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Structure of few-body hypernuclei

Structure of few-body hypernuclei. Emiko Hiyama (RIKEN). Last year and this year, we had two epoch-making data from the view point of few-body problems. Then, in hypernuclear physics, we are so excited. n. n. n. n. 7 He. 6 H. Λ. α. Λ. t. Λ. Λ. JLAB experiment-E011,

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Structure of few-body hypernuclei

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  1. Structure of few-body hypernuclei Emiko Hiyama(RIKEN)

  2. Last year and this year, we had two epoch-making data from the view point of few-body problems. Then, in hypernuclear physics, we are so excited. n n n n 7He 6H Λ α Λ t Λ Λ JLAB experiment-E011, Phys. Rev. Lett. 110, 12502 (2013). FINUDA collaboration & A. Gal, Phys. Rev. Lett. 108, 042051 (2012). Observation of Neutron-rich Λ-hypernuclei These observations are interesting from the view points of few-body physics as well as physics of unstable nuclei.

  3. OUTLINE 7He n n Λ α Λ • Introduction 2. 3. 4. 5. Summary 7He Λ n n 6H 6H Λ Λ t Λ 3n Λ n n If we take triton away, The system is nnΛ system. This was observed at HyPHI collaboration as a bound state. Λ 3n Λ

  4. Section 1 Introduction

  5. In neutron-rich and proton-rich nuclei, n n n n Nuclear cluster Nuclear cluster Nuclear cluster Nuclear cluster n n n n 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. Thereare many interesting phenomena in this field as you know. It was considered that nucleus was hardly compressed by the additional nucleons .

  6. Λ Nucleus Question:How is the structure modified when a hyperon, Λ particle, is injected into the nucleus?

  7. 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.

  8. Λ Λ X X r r’ N N Λ hypernucleus nucleus r > r’ B(E2) value: B(E2) ∝|<Ψi |r2 Y2μ(r) |Ψf>|2 Propotional to 4th-power of nuclear size Bando, Ikeda, Motoba If nucleus is really contracted by the glue-like role of the Λ particle, then E2 transition in the hypernuclei will become much reduced than the corresponding E2 transition in the core nucleus.

  9. E. Hiyama et al., Phys. Rev. C59 (1999), 2351 Theoretical calculation by Hiyama et al. B(E2: 5/2+→ 1/2+) =2.85 e2fm4 reduced by 22% α+ n+p α+Λ+n+p KEK-E419 Then, Tamura et al. Succeeded in measuring this B(E2) value to be 3.6 ±2.1 e2fm4 from 5/2+ to 1/2+ state in 7Li. 3+ B(E2) 7/2+ 1+ 5/2+ Exp.B(E2)= 9.3 e2fm4 B(E2) 6Li 3/2+ Λ n p 1/2+ 7Li n p α Λ Λ α By Comparing B(E2) of 6Li and that of 7Li, Λ The shrinkage effect on the nuclear size included by the Λ particle was confirmed for the first time.

  10. The glue like role of Λ particle provides us with another interesting phenomena. Λparticle can reach deep inside, and attracts the surrounding nucleons towards the interior of the nucleus. Λ Λ There is no Pauli Pricliple between N and Λ. Nucleus hypernucleus Λ Due to the attraction of ΛN interaction, the resultant hypernucleus will become more stable against the neutron decay. Neutron decay threshold γ nucleus hypernucleus

  11. Nuclear chart with strangeness Multi-strangeness system such as Neutron star Extending drip-line! Λ Interesting phenomena concerning the neutron halo havebeen observed near the neutron drip line of light nuclei. How does the halo structure change when a Λ particle is injected into an unstable nucleus?

  12. Question : How is structure change when a Λ particle is injected into neutron-rich nuclei? n n n n 6H 7He Λ t Λ Λ α Λ Observed at JLAB, Phys. Rev. Lett. 110, 12502 (2013). Observed by FINUDA group, Phys. Rev. Lett. 108, 042051 (2012).

  13. In order to solve few-body problem accurately, 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: Exotic atoms / molecules , 3- and 4-nucleon systems, multi-cluster structure of light nuclei, Light hypernuclei, 3-quark systems, 4He-atom tetramer

  14. Section 2 Four-body calculation of 7He Λ n n α Λ

  15. n n 6He : One of the lightest n-rich nuclei 6He α n n 7He: One of the lightest n-rich hypernuclei Λ 7He Λ α Λ Observed at JLAB, Phys. Rev. Lett. 110, 12502 (2013).

  16. CAL: E. Hiyama et al., PRC53, 2075 (1996), PRC80, 054321 (2009) 6He 7He Λ Prompt particle decay 2+ γ α+Λ+n+n 0 MeV 0 MeV α+n+n 5He+n+n 0+ Λ -1.03 MeV 5/2+ Halo states Exp:-0.98 3/2+ -4.57 BΛ: CAL= 5.36 MeV γ BΛ：EXP=5.68±0.03±0.25 1/2+ Jlab experiment Phys. Rev. Lett.110, 012502 (2013). -6.19

  17. CAL: E. Hiyama et al., PRC53, 2075 (1996), PRC80, 054321 (2009) 6He 7He Λ Prompt particle decay 2+ γ α+Λ+n+n 0 MeV 0 MeV α+n+n 5He+n+n 0+ Λ -1.03 MeV 5/2+ Halo states Exp:-0.98 3/2+ -4.57 BΛ: CAL= 5.36 MeV 5/2+→1/2+ 3/2+ →1/2+ ・Useful for the study of the excitation mechanism in neutron-rich nuclei ・Helpful for the study of the excitation mechanism of the halo nucleus γ BΛ：EXP=5.68±0.03±0.25 1/2+ Observed at J-Lab experiment(2012) Phys. Rev. Lett.110, 012502 (2013). -6.19 In n-rich nuclei and n-rich hypernuclei, there will be many examples such as Combination of 6He and 7He. I hope that γ-ray spectroscopy of n-rich hypernuclei will be performed at J-PARC. Λ

  18. Section 3 Four-body calculation of 6H Λ n n t Λ E. H, S. Ohnishi, M. Kamimura, Y. Yamamoto, NPA 908 (2013) 29.

  19. n n 6H t Λ Λ

  20. Phys. Rev. Lett. 108, 042051 (2012). Γ=1.9±0.4 MeV 1/2+ FINUDA experiment 1.7±0.3 MeV t+n+n+Λ t+n+n 5H 4H+n+n EXP: BΛ= 4.0±1.1 MeV Λ 0.3 MeV 6H Λ n n 5H : super heavy hydrogen t Λ

  21. Before the experiment, the following authors calculated the binding energy using shell model picture and G-matrix theory. (1) R. H. Dalitz and R. Kevi-Setti, Nuovo Cimento 30, 489 (1963). (2) L. Majling, Nucl. Phys. A585, 211c (1995). (3) Y. Akaishi and T. Yamazaki, Frascati Physics Series Vol. 16 (1999). Akaishi et al. pointed out that one of the important subject to study this hypernucleus is to extract information about ΛN-ΣN coupling. Motivated by the experimental data, I calculated the binding energy of 6H and I shall show you my result. Λ

  22. Framework: To calculate the binding energy of 6H, it is very important to reproduce the observed data of the core nucleus 5H. Λ transfer reaction p(6He, 2He)5H A. Korcheninnikov, et al. Phys. Rev. Lett. 87 (2001) 092501. Γ= 1.9±0.4 MeV 1/2+ 1.7±0.3 MeV Theoretical calculation N. B. Schul’gina et al., PRC62 (2000), 014321. R. De Diego et al, Nucl. Phys. A786 (2007), 71. calculated the energy and width of 5H with t+n+n three-body model using complex scaling method. 5H is well described as t+n+n three-body model. t+n+n threshold

  23. Then, I think that t+n+n+Λ4-body model is good model to describe 6H. Then. I take t+Λ+n+n 4-body model. Λ Λ n n n n t t Λ 6H 5H Λ

  24. Before doing the full 4-body calculation, it is important and necessary to reproduce the observed binding energies of all the sets of subsystems in 6H. Λ Namely, all the potential parameters are needed to adjust the energies of the 2- and 3-body subsystems. 6H 6H Λ Λ 6H n n Λ n n n n Λ Λ Λ t t t

  25. 6H I take the Λｔpotential to reproduce the binding energies of 0+ and 1+ states of 4H. In this case, ΛN－ΣN coupling is renormarized into the ΛN interaction. n Λ n Λ Λ t 6H Λ n n I take the ΛＮpotential to reproduce the binding energy of 3H. Λ Λ t Λ

  26. Γ=1.9±0.4 MeV  EXP Γ= 2.44MeV  CAL 1/2+ 1.69 MeV 1.7±0.3 MeV I focus on the 0+ state. t+n+n 1+ n n σn・σΛ 0+ Λ t 6H Λ 5H Then, what is the binding energy of 6H? Λ

  27. Exp: 1.7 ±0.3 MeV Even if the potential parameters were tuned so as to reproduce the lowest value of the Exp. , E=1.4 MeV, Γ=1.5 MeV, we do not obtain any bound state of 6H. Γ=1.9 ±0.4 MeV Λ Γ= 2.44 MeV ½+ Γ=0.91 MeV 1.69MeV 1.17 MeV 0 MeV t+n+n+Λ Γ=0.23 MeV t+n+n E=-0.87MeV 0+ 4H+n+n Λ -2.0 4H+n+n 0+ -2.07 MeV Λ On the contrary, if we tune the potentials to have a bound state in 6H, then what is the energy and width of 5H? Λ

  28. Γ= 1.9±0.4 MeV Phys. Rev. Lett. 108, 042051 (2012). 1/2+ FINUDA experiment 1.7±0.3 MeV t+n+n+Λ t+n+n 5H EXP:BΛ=4.0±1.1 MeV 4H+n+n Λ t+n+n+Λ n n 0.3 MeV t 6H Λ n n 5H:super heavy hydrogen t Λ But, FINUDA group provided the bound state of 6H. Λ

  29. How should I understand the inconsistency between our results and the observed data? • We need more precise data of 5H. A. Korcheninnikov, et al. Phys. Rev. Lett. 87 (2001) 092501. Γ=1.9±0.4 MeV To get bound state of 6H, the energy should be lower than the present data. It is planned to measure the energy and width of 5H more preciselyat RCNP by Prof. Tanihata. He submitted his experimental proposal to RCNP and PAC meeting will be held in 11th March. Λ 1/2+ 1.7±0.3 MeV t+n+n

  30. We cited this experiment. However, you have many different decay widths. Width is strongly related to the size of wavefunction. Then, I hope that The decay width will be determined by Tanihata san in the future. [3] A.A. Korosheninnikov et al., PRL87 (2001) 092501 [8] S.I. Sidorchuk et al., NPA719 (2003) 13 [4] M.S. Golovkov et al. PRC 72 (2005) 064612 [5] G. M. Ter-Akopian et al., Eur. Phys. J A25 (2005) 315.

  31. In our model, we do not include ΛＮーΣN coupling explicitly. The coupling effect might contribute to the energy of 6H. Λ

  32. How should I understand the inconsistency between our results and the observed data? • We need more precise data of 5H. • A. Korcheninnikov, et al. Phys. Rev. Lett. 87 (2001) 092501. Γ=1.9±0.4 MeV To get bound state of 6H, the energy should be lower than the present data. Question: Is it possible to measure the energy and width of 5H more preciselysomewhereagain? Λ 1/2+ 1.7±0.3 MeV t+n+n • In our model, we do not include ΛＮーΣN coupling explicitly. The coupling effect might contribute to the energy of 6H. Λ

  33. Non-strangeness nuclei S=-1 Σ Δ N 80 MeV Λ S=-2 ΞN N N 25MeV ΛΛ Δ In hypernuclear physics, the mass difference is very small in comparison with the case of S=0 field. 300MeV N Probability of Δin nuclei is not large. Then, in S=-1 and S=-2 system, ΛN-ΣN and ΛΛ-ΞN couplings might be important.

  34. Gal and D. J. Millener, arXiv:1305.6716v3 (To be published in PLB. They pointed out that Λ N-ΣN coupling is important for 6H. Λ It might be important to perform the following calculation: n n n n 6H + Λ t Λ 3N Σ

  35. Γ=1.9±0.4 MeV Phys. Rev. Lett. 108, 042051 (2012). 1/2+ FINUDA experiment 1.7±0.3 MeV t+n+n+Λ 0 MeV t+n+n 5H Cal: -0.87 MeV EXP:BΛ=4.0±1.1 MeV 4H+n+n Λ ΛN-ΣN coupling？ Exp: -2.3 MeV This year, at J-PARC, they performed a search experiment of (E10 experiment)of 6H. If E10 experiment reports more accurate energy, we can get information about ΛN-ΣN coupling. Λ Σ

  36. t+n+n+Λ No peak?! 4H+n+n Λ 0.3 MeV FINUDA data 6H Λ Theoretically, we might understand by the following reason. If the state is resonant state, the reaction cross section would be much smaller than that we expect. => I should calculate reaction cross section 6Li (π,K) 6H with Harada’s help. Λ

  37. Now, we have open question whether or not 6H is bound state. Λ We should answer to this issue. I think that there is one possibility to perform experiment at Mainz.

  38. Core-to-Core Workshop at Vila Lanna in Czech, 5-7/Dec/2013 Concept of Decay pion spectroscopy Mass resolution : 100 keV Mass accuracy : 30 keV

  39. Core-to-Core Workshop at Vila Lanna in Czech, 5-7/Dec/2013 Hypernuclei from 9Be target Other targets, 7Li or 12C or so, should be measured in future. I hope that at Mainz we can have conclusion about 6H. Λ

  40. In hypernuclear physics, currently, it is extremely important to get information about ΛN-ΣN coupling. Question: Except for 6H, what kinds of Λ hypernuclei are suited for extracting the ΛN-ΣN coupling? Λ Answer: 4H, 4He Λ Λ n n n p Λ Λ p p 4H 4He Λ Λ

  41. -BΛ -BΛ 4He 4H Λ Λ 0 MeV 3He+Λ 0 MeV 3H+Λ 1+ 1+ -1.00 -1.24 0+ 0+ -2.04 -2.39 Exp. Exp. N N 4He Λ Λ 4H N Λ

  42. Σ N Λ N + N N N N + NNNΛ NNNΣ E. Hiyama et al., Phys. Rev. C65, 011301 (R) (2001). H. Nemura et al., Phys. Rev. Lett. 89, 142502 (2002). A. Nogga et al., Phys. Rev. Lett. 88, 172501 (2002).

  43. PΣ=1.12 % PΣ=2.21%

  44. Another interesting role of Σ-particle in hypernuciei, namely effective ΛNN 3-body force generated by the Σ-particle mixing. N1 N2 N3 Λ ② N1 N2 N3 Λ ① Σ Σ N1 N2 N3 Λ N1 N2 N3 Λ 3N+Λ space N1 N2 N3 N1 N2 N3 Λ Λ Effective 3-body ΛNN force Effective 2-body ΛN force How large is the 3-body effect? N1 N2 N3 N1 N2 N3 Λ Λ

  45. Y. Akaishi, T. Harada, S. Shinmura and Khin Swe Myint, Phys. Rev. Lett. 84, 3539 (2000). 3He 3He Σ + + + Λ They already pointed out that three-body force effect is important within the framework of (3He+Λ)+(3He+Σ).

  46. This effect (ΛN-ΣN coupling) might contribute to Another s-shell Λ hypernuclei. n+p+Λ n p Λ d+Λ ½+ Exp. 0.13 MeV bound Take Saito observed bound state of nnΛ system. It is considered that ΛN-ΣN coupling play an important role to make bound state. n n Λ

  47. t If we inject triton cluster into nnΛsystem, we have 6H. Λ n n Λ n n Λ t Then, it is expected that ΛN-ΣN coupling might contribute to 6H. Λ

  48. At GSI, they observed a bound state of nnΛ system. n n nnΛ Λ ½+ They did not report binding energy.

  49. n n n n + Λ Σ NN interaction : to reproduce the observed binding energies of triton and 3He YN interaction: to reproduce the observed binding energies of 3H, 4H and 4He Λ Λ Λ What is the binding energy for nnΛ?

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