1. Structure of light Λ hypernuclei Emiko Hiyama (RIKEN)

2. Nuclear chart with strangeness Λ Multi-strange system such as Neutron star Λ Here, I will report the structure of S=-1 hypernuclei.

3. Observation of Neutron-rich Λ -hypernuclei These observations are interesting from the view points of few-body physics as well as unstable nuclear physics. Recently, we had three epoch-making data from the view point of few-body problems. FINUDA collaboration & A. Gal, Phys. Rev. Lett. 108, 042051 (2012). t Λ 6 H6 H n n α Λ 7 He Λ n JLAB experiment-E011, Phys. Rev. Lett. 110, 12502 (2013). n Λ nn Λ 3n3n Λ C. Rappold et al., HypHI collaboration Phys. Rev. C 88, 041001 (R) (2013)

4. Λ 7 He Λ nn α

5. Λ Λ nn Λ α What is interesting to study this hypernucleus? It is important to obtain information about charge symmetry breaking effect of n-Λ and p-Λ.

6. The major goal of hypernuclear physics Fundamental and important for the study of nuclear physics To understand the baryon-baryon interaction, two-body scattering experiment is most useful. YN and YY potential models so far proposed (ex. Nijmegen, Julich, Kyoto-Niigata) have large ambiguity. 1) To understand baryon-baryon interactions Total number of Nucleon (N) -Nucleon (N) data: 4,000 ・ NO YY scattering data ・ Total number of differential cross section Hyperon (Y) -Nucleon (N) data: 40

7. Therefore, as a substitute for the 2-body limited YN and non-existent YY scattering data, the systematic investigation of the structure of light hypernuclei is essential.

8. Hypernuclear  -ray data since 1998 (figure by H.Tamura) ・ Millener (p-shell model), ・ Hiyama (few-body)

9. In S= -1 sector, what are important to study YN interaction? (1) Charge symmetry breaking (2) ΛN － ΣN coupling J-PARC : Day-1 experiment E13 Jlab E05-115, Mainz nn p Λ 4H4H Λ Λ Λ nn 7 He α

10. (1) Charge Symmetry breaking N+N+N 1/2 + - 8.48 MeV 0 MeV - 7.72 MeV 1/2 + 3H3H 3 He nn p n p p 0.76 MeV Energy difference comes from dominantly Coulomb force between 2 protons. Charge symmetry breaking effect is small. In S=0 sector Exp.

11. In S= -1 sector 3 He+Λ 0 MeV -1.24 -2.39 1+1+ 0+0+ 3 H+Λ 0 MeV -2.04 1+1+ 0+0+ 0.35 MeV nn p Λ 4H4H Λ n p Λ 4 He Λ p Exp. 0.24 MeV n Λ p Λ

12. n p Λ 4 He Λ p nn p Λ 4H4H Λ However, Λ particle has no charge. n p Λ p p Σ- pp p Σ0 p n p Σ+ nn + + + + 4 He Λ n p Λ Σ- pp Σ0 p n Σ+ nn + + + + 4H4H Λ n n n n

13. In order to explain the energy difference, 0.35 MeV, NN N Λ + NN N Σ (3N+Λ ） (3N+Σ ） ・ E. Hiyama, M. Kamimura, T. Motoba, T. Yamada and Y. Yamamoto, Phys. Rev. C65, 011301(R) (2001). ・ A. Nogga, H. Kamada and W. Gloeckle, Phys. Rev. Lett. 88, 172501 (2002) ・ H. Nemura. Y. Akaishi and Y. Suzuki, Phys. Rev. Lett.89, 142504 (2002). Coulomb potentials between charged particles (p, Σ ± ) are included.

14. 3 He+Λ 0 MeV -1.24 -2.39 1+1+ 0+0+ 3 H+Λ0 MeV -2.04 1+1+ 0+0+ nn p Λ 4H4H Λ n p Λ 4 He Λ p ・ A. Nogga, H. Kamada and W. Gloeckle, Phys. Rev. Lett. 88, 172501 (2002) (Exp: 0.24 MeV) (Exp: 0.35 MeV) (cal. 0.07 MeV(NSC97e)) (cal: -0.01 MeV(NSC97e)) ・ E. Hiyama, M. Kamimura, T. Motoba, T. Yamada and Y. Yamamoto, Phys. Rev. C65, 011301(R) (2001). ・ H. Nemura. Y. Akaishi and Y. Suzuki, Phys. Rev. Lett.89, 142504 (2002). N Λ N NN NN Σ +

15. 3 He+Λ0 MeV -1.24 -2.39 1+1+ 0+0+ 3 H+Λ0 MeV -2.04 1+1+ 0+0+ nn p Λ 4H4H Λ n p Λ 4 He Λ p (Exp: 0.24 MeV) (Exp: 0.35 MeV) (cal. 0.07 MeV(NSC97e)) (cal: -0.01 MeV(NSC97e)) For the study of CSB interaction, we need more data. There exist NO YN interaction to reproduce the data.

16. It is interesting to investigate the charge symmetry breaking effect in p-shell Λ hypernuclei as well as s-shell Λ hypernuclei. For this purpose, to study structure of A=7 Λ hypernuclei is suited. Because, core nuclei with A=6 are iso-triplet states. α n α np n α pp 6 He 6 Li(T=1) 6 Be

17. α n α n p n α p p 7 He 7 Li(T=1) 7 Be Λ Λ Λ Λ Λ Λ Then, A=7 Λ hypernuclei are also iso-triplet states. It is possible that CSB interaction between Λ and valence nucleons contribute to the Λ-binding energies in these hypernuclei.

18. Exp. 1.54 -3.79 B Λ =5.16 MeV B Λ =5.26 MeV JLabE05-115 exp.: 5.68±0.03±0.25 7 Be Λ (T=1) 7 Li Λ 7 He Λ 6 He 6 Li (T=1) 6 Be Emulsion data

19. Important issue: Can we describe the Λ binding energy of 7 He observed at JLAB using ΛN interaction to reproduce the Λ binding energies of 7 Li (T=1) and 7 Be ? To study the effect of CSB in iso-triplet A=7 hypernuclei. Λ Λ Λ α n α np n α p p 7 He 7 Li(T=1) 7 Be Λ Λ Λ Λ Λ Λ For this purpose, we study structure of A=7 hypernuclei within the framework of α+Λ+N+N 4-body model. E. Hiyama, Y. Yamamoto, T. Motoba and M. Kamimura,PRC80, 054321 (2009)

20. Now, it is interesting to see as follows: (1)What is the level structure of A=7 hypernuclei without CSB interaction? (2) What is the level structure of A=7 hypernuclei with CSB interaction?

21. B Λ ： CAL= 5.21 B Λ ： CAL= 5.28 6 Be 6 Li 7 Be Λ (T=1) 7 Li Λ 6 He 7 He Λ EXP= 5.26 EXP= 5.16 CAL= 5.36 B Λ ： EXP= 5.68±0.03±022 preliminary (Exp: 1.54) (Exp: -0.14) (exp:-0.98) JLAB:E01-011 experiment Without CSB

22. Now, it is interesting to see as follows: (1)What is the level structure of A=7 hypernuclei without CSB interaction? (2) What is the level structure of A=7 hypernuclei with CSB interaction?

23. Next we introduce a phenomenological CSB potential with the central force component only. 3 He+Λ0 MeV -1.24 -2.39 1+1+ 0+0+ 3 H+Λ0 MeV -2.04 1+1+ 0+0+ 0.35 MeV nn p Λ 4H4H Λ n p Λ 4 He Λ p Exp. 0.24 MeV Strength, range are determined so as to reproduce the data.

24. B Λ ： EXP= 5.68±0.03±0.22 α p n 5.36(without CSB) 5.16(with CSB) 5.44(with CSB) With CSB Inconsistent with the data 5.28 MeV( withourt CSB) 5.29 MeV (With CSB) 5.21 (without CSB)

25. Comparing the data of A=4 and those of A=7, tendency of B Λ is opposite. In order to investigate CSB interaction, it was necessary to perform the energy spectra of A=4 hypernuclei again at JLab, Mainz and J-PARC.

26. In S= -1 sector 3 He+Λ 0 MeV -1.24 -2.39 1+1+ 0+0+ 3 H+Λ 0 MeV -2.04 1+1+ 0+0+ 0.35 MeV nn p Λ 4H4H Λ n p Λ 4 He Λ p Exp. 0.24 MeV n Λ p Λ -2.12±0.01±0.09 MeV A.Esser et al., PRL114, 232501 (2015) Reported by P. Achenbach 1.406±0.002±0.003 Reported by J-PARC 0.984 MeV

27. In S= -1 sector 3 He+Λ 0 MeV -0.98 -2.39 1+1+ 0+0+ 3 H+Λ 0 MeV 1+1+ 0+0+ 0.35 MeV nn p Λ 4H4H Λ n p Λ 4 He Λ p Exp. 0.24 MeV -2.12±0.01±0.09 MeV Homework: (1)The ground state of 4 Λ He =>J-PARC or analysis by emulsion data (2) The excited state of 4 Λ H => JLab In this way, it is important to confirm all of four states in A=4 Λ hypernuclei.

28. NN N Λ + NN N Σ (3N+Λ ） (3N+Σ ） α n n Λ α n n Σ ＋ A=7 hypernuclei After confirmation by experiment, We have a new stage. Namely, as a few-body physicist, we should perform both of four-body NNNΛ +NNNΣ coupled channel calculation And (α+Λ+N+N)+(α+Σ+N+N)coupled channel calculation with updated YN realistic interaction.

29. Why is it interesting to study neutron-rich Λ hypernucleus such as 7 Λ He? Second of major goals in hypernuclear physics To study the structure of multi-strange systems

30. In neutron-rich and proton-rich nuclei, When some neutrons or protons are added to clustering nuclei, additional neutrons are located outside the clustering nuclei due to the Pauli blocking effect. As a result, we have neutron/proton halo structure in these nuclei. There are many interesting phenomena in this field as you know. Nuclear cluster Nuclear cluster Nuclear cluster Nuclear cluster n n n n nn nn

31. Hypernucleus No Pauli principle Between N and Λ Λ γ nucleus hypernucleus Due to the attraction of Λ N interaction, the resultant hypernucleus will become more stable against the neutron decay. neutron decay threshold Λ N Λ particle can reach deep inside, and attract the surrounding nucleons towards the interior of the nucleus.

32. 0+ 2+ α+n+n -1.03 MeV 0 MeV B Λ : CAL= 5.36 MeV 1/2+ 3/2+ 5/2+ 5He+n+n Λ α+Λ+n+n 0 MeV -6.19 MeV - 4.57 Neutron halo states 6He 7He Λ CAL: E. Hiyama et al., PRC 53, 2075 (1996), PRC 80, 054321 (2009) B Λ ： EXP= 5.68±0.03±0.25 Observed at J-Lab experiment Phys. Rev. Lett.110, 012502 (2013). Exp:-0.98 Λ One of the excited state was observed at JLab. Another interesting issue is to study the excited states of 7 He. Λ

33. 7 Li(e,e’K + ) 7 Λ He (FWHM = 1.3 MeV) Fitting results At present, due to poor statics, It is difficult to have the third peak. Theoretically, is it possible to have new state? Let’s consider it. Good agreement with my prediction

34. Question: In 7 He, do we have any other new states? If so, what is spin and parity? Λ First, let us discuss about energy spectra of 6 He core nucleus.

35. 0+ 2+ α+n+n0 MeV 6 He -0.98 1.797 MeV Γ=0.11 ±0.020 MeV (2 +,1 -,0 + )? Γ ＝ 12.1 ±1.1 MeV Exp. Core nucleus Data in 2002 0+ 2+ α+n+n0 MeV 6 He -0.98 1.8 MeV Γ=0.12 MeV Exp. 2+2+ 1 2 2.6±0.3 MeV Γ=1.6 ±0.4 MeV Data in 2012 X. Mougeot et al., Phys. Lett. B 718 (2012) 441. p( 8 He, t) 6 He

36. 0+ 2+ α+n+n0 MeV 6 He -0.98 0.8 MeV Γ=0.12 MeV Exp. 2+2+ 1 2 1.6±0.3 MeV Γ=1.6 ±0.4 MeV Data in 2012 X. Mougeot et al., Phys. Lett. B 718 (2012) 441. p( 8 He, t) 6 He -0.97 MeV 0.79 MeV 2.5 MeV Γ= theory Myo et al., PRC 84, 064306 (2011). How about theoretical result? Decay with Is smaller than Calculated with. What is my result?

37. Question: What are theoretical results? 0+ 2+ α+n+n0 MeV 6 He -0.98 1.8 MeV Γ=0.12 MeV Exp. 2+2+ 1 2 2.6±0.3 MeV Γ=1.6 ±0.4 MeV Data in 2012 X. Mougeot et al., Phys. Lett. B 718 (2012) 441. p( 8 He, t) 6 He These are resonant states. I should obtain energy position and decay width. To do so, I use complex scaling method which is one of powerful method to get resonant states.

38. My result E=0.96 + 0.14 MeV E=2.81 +4.81 MeV

39. Question: What are theoretical results? 0+ 2+ α+n+n0 MeV 6 He -0.98 0.8 MeV Γ=0.12 MeV Exp. 2+2+ 1 2 1.6±0.3 MeV Γ=1.6 ±0.4 MeV Data in 2012 X. Mougeot et al., Phys. Lett. B 718 (2012) 441. p( 8 He, t) 6 He 0+ 2+ α+n+n0 MeV 6 He -0.98 0.8 MeV Γ=0.14 MeV 2+2+ 1 2 2.81 MeV Γ=4.81 MeV Cal.

40. How about energy spectra of 7 He? Λ 0+ 2+ α+n+n0 MeV 6 He -0.98 0.8 MeV Γ=0.14 MeV 2+2+ 1 2 2.81 MeV Γ=4.81 MeV Cal. Λ 3/2 +,5/2 +

41. E=0.07 MeV+1.13 MeV The energy is measured with respect to α+Λ+n+n threshold.

42. I propose to experimentalists to observe these states. Motoba san recently estimated differential cross sections for each state. At E lab =1.5 GeV and θ=7 deg (E05-115 experimental kimenatics) 49.0 nb/sr I think that It is necessary to estimate reaction cross section 7 Li (e,e’K + ). 10.0 nb/sr 11.6 nb/sr 3.4 nb/sr 4.3 nb/sr Motoba’s Cal. 40% reduction

43. FINUDA collaboration & A. Gal, Phys. Rev. Lett. 108, 042051 (2012). t Λ 6 H6 H n n α Λ 7 He Λ n JLAB experiment-E011, Phys. Rev. Lett. 110, 12502 (2013). n Λ nn Λ 3n3n Λ C. Rappold et al., HypHI collaboration Phys. Rev. C 88, 041001 (R) (2013) Conclusion

44. Thank you!

45. Complex scaling is defined by the following transformation. As a result, I should solve this Schroediner equation. E=E r + iΓ/2