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Three- and four-body structure of hypernuclei

Three- and four-body structure of hypernuclei. E. Hiyama (RIKEN). Introduction. Major goals of hypernuclear physics. 1) To understand baryon-baryon interactions. Fundamental and important for the study of nuclear physics. 2) To study the structure of multi-strange systems.

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Three- and four-body structure of hypernuclei

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  1. Three- and four-body structure of hypernuclei E. Hiyama (RIKEN)

  2. Introduction

  3. Major goals of hypernuclear physics 1) To understand baryon-baryon interactions Fundamental and important for the study of nuclear physics 2) To study the structure of multi-strange systems To understand the baryon-baryon interaction,two-body scattering experiment is most useful. Total number of Nucleon (N) -Nucleon (N) data: 4,000 YN and YY potential models so far proposed (ex. Nijmegen, Julich, Kyoto-Niigata) have large ambiguity. ・ Total number of differential cross section Hyperon (Y) -Nucleon (N) data: 40 ・ NOYY scattering data

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

  5. Strategy to determine YN and YY interactions from the studies of light hypernuclear structure YN and YY interactions based on meson theory: Nijmegen, Ehime, Julich・・ based on constituent quark model: Kyoto-Niigata,・・ using a few-body method My role ① ③ Use Suggest to improve Accurate calculation of hypernuclear structure Few-body, cluster model, shell model, ….. Compare theoretical results with experimental data X ② No direct information Spectroscopy experiments 　　・ High-resolution γ-ray spectroscopy experiment by Tamura and his collaborators 　　・ Emulsion experiment by Nakazawa and his collaborators

  6. 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 calculationsof various 3- and 4-body systems: Exotic atoms / molecules , 3- and 4-nucleon systems, Multi-cluster structure of light nuclei, Light hypernuclei, 3-quark systems, ……….

  7. Strategy to determine YN and YY interactions from the studies of light hypernuclear structure YN and YY interactions based on meson theory: Nijmegen, Ehime, Julich・・ based on constituent quark model: Kyoto-Niigata,・・ using a few-body method My role ① ③ Use Suggest to improve Accurate calculation of hypernuclear structure Few-body, cluster model, shell model, ….. Sec. 2. S=-1 hypernuclei and YN interaction Compare theoretical results with experimental data X ② No direct information Spectroscopy experiments 　　・ High-resolution γ-ray spectroscopy experiment by Tamura and his collaborators 　　・ Emulsion experiment by Nakazawa and his collaborators

  8. Section 2. S= -1 hypernuclei andYN interaction

  9. One of the important issue ΛN interaction(effectively including ΛN -ΣN coupling) Almost determined since 1998 ----- SLS (Symmetric LS) ----- ALS (Anti symmetric LS)

  10. YN LS force and energy-splitting in 9Be and 13C Λ Λ Λ Λ ----- SLS (Symmetric LS) 12C 8Be 9Be ----- ALS (Antisymmetric LS) 13C Λ Λ [vanishes in S=0 nuclei, Pauli] [breaks charge symmetry] In the ALS part : 0 < VALS(meson theory) VALS (constituent quark model) << Kyoto-Niijata FSS potential Nijgemen model D, F , soft core ’97a-f It is important to extract information about these LS force from the study of the structure of Λ hypernuclei.

  11. BNL-E929 BNL-E930 1/2- (0p) Λ (0s) ΔE Λ 3/2- 3/2+ ΔE LS splitting γ γ 2+ 5/2+ γ γ 0+ 1/2+ 0+ 1/2+ 12C 13C 8Be 9Be Λ Λ 3- and 4-body calculations: E. Hiyama, M. Kamimura, T. Motoba, T. Yamada and Y. Yamamoto Phys. Rev. Lett. 85 (2000) 270. Λ α Λ 13C 9Be α α Λ Λ α α YN LS force 1) Meson theory : Nijmegen Model D, F, soft core’97 a – f. 2) Qurak model : Kyoto-Niigata, FSS

  12. H. Akikawa et al. Phys. Rev. Lett. 88 (2002) 082501; H. Tamura et al. Nucl. Phys. A754 (2005) 58c BNL-E930 35 40 keV 3/2+ 3/2+ ～ 5/2+ 5/2+ 43±5 2) Quark Exp. keV BNL-E929 150 200 keV 1/2- 1/2- ～ 3/2- 3/2- 152 54 36 keV Exp. ± ± 2) Quark S.Ajimura et al. Phys. Rev. Lett. 86,(2001) 4255 ΛN LS force and 9Be and 13C Λ Λ 9Be Λ 3/2+ 80 200 keV ～ 5/2+ 1) Meson Nijmegen model D,F Soft core ’97a-f 13C Λ 1/2- 360 960 keV ～ 3/2- 1) Meson

  13. We suggested there are 2 paths to improve the Meson models : reduce the SLS strength or enhance the ALS strength so as to reproduce the observed LS splittings in 9Be and 13C. LS splitting in9Be Λ Meson Theory (Large) (Small) SLS SLS +ALS 5/2+ 5/2+ Λ Λ 80～200 keV 140～250 keV 3/2+ 3/2+ 3/2+ 5/2+ keV 43±5 (Large) - (Large) Exp. SLS + ALS 5/2+ Λ 35～40keV 3/2+ α α Quark-based 9Be Λ

  14. LS splitting in 9Be Λ Recently, a new YN interaction based on meson theory, extended soft core potential 06 (ESC06) by Th. A Rijken 9Be Λ BNL-E930 (small) SLS + ALS 3/2+ 3/2+ 39 keV 5/2+ 5/2+ keV 43±5 Exp. ESC06 Good agreement Hiyama (2007) H. Akikawa et al. Phys. Rev. Lett. 88,(2002)82501; H. Tamura et al. Nucl. Phys. A754,58c(2005)

  15. Strategy to determine YN and YY interactions from the studies of light hypernuclear structure Meson theory :Nijmegen Quark model :Kyoto-Niigata YN SLS+ALS potentials ① Use ③ ④ new version potential (ESC06) Suggest to improve Accurate calculation of energy splitting (9Be and 13C) using the YN SLS+ALS potentials Λ Λ comparison again: good agreement ② comparison ⑤ Spectroscopy experiments High-resolution γ-ray spectroscopy experiment in 9Be and 13C by Tamura and his collaborators by Kishimoto and his collaborators Λ Λ

  16. Taken by Tamura Hypernuclear g-ray data since 1998 Λ N ・Millener (p-shell model), ・Hiyama (few-body)

  17. In S= -1 sector, what are the open questions inYN interaction? • spin-orbit force of ΣN interaction • ΣN interaction-> Σ hypernuclei Now, we know that spin-orbit force in ΛN interaction is so small. Then, how about spin-orbit force in ΣN interaction? Next, we want to know about it. Please perform experiment to get information about ΣN interaction.

  18. In S= -1 sector, what are the open questions inYN interaction? (2) ΣN interaction-> Σ hypernuclei Σ N N N 4He Σ First observation of Σ hypernucleus

  19. Possibility of another Σ hypernucleus n p Σ Possible existence of bound 7Li state α Σ T. Yamada and K. Ikeda, PRC46, 1315 (1992). p p n n n p α α α 6Be 6Li(T=1,T=0) 6He A=6 nuclear system is iso-triplet system. Let’s add Σparticle into these nuclei. According to Yamada et al, 7Li has possibility to have bound state. Σ 7Li (K-(in-flight), π-) ?? Σ separation energy is 1.6 MeV. Γ=6.0 MeV.

  20. In S= -1 sector, what are the open questions inYN interaction? (3)Charge symmetry breaking (4) ΛN－ΣN coupling JLAB J-PARC : Day-1 experiment ・E13 “γ-ray spectroscopy of light hypernuclei” by Tamura and his collaborators 11B 4He Λ Λ ・E10 “Study on Λ-hypernuclei with the doubleCharge-Exchange reaction” by Sakaguchi , Fukuda and his collaboratiors 9He 6H Λ Λ

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

  22. In S= -1 sector Exp. 3He+Λ 3H+Λ 0 MeV 0 MeV -1.00 -1.24 1+ 1+ 0.24 MeV -2.04 -2.39 0+ 0.35 MeV 0+ n n p n Λ p Λ p 4H 4He Λ Λ

  23. In order to explain the energy difference, 0.35 MeV, N N N N + N Λ 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.

  24. 3He+Λ 0 MeV 3H+Λ 0 MeV -1.00 -1.24 1+ 1+ (Exp: 0.24 MeV) (cal: -0.01MeV(NSC97e)) -2.04 0+ -2.39 0+ (Exp: 0.35 MeV) (cal. 0.07MeV(NSC97e)) n n p n Λ p Λ p 4H ・A. Nogga, H. Kamada and W. Gloeckle, Phys. Rev. Lett. 88, 172501 (2002) 4He Λ Λ ・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 N N N + Σ N Λ N

  25. 0 MeV 3H+Λ 0 MeV 3He+Λ -1.00 -1.24 1+ 1+ (Exp: 0.24 MeV) (cal: -0.01MeV(NSC97e)) -2.04 0+ -2.39 0+ (Exp: 0.35 MeV) (cal. 0.07MeV(NSC97e)) n n p n Λ p Λ p 4H 4He Λ Λ There exist NO YN interaction to reproduce the data. why can not we reproduce the data? Let’s discuss experimental data again.

  26. We get binding energy by decay π spectroscopy. decay π-+1H+3He →2.42 ±0.05 MeV 4He Λ π-+1H+1H+2H → 2.44 ±0.09 MeV Total: 2.42 ±0.04 MeV Then, binding energy of 4He is reliable. Λ decay π-+1H+3H →2.14 ±0.07 MeV Two different modes give 0.22 MeV 4H Λ π-+2H+2H → 1.92 ±0.12 MeV Total: 2.08 ±0.06 MeV This value is so large to discuss CSB effect. Then, for the detailed CSB study, we should perform experiment to confirm the Λ separation energy of 4H. Λ For this purpose, at JLAB, it is planned to to perform ・・・ Key experiment to get information about CSB. 4He (e, e’K+) 4H Λ

  27. If the binding energy of 4H is the same as that of 4He, • we find that we have no charge symmetry breaking effect • in S=-1 sector. Λ Λ (2) If the binding energy of 4H is quite different from that of 4He, we find that we have charge symmetry breaking (CSB) effect between Λn and Λp interaction. (It should be noted that CSB interaction in S=0 is very small.) We need the JLAB experiment. Λ Λ JLAB experiment 4He (e, e’K+) 4H Λ Possible new understanding

  28. Furthermore, we need more Λ hypernuclear data to get information on CSB.

  29. For this purpose, 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. p p n n n p α α α 6Be 6Li(T=1) 6He

  30. p n n p p n Λ Λ Λ α α α 7He 7Be 7Li(T=1) Λ Λ Λ Then, A=7Λ 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.

  31. Exp. 1.54 Emulsion data Emulsion data 6He 6Be 6Li (T=1) BΛ=5.16 MeV BΛ=5.26 MeV JLAB:E01-011 experiment Preliminary data: 5.68±0.03±0.22 -3.79 7Be Λ 7Li (T=1) Λ 7He Λ

  32. Important issue: Can we describe the Λ binding energy of 7He observed at JLAB usingΛNinteraction to reproduce the Λ binding energies of 7Li (T=1) and 7Be ? To study the effect of CSB in iso-triplet A=7 hypernuclei. Λ Λ Λ p n n n p p Λ Λ Λ α α α 7He 7Be 7Li(T=1) 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)

  33. 7 Li Λ ΛN interaction: Nijmegen ’97f n Not original one but simulated one p Λ The ΛN-ΣN coupling interaction can be renomalized into the ΛN-ΛN interaction effectively. α VΛN=V0+σΛ・σNVs+(σΛ+σN)/2・VSLS+(σΛ-σN)/2・VALS Made by Yamamoto so as to reproduce the phase shifts given by the original one Strengths of Vs,VSLS,VALS are adjusted so as to reproduce of the observed data of 4H, 7Li(T=0), 9Be and 13C. Λ Λ Λ Λ

  34. Now, it is interesting to see as follows: • 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?

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

  36. Next we introduce a phenomenological CSB potential with the central force component only. Strength, range are determined ao as to reproduce the data. 0 MeV 3He+Λ 0 MeV 3H+Λ -1.00 -1.24 1+ 1+ 0.24 MeV -2.04 -2.39 0+ 0.35 MeV 0+ n n p n Λ p Λ p Exp. 4H 4He Λ Λ

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

  38. Comparing the data of A=4 and those of A=7, tendency of BΛ is opposite. How do we understand these difference?

  39. Why CSB interaction which reproduce the energy difference of A=4 hypernuclei, do not reproduce the energy difference in p-shell hypernuclei such as A=7 system? • In my calculation, ΛN-ΣN coupling effect is not included • explicitly and mass difference of Σ. (2) The binding energy of 4H is incorrect. Then, we should measure the binding energy of this hypernucleus again. If the experiment will be done successful, It might the energies of 4H and 4He are the same. Λ Λ Λ (3) odd-state CSB interaction whose contribution is negligible in A=4 hypernuclei, contribute to p-shell Λ hypernuclei with opposite sign of the even state of CSB interaction.

  40. p n n p p n Λ Λ Λ α α α 7He 7Be 7Li(T=1) Λ Λ Λ A=7Λ hypernuclei are p-shell nuclei. Then, it is possible that odd state CSB interaction contribute to those hypernuclei. Now, let me introduce a phenomenological odd state CSB interaction. Parameters are adjusted so as to reproduce the observed binding energy of 7He. Λ

  41. In order to check the validity of the odd CSB interaction, It is suited for study the structure of A=10 Λ hypernuclei such as 10B and 10Be. Λ Λ These are p-shell Λ hypernuclei. Λ Λ n p α α α α 10B 10Be Λ Λ Exp. BΛ=9.11±0.22 MeV Number of event (emulsion data): 3 Exp. BΛ=8.89±0.12 MeV Number of event (emulsion data): 10 At JLAB, the analysis is in progress.

  42. Λ Λ n p α α α α 10B 10Be Λ Λ Exp. BΛ=9.11±0.22 MeV Number of event (emulsion data): 3 Exp. BΛ=8.89±0.12 MeV Number of event (emulsion data): 10 At JLAB, the analysis is in progress. If the odd CSB interaction to reproduce the binding energy of 7He reproduce the binding energy of 10Be which will be reported soon, we can check the validity of odd state CSB interaction. Λ Λ

  43. (Exp: 1.54) 6Be (Exp: -0.14) (exp:-0.98) 6Li 6He (T=1) EXP= 5.16 BΛ：CAL= 5.21 EXP= 5.26 BΛ：CAL= 5.28 BΛ：EXP= 5.68±0.03±022 JLAB:E01-011 experiment CAL= 5.18 →5.66 preliminary 7Be Λ 7Li (T=1) Λ 7He Λ

  44. Now, I shall show you the Λ separation energy of 10B and 10Be. Λ Λ • Results without CSB interaction • Results with CSB interaction Λ Λ n p α α α α 10B 10Be Λ Λ Exp. BΛ=9.11±0.22 MeV Number of event (emulsion data): 3 Exp. BΛ=8.89±0.12 MeV Number of event (emulsion data): 10 At JLAB, the analysis is in progress.

  45. Without CSB interaction Λ Λ p n α α α α 10B 10Be Λ Λ CAL:BΛ=8.76 MeV CAL:BΛ=8.56 MeV Exp. BΛ=9.11±0.22 MeV Number of event (emulsion data): 3 Exp. BΛ=8.89±0.12 MeV Number of event (emulsion data): 10 At JLAB, the analysis is in progress.

  46. With CSB interaction which reproduce the observed binding energy of 7He Λ Λ Λ p n α α α α Where? Please measure BΛ precisely. Jlab 10B 10Be Λ Λ BΛ=8.56 MeV (without CSB) BΛ=8.76 MeV(without CSB) BΛ=8.35 MeV (with CSB) BΛ= 8.97 MeV (with CSB) Exp. BΛ=8.89±0.12 MeV Number of event (emulsion data): 10 Exp. BΛ=9.11±0.22 MeV Number of event (emulsion data): 3 If the calculated results are consistent with the observed data at JLAB in the future, we can extract information on the odd state of CSB interaction.

  47. Major goals of hypernuclear physics 1) To understand baryon-baryon interactions Fundamental and important for the study of nuclear physics 2) To study the structure of multi-strange systems To understand the baryon-baryon interaction,two-body scattering experiment is most useful. Total number of Nucleon (N) -Nucleon (N) data: 4,000 YN and YY potential models so far proposed (ex. Nijmegen, Julich, Kyoto-Niigata) have large ambiguity. ・ Total number of differential cross section Hyperon (Y) -Nucleon (N) data: 40 ・ NOYY scattering data

  48. Λ Hypernuclear physics Λ Λ particle can reach deep inside, and attract the surrounding nucleons towards the interior of the nucleus. There is no Pauli Pricliple between N and Λ. Nucleus Hypernucleus Λ particle plays a ‘glue like role’ to produce a dynamical contraction of the core nucleus. How do we observe nuclear shrinkage effect by experiment?

  49. Theoretical calculation by Hiyama et al. B(E2: 5/2+→ 1/2+) =2.85 e2fm4 reduced by 22% KEK-E419 Λ n Λ n α α 7Li Rα-np Λ p p 6Li Rα-np(6Li) > Rα-np(7Li) Reduced by about 19 % Λ B(E2: 3+→1+:6Li)=9.3 ±0.5e2fm4→B(E2:5/2+→1/2+:7Li)= 3.6 ±2.1 e2fm4 Λ The shrinkage effect on the nuclear size included by the Λ particle was confirmed for the first time.

  50. Are all nuclei compressed by the injection of a Λ? or not? Ground states of stable nuclei with A ≥ 11 :Not compressed :shrunk by as much as 30 % Some excited states of stable nuclei with A ≥ 11 E. Hiyama et al., Prog. Theor. Phys. 97, 881 (1997). α α 13C Λ α Λ

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