Structure of few-body li of few-body li f few-body lie of few-body liw-body li li ght hypernuclei hy lipe of few-body lirnucle of few-body lii Emiko Hiyama (RIKEN) Recently, we had three epoch-making data from the view point of few-body problems. n He n n 6 H 7 n n t 3

JLAB experiment-E011, Phys. Rev. Lett. 110, 12502 (2013). n n C. Rappold et al., HypHI collaboration Phys. Rev. C 88, 041001 (R) (2013) FINUDA collaboration & A. Gal, Phys. Rev. Lett. 108, 042051 (2012). E. Hiyama, S. Ohnishi, and M. Kamimura, Nucl. Phys. A908, 29 (2013). E. Hiyama, S. Ohanishi. B. F. Gibson, And Th. A. Rijken, Phys. Rev. C89, 061302 (R), (2014). Observation of Neutron-rich -hypernuclei These observations are interesting from the view points of few-body physics as well as unstable nuclear physics. n n

He 7 He 7 n He 7 n What is interesting to study this hypernucleus? (1) It is important to obtain information about charge symmetry breaking effect of n- and p-. (2) To study structure of hypernuclei due to the glue-like role of particle. The major goal of hypernuclear physics 1) To understand baryon-baryon interactions Fundamental and important for the study of nuclear physics

To understand the baryon-baryon interaction, two-body scattering experiment is most useful. Total number of Nucleon (N) -Nucleon (N) data: 4,000 Total number of differential cross section Hyperon (Y) -Nucleon (N) data: 40 NO YY scattering data YN and YY potential models so far proposed (ex. Nijmegen, Julich, Kyoto-Niigata) have large ambiguity. 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. Hy lipe of few-body lirnucle of few-body liar g-ray li data since of few-body li 1998 (figure of few-body li by li H.Tamura) Millener (p-shell model), Hiyama (few-body) In S= -1 sector, what are important to study YN interaction? (1) Charge symmetry breaking (2) NN N couplingN coupling J-PARC : Day-1 experiment E13 n n p

Jlab E05-115, n n 4 H He 7 Mainz In S= -1 sector Exp. 3 0 MeV He+ -1.24 3

0 MeV H+ -1.00 1+ 0.24 MeV -2.39 1+ -2.04 0+ 0+ 0.35 MeV n p 4 He p 4 n n p

H n p n p p n p 4 n 4 He

H However, particle has no charge. 4 n p p 4 He + + p p p n p + 0 n p p

- n + + + p n H n + p n p n p - + n + 0 n n

n + In order to explain the energy difference, 0.35 MeV, N N (3N+ N + N N N (3N+ 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, N coupling) are included. 3 0 MeV 1+

He+ 0 MeV 3 -1.00 -1.24 H+ 1+ (cal: -0.01 MeV(NSC97e)) (Exp: 0.24 MeV) -2.04 (Exp: 0.35 MeV) -2.39 0+ (cal. 0.07 MeV(NSC97e)) n p 4 He n p p A. Nogga, H. Kamada and W. Gloeckle,

Phys. Rev. Lett. 88, 172501 (2002) 0+ n 4 H 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 N N 0 MeV 1+ 3

He+ 0 MeV 3 -1.00 -1.24 (cal: -0.01 MeV(NSC97e)) -2.39 1+ (Exp: 0.24 MeV) -2.04 (cal. 0.07 MeV(NSC97e)) n p 0+ (Exp: 0.35 MeV) 0+ 4 H+ He n

p p n 4 H There exist NO YN interaction to reproduce the data. For the study of CSB interaction, we need more data. It is interesting to investigate the charge symmetry breaking effect in p-shell hypernuclei as well as s-shell hypernuclei. For this purpose, to study structure of A=7 hypernuclei is suited. Because, core nuclei with A=6 are iso-triplet states. n n n 6 He p p

p 6 Li(T=1) Be 6 n n n He p 7 p

p Li(T=1) 7 7 Be Then, A=7 hypernuclei are also iso-triplet states. It is possible that CSB interaction between and valence nucleons contribute to the -binding energies in these hypernuclei. Exp. 1.54 Emulsion data 6 He 6 Be eV M 6 1

. 5 = B eV B =5.26 M 0.0 8 6 . 5 .: p x e 5 JLabE05-11 30.25 6 Li (T=1) 7He Emulsion data -3.79 7 Li 7 (T=1)

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

p 7 Li(T=1) Be 7 For this purpose, we study structure of A=7 hypernuclei within the framework of ++N+N 4-body model. E. Hiyama, Y. Yamamoto, T. Motoba and M. Kamimura,PRC80, 054321 (2009) 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? 6 He 7 He

6 Li (T=1) 6 EXP= 5.1 5.21 = L A C B (exp:-0.98) 26 EXP= 5. 5.28 B CAL= riment e p x e 5 1 -1 5 0 :E JLAB 3022 .0 0

8 .6 5 B EXP= CAL= 5.36 (Exp: 1.54) Without CSB (Exp: -0.14) 6 7 Li (T=1) Be 7 Be 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? Next we introduce a phenomenological CSB potential with the central force component only.

Strength, range are determined so as to reproduce the data. 0 MeV 3 He+ -1.24 0 MeV 3 -1.00 1+ 0.24 MeV -2.39 H+ 1+ -2.04 0+ 0+ 0.35 MeV n p 4 He p

Exp. 4 n n p H ) p n 5.21 C SB ) CSB t u o h t (wi 5.44(with

) t CSB) r u o h it w ( 5.28 MeV h C SB t i W ( V e 5.29 M ) 5.16(with CSB t CSB) u o h it w ( 6 3 . 5 30.22 .0 0

8 .6 5 B EXP= With CSB Inconsistent with the data Comparing the data of A=4 and those of A=7, tendency of B 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. In S= -1 sector Exp. 3 0 MeV 0.984 MeV He+ -1.24 H+ -1.00 1+ 0.24 MeV 1.4060.0020.003 Reported by H. Tamura

3 0 MeV -2.39 1+ -2.04 0 + A. Esser et al., PRL114, 232501 (2015) Reported by P. Achenbach 0+ 0.35 MeV n p 4 He -2.120.010.09 MeV p 4 n n

p H n p Questions to experimentalist: (1) The ground state of 4He is confirmed? (2) The excited state of 4H is confirmed? In S= -1 sector Exp. 3 0 MeV He+ -0.98 H+ -1.00 1+ 0.24 MeV

1.4060.0020.003 Reported by H. Tamura 3 0 MeV -2.39 1+ -2.120.010.09 MeV 0+ 0+ 0.35 MeV n p 4 He p 4 n n p H

If the answer is no, It is important to measure the excited state of 4H at JLab. 4 He(e,eK+) 4H reaction at JLab is very powerful way to obtain it. It is important to measure the ground state of 4He at J-PRAC. Or please analyze all states of A=4 hypernuclei by emulsion data by Prof. Nakazawa and his collaborators. In S= -1 sector Exp. 3 0 MeV He+ -0.98 1 -2.39 0+ 0.35 MeV n p 4 He p

H+ If the answer is yes, 1+ From now, this is homework to theory side. -2.120.010.09 MeV In A. Gal, PLB 744, 352 (2015), 0+ Using purely central-type NN coupling reproduce the current energy-splittings of A=4 hypernuclei, n n and p-shell nuclei of A=7, 8,10. p However, I do not think that N-N coupling should be purely central force. 4 -1.00 + 0.24 MeV 1.4060.0020.003 Reported by H. Tamura 3 0 MeV Questions to experimentalist: (1) The ground state of 4He is confirmed? (2) The excited state of 4H is confirmed?

H Charge Symmetry breaking In S=0 sector Exp. N+N+N 0 MeV M eV Charge symmetry breaking effect is small. - 8.48 MeV 3 0. 76 1/2+ Energy difference comes from dominantly Coulomb force between 2 protons. H - 7.72 MeV 1/2+ 3 He

n n n p p p Question: Why we have large CSB effect in A=4 hypernuclei? I cannot understand this physics. N N N + (3N+ N N N (3N+ n n

Now, as a few-body physicist, we should perform both of four-body NNN +NNN coupled channel calculation And (++N+N)+(++N+N)coupled channel calculation with updated YN realistic interaction. n n A=7 hypernuclei Now, we have next stage to discuss on which part, theory side or experiment side should have homework. He 7 n He

7 n What is interesting to study this hypernucleus? (1) It is important to obtain information about charge symmetry breaking effect of n- and p-. (2) To study structure of hypernuclei due to the glue-like role of particle. Why is it interesting to study neutron-rich hypernucleus such as 7He? Second of major goals in hypernuclear physics To study the structure of multi-strange systems In neutron-rich and proton-rich nuclei, n Nuclear cluster n Nuclear cluster Nuclear cluster n Nuclear cluster n

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. There are many interesting phenomena in this field as you know. No Pauli principle Between N and particle can reach deep inside, and attract the surrounding nucleons towards the interior of the nucleus. N Due to the attraction of N N interaction, the resultant hypernucleus will become more stable against the neutron decay. Hypernucleus neutron decay threshold

nucleus hypernucleus CAL: E. Hiyama et al., PRC 53, 2075 (1996), PRC 80, 054321 (2009) 6He Another interesting issue is to study the excited states of 7He. 7He 2+ 0 MeV 0+ Exp:-0.98 ++n+n 0 MeV +n+n 5He+n+n -1.03 MeV B

B :C AL EX Observed at J-Lab experiment Phys. Rev. Lett.110, 012502 (2013). P= = 5. -4.57 36 5. 68 M eV 0 .0 3 -6.19 MeV

0 .2 5 One of the excited state was observed at JLab. 5/2+ 3/2+ 1/2+ Neutron halo states 7 Li(e of few-body li,e of few-body liK ) hypernucleiHe of few-body li + 7 (FWHM = 1.3 MeV) Fitting results Cal: Ex=1.70MeV Good agreement with my prediction Question: In 7He, do we have any other new states? If so, what is spin and parity? First, let us discuss about energy spectra of 6He core nucleus. 12.1 1.1 MeV (2+,1-,0+)? =1.6 0.4 MeV 2.60.3 MeV

2+ 2 =0.11 0.020 MeV 1.797 MeV 2+ 0 MeV +n+n =0.12 MeV 2+ 1 0 MeV +n+n -0.98 0+ -0.98 0+ He 6 Exp. Data in 2002 Core nucleus 1.8 MeV

6 He Exp. Data in 2012 X. Mougeot et al., Phys. Lett. B 718 (2012) 441. p(8He, t)6He How about theoretical result? =1.6 0.4 MeV 2.5 MeV = 1.60.3 MeV 2 Decay with =0.12 MeV Is smaller than 2+ 0.8 MeV 1 Calculated with. +n+n 2+ 0 MeV 0+ = 0.79 MeV -0.98 What is my result? 6

He Exp. Data in 2012 X. Mougeot et al., Phys. Lett. B 718 (2012) 441. p(8He, t)6He -0.97 MeV theory Myo et al., PRC 84, 064306 (2011). Question: What are theoretical results? =1.6 0.4 MeV 2.60.3 MeV 2+ 2 These are resonant states. =0.12 MeV 2+ 1 0 MeV 1.8 MeV I should obtain energy position and decay width. +n+n -0.98 0+

6 He Exp. Data in 2012 X. Mougeot et al., Phys. Lett. B 718 (2012) 441. p(8He, t)6He To do so, I use complex scaling method which is one of powerful method to get resonant states. My result E=0.96 + 0.14 MeV E=2.81 +4.81 MeV Question: What are theoretical results? =4.81 MeV 2+ 2.81 MeV 2 =1.6 0.4 MeV 1.60.3 MeV 2+ 2 =0.12 MeV 2+ 1

0.8 MeV +n+n -0.98 0 MeV 0+ 6 He Exp. Data in 2012 X. Mougeot et al., Phys. Lett. B 718 (2012) 441. p(8He, t)6He =0.14 MeV 2+ 1 0.8 MeV +n+n -0.98 0 MeV 0+ 6 He Cal. How about energy spectra of 7He? =4.81 MeV

2.81 MeV 2+ 2 =0.14 MeV 2+ 1 0 MeV 3/2+,5/2+ 0.8 MeV +n+n -0.98 0+ 6 He Cal. E=0.07 MeV+1.13 MeV The energy is measured with respect to ++n+n threshold. 4.3 nb/sr 3.4 nb/sr I propose to experimentalists to observe these states. 40% reduction 11.6 nb/sr 10.0 nb/sr

I think that It is necessary to estimate reaction cross section 7 Li (e,eK+). 49.0 nb/sr Motobas Cal. Motoba san recently estimated differential cross sections for each state. At Elab=1.5 GeV and =7 deg (E05-115 experimental kimenatics) Conclusion n He n n n 7 6 H

n n t 3 JLAB experiment-E011, Phys. Rev. Lett. 110, 12502 (2013). n C. Rappold et al., HypHI collaboration Phys. Rev. C 88, 041001 (R) (2013) FINUDA collaboration & A. Gal, Phys. Rev. Lett. 108, 042051 (2012). Thank you! (1) Charge Symmetry breaking In S=0 sector Energy difference comes from dominantly Coulomb force between 2 protons. Exp.

N+N+N 0 MeV 1/2 + - 8.48 MeV 3 0. 76 M eV Charge symmetry breaking effect is small. H - 7.72 MeV 1/2+ 3 He n n n p p p

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