1. Ξ bound sates and ΛΛ hypernclei E. Hiyama (Nara Women’s Univ.) Y. Yamamoto(Tsuru Univ.) Th. Rijken(Nijmegen) T. Motoba (Osaka E.C. Univ.)

2. N N N Ξ NNNΞ NN Ξ NNΞ Outline of my talk α Ξ-p α α t ΞーΞー α n ΞーΞー n

3. J-PARC PANDA project at GSI Double Λ hypernuclei Ξ hypernuclei These projects will give a great contribution to the study of the structure of S=-2 hypernuclei as the entrance to the multi-strangeness world. However, even at these projects, we cannot determine spin-parities of the S=-2 hypernuclei. Namely, we can obtain only binding energies. For determination of spin-parities, we need a help of theoretical calculation. Therefore, it is required,before measurement, to predict spin-parities and binding energies of the ground states and the excited states as bound states.

4. For example, in the case of double Λ hypernuclei, Hoping to measure much more double Λ hypernuclei at J-PARC and GSI in the future, I predicted the level structure of A=7 to 10 double Λ hypernuclei within the framework of α+x+Λ+Λ 4-body model. α x Λ Λ x = Npd t 3 He == = = = 7 He 7 Li 8 Li ΛΛ 8 Li 9 Be ΛΛ E. Hiyama et al. Phys. Rev. C66, 024007 (2002) Talk at HYP03 conference, TJLAB

5. For the future experiment at J-PARC and PANDA project, it should be required that our level structure calculation is predictive. It is important to reproduce the existing observed data. (1) The nuclear parts are well reproduced by α ＋ x cluster model. As for the potential between α and cluster x, we employed potentials which reproduce reasonably well the low-lying states And low-energy scattering phase shifts of αx systems. (2)As for the YN interaction, I employed Nijmegen model YNG interaction and folded into the density of the x cluster.

6. α V NN 0+0+ α＋Λ＋Λα＋Λ＋Λ 7.25±0.1 MeV NAGARA event (3)As for the ΛΛ interaction, I employed Nijmegen model D. But this is not original one but simulated one. And I adjusted the strength so as to reproduce the binding energy of NAGAR event.

7. In our model, the following observed quantities are reasonably reproduced: (i)Energies of the low-lying states and scattering phase shifts of the α+x nuclear systems (ii) B Λ of hypernuclei composed of x+Λ (iii) B Λ of hypernuclei composed of α+x+Λ (iv) B ΛΛ of 6 He=α+Λ+Λ ΛΛ α x Λ Λ α x Λ Λ α x Λ Λ α x Λ Λ

8. This encourage us to perform 4-body calculation, with NO adjustable parameters at this stage, expecting high reliability of the results. A good example in the case of 10 Be ΛΛ αα ΛΛ

9. 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? Experiment at KEK-E373

10. ←KEK-E373 Demachi- Yanagi event

11. 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

12. Spectroscopy of ΛΛ-hypernuclei prediction

13. Let me discuss about Ξ hypernuclei

14. Spectroscopy of ΛΛ-hypernuclei prediction

15. 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

16. So far, how many Ξ hypernuclei did they observe with NO ambiguity? Answer:0 There was NO experimental data about Ξ hypernuclei To observe Ξ hypernuclei for the first time is one of the main experimental project at J-PARC.

17. Theoretical important issues: (1)What kind of Ξ hypernuclei exist as bound states? (2)What part of ΞN interaction can we determine from study of structure of Ξ hypernuclei?

18. The first part of my strategy N N N Ξ NNNΞ NN Ξ NNΞ α Ξ-p α α t ΞーΞー α n ΞーΞー n (1) Firstly, I do not mind whether these Ξ hypernuclei can be observed experimentally or not.

19. (2) ΞN interaction Extended soft core potential ’04 (ESC04) proposed by Nijmegen group very recently Only one information about ΞN interaction 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 11 B:-14 MeV Among all of the Nijmegen model, ESC04 and ND(Nijmegen Model D) reproduce the experimental value. ΞN interaction of the others are repulsive. Presented by Prof. Rijken in 13 Oct. in the morning session

20. n Ξ0Ξ0 T=0, L=0,2,S=1,J=1 + -0.60MeV V(T=0,S=0),V(T=1,S=0),V(T=1,S=1) Not so strong attractive or weak repulsive p Ξ-Ξ- T=0, L=0,2,S=1,J=1 + -1.60MeV attractive Coulomb force Ξ - :1321.3MeV Ξ 0 :1314.9MeV The characteristic property of ESC04 potential V(T=0,S=1): strongly attractive U Ξ =-18 MeV

21. Now, it is interesting to use ESC04 potential and study what kind of Ξ hypernuclei exist as bound states theoretically. N N N Ξ NNNΞ NN Ξ NNΞ α Ξ-p α α t ΞーΞー α n ΞーΞー n

22. N N N Ξ NNNΞ NN Ξ NNΞ (1) s-shell Ξ hypernuclei

23. NN interaction: Minnessota potential consisting only central force YY interaction: Extended soft core potential 04 (ESC04) proposed by Nijmegen group

24. ESC04 Results (np)-Ξ -0.15 MeV 1/2 + 0 MeV NN Ξ NNΞ

25. 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 T=0 NNNΞ

26. By the structure calculation, we find that in the case of ESC04, V(T=0,S=1) is a key to make bound A=3 and 4 Ξ hypernuclei. So, it is important to obtain information on V(T=0,S=1) from the structure study of ΞN interaction.

27. p Ξ-Ξ- T=0, L=0,2,S=1,J=1 + Binding energy : -1.60MeV + α Adding α particle to p+Ξ- system α p Ξ This system is suitable for getting information about V(T=0,S=1).

28. α Ξ-p α+p+Ξ - p+Ξ- α+Ξ- 2-2- 1-1- -2.22 -0.05 0MeV T=0 ESC04 This state is dominated by V(T=0,S=1). If this Ξ hypernucleus is observed in the future, we can get Information about V(T=0,S=1).

29. So far, I have discussed about what kind of Ξ hypernuclei exist theoretically. But, we all are interested in what kind of Ξ hypernuclei can be observed as bound states experimentally.

30. The way to produce Ξ hypernuclei Ξ- p K- K+ N N N Nucleus N N N Ξhypernuclues ΔT z =1 T z =+1/2 T z =-1/2

31. α n Ξ-Ξ- α n p K-K- K+ 6 Li(T=0) For example, if we use 6 Li nucleus target ・・ T=1 state No bound state In T=1

32. α Ξ-p α+p+Ξ - p+Ξ- α+Ξ- 2-2- 1-1- -2.22 -0.05 0MeV T=0 ESC04 This state is dominated by V(T=0,S=1). If this Ξ hypernucleus is observed in the future, we can get Information about V(T=0,S=1).

33. What kind of Ξ hypernuclei can be observed as bound states experimentally? ・ ３ He ・ ４ He ・ ６ Li ・ ７ Li ・ 10 B ・ １２ C Now, let me consider available light target nuclei to produce Ξ hypernuclei. NO bound state with T=1 To produce T=1 NNNΞ

34. Results ESC04 (3N)+Ξ 0 MeV 0+0+ 1+1+ -2.3 -0.86 NN N Ξ T=0 I also calculated NNNΞ system with T=1. We have NO bound states.

35. ・ ３ He ・ ４ He ・ ６ Li ・ ７ Li ・ 10 B ・ １２ C Is it possible to have bound states using 3 He, 7 Li and 12 C?

36. pp n n p Ξ- T=1/2, Tz=1/2 T=1/2,Tz=-1/2

37. ESC04 Results (np)-Ξ -0.15 MeV 1/2 + 0 MeV NN Ξ NNΞ

38. α p n n 7 Li(T=1/2) α n n T=3/2 Ξ- K+K+ K-K-

39. α n n T=3/2 Ξ- NN: AV8 realistic potential αN: potential to reproduce low-energy scattering phase shift ΞN αΞ ESC04 potential ΛΛ-ΞN coupling effect Renomalized into imaginary part

40. α+n+n+Ξ- (αΞ-)+n+n 6 He+Ξ- 0 MeV -0.672 MeV Γ=2.18MeV α n n Ξ- We can expect to have bound state using 7 Li target. J=1/2 +

41. α+n+n+Ξ- (αΞ-)+n+n 6 He+Ξ- 0 MeV α n n Ξ- -2.0MeV Γ=0.75 MeV Decay into 5 H+n+n ΛΛ I. Fuse and Y. Akaishi, Phys. Rev. C54, R24 (1996) They tentatively assigned binding energy to be 2.0 MeV so as to estimate branching ratio to go to 5 H. ΛΛ

42. α α t Ξ- αα t p K - K + 12 C 11 B-Ξ Day-1 experiment at J-PARC We want to know whether this Ξ hypernucleus exist as bound state or not. T=1, J=1 -

43. 11 B+Ξ- 0 MeV 1-1- -5.70 T=1 ESC04d -2.99 The shell-model calculation using ESC04 by Motoba will be reported soon. α α t Ξ- 11 B-Ξ 1 - Presentation by Yamamoto in the parallel session B1 Γ=6.7 MeV Γ=6.3 MeV

44. 12 C(K -,K + ) 12 Be (Day-1 experiment) is a key experiment to determine the future plan searching Ξ hypernuclei. Ξ If there is NO bound state in 11 B+Ξ system experimentally, then, it would be meaningless to do search-experiment of Ξ hypernucei using lighter target such as 3 He and 7 Li. Because, we shall have no bound states in d+Ξ 、 6 Li+Ξ systems. Then, we should do search-experiment of Ξ hypernuclei using heavier targets than 12 C after Day-1 experiment.

45. If there is bound state in 11 B+Ξ system, I shall be very happy. And we can get information about well-depth of one-body potential between 11 B and Ξ. Furthermore, there is a possibility to have bound states in lighter Ξ hypernuclei. Please perform search-experiment using lighter targets such as 3 He and 7 Li. In this way, I hope that search-experiment of Ξ hypernucleus using 12 C target will be performed successfully at J-PARC.

46. Furthermore, I think (K -,K 0 ) reaction is very important to get information on ΞN interaction with T=0 and to produce Ξ hypernuclei with T=0 or T=1/2. I know that this experiment is so difficult presently. But, I hope that this experiment will be successfully performed in the future within twenty or thirty years before my retirement. n Ξ-Ξ- K+K+ K0K0 T z =-1/2 ΔT z =0 p Ξ0Ξ0 K+K+ K0K0 T z =+1/2 ΔT z =0

47. N N N Ξ NNNΞ NN Ξ NNΞ α Ξ-p α α t ΞーΞー α n ΞーΞー n

48. Please observe Ξ hypernuclei for the first time at J-PARC!