Five-body Cluster Structure of the double Λ hypernucleus 11 Be

1. Five-body Cluster Structure of the double Λ hypernucleus 11Be ΛΛ Emiko Hiyama (RIKEN)

2. Λ Λ n α α Outline of my talk ・Introduction ・Four-body structure of 7He, 7Li, 8Li, 9Li, 9Be, 10Be ΛΛ ΛΛ ΛΛ ΛΛ ΛΛ ΛΛ Λ Λ Λ Λ Λ Λ Λ ｎ Λ Λ Λ p d t 3He α α α α α ・ Five-body structure of 11Be ΛΛ

3. Introduction

4. What is the structure when one or more Λs are added to a nucleus? + + + + ・・・・ Λ Λ Λ Λ Λ It is conjectured that extreme limit, which includes many Λs in nuclear matter, is the core of a neutron star. nucleus In this meaning, the sector of S=-2 nuclei , double Λhypernuclei and Ξhypernuclei is just the entrance to the multi-strangeness world. However, we have hardly any knowledge of the YY interaction because there exist no YY scattering data. Then, in order to understand the YY interaction, it is crucial to study the structure of double Λ hypernuclei and Ξ hypernuclei.

5. In 2001, the epoch-making data has been reported by the KEK-E373 experiment. Observation of 6He ΛΛ Uniquely identified without ambiguity forthe first time Λ Λ α+Λ+Λ α ６．９1±0.16 MeV 0+

6. Strategy of how to determine YY interaction from the study of light hypernuclear structure YY interaction Nijmegen model D 6He Suggest reducing the strength of spin-independent force by half ① use ③ ΛΛ Λ Λ Accurate structure calculation α compare between the theoretical result and the experimental data of the biding energy of 6He ② prediction of energy spectra of new double Λ hypernuclei ④ ΛΛ Spectroscopic experiments Emulsion experiment (KEK-E373) by Nakazawa and his collaborators

7. My theoretical contribution using few-body calculation KEK-E373 experiment analysis is still in progress. Approved proposal at J-PARC ・E07 “Systematic Study of double strangness systems at J-PARC” by Nakazawa and his collaborators It is difficult to determine (1) spin-parity (2) whether the observed state is the ground state or an excited state comparison Emulsion experiment Theoretical calculation input: ΛΛ interaction to reproduce the observed binding energy of 6He ΛΛ the identification of the state

8. Our few-body caluclational method Gaussian Expansion Method (GEM) , since 1987 , ・A variational method using Gaussian basis functions ・Take all the sets of Jacobi coordinates Developed by Kyushu Univ. Group, Kamimura and his collaborators. Review article : E. Hiyama, M. Kamimura and Y. Kino, Prog. Part. Nucl. Phys. 51 (2003), 223. High-precision calculations of various 3- and 4-body systems: Exsotic atoms / molecules , 3- and 4-nucleon systems, multi-cluster structure of light nuclei, Light hypernuclei, 3-quark systems,

9. My theoretical contribution using few-body calculation KEK-E373 experiment analysis is still in progress. Approved proposal at J-PARC ・E07 “Systematic Study of double strangness systems at J-PARC” by Nakazawa and his collaborators It is difficult to determine (1) spin-parity (2) whether the observed state is the ground state or an excited state comparison Emulsion experiment Theoretical calculation input: ΛΛ interaction to reproduce the observed binding energy of 6He ΛΛ the identification of the state

10. Successful example to determine spin-parity of double Λhypernucleus --- Demachi-Yanagi event for 10Be ΛΛ Observation of 10Be --- KEK-E373 experiment ΛΛ Λ Λ 8Be+Λ+Λ α α 11.90±0.13 MeV 10Be ground state ? excited state ? ΛΛ 10Be ΛΛ Demachi-Yanagi event

11. Successful interpretation of spin-parity of Λ Λ α α E. Hiyama, M. Kamimura,T.Motoba, T. Yamada and Y. Yamamoto Phys. Rev. 66 (2002) , 024007 11.83 11.90 α+Λ+Λ 6.91 ±0.16 MeV Λ Λ Demachi-Yanagi event α -14.70

12. Hoping to observe newdouble Λ hypernuclei in future experiments, I predicted level structures of thesedouble Λ hypernuclei within the framework of the α+x+Λ+Λ 4-body model. E. Hiyama, M. Kamimura, T. Motoba, T.Yamada and Y. Yamamoto Phys. Rev. C66, 024007 (2002) Λ Λ 3He t x = p d n = = = = = α x 9Be 8Li 7Li 8Li 7He ΛΛ ΛΛ ΛΛ ΛΛ ΛΛ

13. Spectroscopy of ΛΛ-hypernuclei E. Hiyama, M. Kamimura,T.Motoba, T. Yamada and Y. Yamamoto Phys. Rev. 66 (2002) , 024007 > A 11 ΛΛhypernuclei new data (2009) I have been looking forward to having new data in this mass-number region.

14. Observation ofHida event KEK-E373 experiment Λ Λ Λ Λ n n n α α α α 11Be 12Be ΛΛ ΛΛ BΛΛ= 20.49±1.15 MeV BΛΛ= 22.06±1.15 MeV Important issue: Is the Hida event the observation of a ground state or an excited state? It is neccesary to perform 5-body calculation of this system. Why 5-body?

15. Core nucleus, 9Be is well described as α+α+ n three-cluster model. 11Be ΛΛ Λ Λ Then, 11Be is considered to be suited for studying with α+α+ n +Λ+Λ 5-body model. ΛΛ n α α Difficult 5-body calculation: 1) 3 kinds of particles (α, Λ, n) 2) 5 different kinds of interactions Λ Λ Λ n 3) Pauli principle between α and α, and between α and n α Λ α But, I have succeeded in performing this calculation. n α α

16. 5-body calculation of 11Be ΛΛ 11Be ΛΛ Λ Λ n α α (γ～10000 MeV is sufficient.) rules out the Pauli-forbidden states from the 5-body wave unction. The Pauli-forbidden states (f ) arethe 0S, 1S and 0Dstates of theα αrelative motion, and the0S states of the α nrelative motion. This method for the Pauli principle is often employed in the study of light nuclei using microscopic cluster models.

17. 11Be 5-body calculation of 11Be ΛΛ ΛΛ Λ Λ n α α A variational method: Gaussian Expansion Method (GEM) (review paper) E. H., Y. Kino and M. Kamimura, Prog. Part. Nucl. Phys., 51 (2003) 223. expansion coefficient specifies 5-body basis functions of each Jacobi-coordinate set specifies many sets of Jacobi coordinates

18. Some of important Jacobi corrdinates of theα+ α+ n + Λ+ Λsystem. Two αparticles are symmetrized. Two Λparticles are antisymmetrized. 120 sets of Jacobi corrdinates are employed.

19. Before doing full 5-body calculation, it is important and necessary to reproduce the observed binding energies of all the sets of subsystems in 11Be. In our calculation, this was successfully done using the same interactions for all subsystems: ΛΛ Λ Λ Λ Λ Λ Λ n n n α α α α α α 8Be (0+) 9Be (3/2-) 5He (3/2-) CAL : +0.80 MeV EXP : +0.80 MeV CAL : +0.09 MeV EXP : +0.09 MeV CAL : -1.57 MeV EXP : -1.57 MeV

20. Λ Λ Λ Λ Λ Λ n n n α α α α α α 6He (1-) 9Be (1/2+) 5He (1/2-) Λ Λ Λ CAL : -3.12 MeV EXP : -3.12 MeV CAL : -3.29 MeV EXP : -3.29 MeV CAL : -6.64 MeV EXP : -6.62 MeV (The energy is measured from the full-breakup threshold of each subsystem)

21. adjusted predicted n Λ n Λ Λ Λ Λ Λ n α α α α α α ΛΛ ΛΛ ΛΛ 10Be (0+, 2+ ) 6He (0+ ) 10Be (1-) Λ Λ Λ Λ Λ CAL (0+): -6.93 MeV EXP (0+): -6.93 MeV CAL (2+): -10.96 MeV EXP (2+): -10.98 MeV CAL : -10.64 MeV EXP : -10.64 MeV CAL (0+): -14.74 MeV EXP (0+): -14.69 MeV All the potential parameters have been adjusted in the 2- and 3-body subsystems. Therefore, energies of these 4-body susbsystems and the 5-body system are predicted with no adjustable parameters. 11Be Λ Λ

22. Convergence of the ground-state energy of theα+α+ n +Λ+Λ5-body system ( ) 11Be ΛΛ J=3/2-

23. To be published in Phys. Rev. Lett.

24. What is structure of 11Be? ΛΛ No Pauli principle Between N and Λ Λ particle can reach deep inside, and attract the surrounding nucleons towards the interior of the nucleus. Λ Hypernucleus Λ particle plays a ‘glue like role’ to produce a dynamical contraction of the core nucleus.

25. By reduction of B(E2) due to the addition of Λ particle to the core nucleus, we can find the contraction of nucleus by glue-like role of Λ particle. Theoretical calculation E. Hiyama et al. Phys. Rev. C59 (1999), 2351. KEK-E419 Λ n Λ n α α 7Li Rα-np Λ p p 6Li Rα-np(6Li) > Rα-np(7Li) Reduced by about 20 % B(E2: 3+→1+:6Li)=9.3 ±0.5e2fm4→B(E2:5/2+→1/2+:7Li)= 3.6 ±2.1 e2fm4

26. 20% reduction 8% reduction Λ Λ Λ Λ n Λ n n α α α α α α 11Be 9Be 10Be ΛΛ Λ

27. n Λ Λ α α 11Be ΛΛ

28. As mentioned before, Hida event has another possibility, namely, observation of 12Be. ΛΛ Λ Λ BΛΛ= 22.06±1.15 MeV n n 12Be α α ΛΛ For this study, it is necessary to calculate 6-body problem. At present, it is difficult for me to perform 6-body calculation. However, I think, it is good chance to develop my methodfor 6-body problem. Fortunately, we will have much more powerful supercomputer (HITACHI SR16000) at KEK in June in 2011. This supercomputer enable me to make six-body calculation. For the confirmationof Hida event, we expect to have more precise data at J-PARC. ΛΛ

29. Spectroscopy of ΛΛ-hypernuclei At J-PARC A=12, 13, …… 11Be , ΛΛ For the study of this massregion, we need to perform more of 5-body cluster-model calculation.

30. Therefore, we intend to calculate the following 5-body systems. Λ Λ Λ Λ Λ Λ Λ Λ t p 3He d α α α α α α α α 13B 11B 13C 12B ΛΛ ΛΛ ΛΛ ΛΛ Λ Λ To study 5-body structure of these hypernuclei is interesting and important as few-body problem. α α α 14C ΛΛ

31. Concluding remark Multi-strangeness system such as Neutron star J-PARC GSI JLAB DAΦN E J-PARC

32. Thank you!