be ΛΛ ΛΛ ΛΛ ΛΛ ΛΛ ΛΛ Λ Λ Λ Λ Λ Λ Λ Λ Λ Λ Λ Λ N p α ｔ d α α α α α α ３He (2)To predict level structure of Ξ hypernucleus N N Ξ N NNNΞ

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 6He ΛΛ Uniquely identified without ambiguity for the first time α+Λ+Λ Λ Λ 7.25 ±0.1 MeV 0+ α NAGARA Event

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

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

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

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. 5H, 5He 4H ΛΛ ΛΛ ΛΛ Λ Λ Λ Λ x Λ Λ α 3N n p 3He x t = N p d = = = = = 9Be 7He 7Li 8Li 8Li ΛΛ ΛΛ ΛΛ ΛΛ ΛΛ

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

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

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

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

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

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

21. 4H is very suitable hypernucleus to get information on ΛΛ-ΞN coupling interaction. Up to now, there is NO experimental data about 4H. ΛΛ ΛΛ p n 4H ΛΛ Λ Λ The important issue: Does the YY interaction which designed to reproduce the binding energy of 6He make 4H bound? And how does the effect of ΛΛーΞN coupling play important role in the binding energy of 6He and 4H? ΛΛ ΛΛ ΛΛ 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) 6He Λ n Λ Λ ΛΛ VΛΛ Λ p α NAGARA event NOT BOUND ! α+Λ+Λ 4H ΛΛ 7.25±0.1 MeV 0+

23. Did not include ΛΛ-ΞN coupling ΛΛ-ΞNcoupling => ・ significant in 4H ΛΛ n p 4H ΛΛ Λ Λ ・Not so important in6He ΛΛ Λ Λ 6He ΛΛ α

24. 6He Forbidden ΛΛ V ΛΛーΞN P3/2 Ξ０ Λ Λ n n p p S1/2 n The effect of ΛΛ-ΞN coupling is small in 6He and the p-shell double Λhypernuclei ・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

25. 4H ΛΛ allowed P3/2 Ξ０ Λ Λ n p S1/2 n (Ξ- p) There is NO Pauli blocking and the ΛΛーΞN effect can be large.

26. N N n p + Ξ Λ Λ N 4H ΛΛ One of the most numerically difficult 4-body problem E. Hiyama Dr. Nemura n n n n Σ Σ Λ Σ

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

28. ΛΛ It is possible that ΛΛーΞN coupling potential makes the lightest double Λ hypernucleus, 4H bound. If the bound state of 4H 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. E(MeV) n+p+Λ+Λ 3H+Λ Λ 0.1MeV 28MeV NNNΞ？？ 4H ΛΛ 0

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. The strategy of this study N N (1)I should perform 4-body calculation using realistic force directly. Ξ N (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. NNNΞ (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. (3N)+Ξ Results ESC04 0 MeV 1+ -0.86 0+ N N -2.3 Ξ N T,S strongly attractive repulsive = = 1+: [12V(1,1)+V(1,0)+10V(0,1)+3V(0,0)]/26 0+:[V(1,0)+V(0,1)]/2 repulsive strongly attractive weakly repulsive NNΛΛ NNNΞ

35. N N unbound Ξ unbound N Results 3N+Ξ 3N+Ξ NNNΞ NSC97f NSC97e 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. Spectroscopy of Ξ hypernuclei at J-PARC 6He 7He 8Li 9Li 9Be 7Li 10Be Ξ Ξ Ξ Ξ Ξ Ξ Ξ α +x+N+Ξ 28MeV ? ? ? ? ? ? ? x =n,p,d,t,3He,α N Ξ 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,3He,α Ξ Ｘ N α

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

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