10 Structure of 10Be and B hyp ernuclei studied with four-body cluster model E. Hiyama (RIKEN) Submitted in PRC last August and waiting for referees comment Hypernuclear -ray data since 1998 ray data since 1998 (figure by H.Tamura) Millener (p-shell model), Hiyama (few-body) Four-body structure of these hypernuclei is important for the study of N spin-dependent force and CSB interaction. n 10 Be Exp. B=9.110.22 MeV Number of event (emulsion data): 3 At JLAB, the analysis is in progress. p

10 B Exp. B=8.890.12 MeV Number of event (emulsion data): 10 p To obtain information about N spin-dependent force 10 B(K-,-) 10B BNL-E930 10 B 3/2- ++p+ ++p p 9

B 21- E<100keV?E<100keV? or 2- is ground state? We could not obtain observed -ray. Important issue: which part is supported theoretically? p To obtain information about N spin-spin force BNL-E930 10 B D.J. Millener tried to calculate spin-doublet splitting by shell model. The calculated result was more than 100 keV. 3/2- ++p+ ++p p

9 B 21- E<100keV?E<100keV? or 2- is ground state? We could not obtain observed -ray. What value in my calculation? p 10 B N interaction: Nijmegen 97f Not original one but simulated one The N-N coupling interaction can beN coupling interaction can be renomalized into the N-N interaction effectively. VN=V0+ NVs+(+N)/2 VSLS+(-N)/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. J=2- =>S=1,0 J=1- =>S=0

p 10 -8.34 B 40 keV E<100keV?E<100keV? or 2- is ground state? p B 10 Experimentally, we need to conclude Which is final conclusion?, namely E<100keV?E<100keV? or 2- is ground state? For this study, it might be good way to observe weak decay from 10 B and to measure angular distribution to determine spin and parity. 3/2-

++p+ ++p BNL-E930 21- E<100keV?E<100keV? or 2- is ground state? p B 10 3/2- Problem: if the ground state is 1- state, We have weak-decay both from 1- and 2- state. Because splitting energy is less than 100 keV, Transition probability T(M1,2-1-) is small. Then, the weak decay occurs from 2-. So, it might be difficult to identify which is the Ground state by observing weak decay. ++p+ ++p BNL-E930 M1 21- E<100keV?E<100keV? or 2- is ground state?

Then, in order to solve this issue, I propose to measure weak decay from mirror hypernucleus, 10 Be. n ++n+ 10 Be M1 21- E<100keV?E<100keV? or 2- is ground state? Example: Fragmentation Process + K Ac two bc two bess to variety decay (~10 of l l e 12 ight and exotic two b hy decay (~10per nuc two blei, some of whic some of l whic two b h c two bannot be produc two be d or measured prec two bis ely decay (~10 by decay (~10 other means

C e p 12 * B 4 H - -16 Fragmentation (<10 s) Weak mesonic two b mesonic two b two b He ody decay (~10 dec two bay decay (~10 (~10-10s) 4 n Decay pion spectroscopy at Mainz

10 Be I think it is possible to get spin and parity of 10 Be from decay pion spectroscopy. If the spin and parity of 10 Be is determined, then we can determine spin and parity of mirror hypernucleus 10 10 10 B. Because spin-structure of Be is the same as B. So, I hope that this experiment will be done in the future. Furthermore, four-body structure of these hypernuclei is important for the study of CSB interaction. n 10

Be Exp. B=9.110.22 MeV Number of event (emulsion data): 3 At JLAB, the analysis is in progress. p 10 B Exp. B=8.890.12 MeV Number of event (emulsion data): 10 Charge Symmetry breaking Exp. 0 MeV 3 -1.24 He+ 0 MeV 3 -1.00 1+ 0.24 MeV -2.39

1+ -2.04 0+ 0+ 0.35 MeV n p p 4 He H+ n n p 4 H p n Furthermore, 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 and 10 hypernuclei is suited. Because, core nuclei with A=6 are iso-triplet states and core nuclei with A=9 are iso-doublet states. n n n 9 He Be 6 p Li(T=1) 9 n p 6 p B 6

p Be n n n 7 7 n Be He Then, A=7 p 10

p p 7 Li(T=1) Be hypernuclei are also iso-triplet states. p 10 And A=10 hypernuclei are iso-doublet states. B It is possible that CSB interaction between and valence nucleons contribute to the -binding energies in these hypernuclei. 7He Me B =5.16

6 Li (T=1) V He eV B =5.26 M experiment 1 1 -0 1 0 :E B A JL 6 .22 0 3 0 . 0 8 ta: 5.6 a d y r a in m Preli Exp.

1.54 Emulsion data 7 Li (T=1) Emulsion data 6 Be -3.79 7 Be Exp. Be+ 9 0 MeV 9 0 MeV B+ Recently, 10B(e,eK+) 10Be has been done at JLab. Analysis is in progress. Exp: -8.89 0.12 MeV Exp: -9.11 0.22 MeV Exp: 0.22 0.25 MeV n Be

10 p 10 B Important issue: Can we describe the binding energies of A=7 and 10 hypernuclei? To study the effect of CSB in iso-triplet A=7 and 10 hypernuclei. n n n p 7 p

p He 7 7 Be Li(T=1) E. Hiyama, Y. Yamamoto, T. Motoba and M. Kamimura,PRC80, 054321 (2009) n Be 10 p 10 B

Now, it is interesting to see as follows: (1)What is the level structure of A=7 and 10 hypernuclei without CSB interaction? (2) What is the level structure of A=7 and 10 hypernuclei with CSB interaction? (Exp: 1.54) Without CSB = B CAL 5.21 Be .16 EXP= 5 6 Li (T=1) 5.26 EXP= = B CAL 5.28 periment x e 1 1 -0 1 0 :E JLAB He preliminary 03022

. 0 8 6 . 5 = B EXP 6 CAL= 5.3 6 6 (Exp: -ray data since 1998 0.14) (exp:-ray data since 1998 0.98) 7 Be 7 7 He Li (T=1) Without CSB interaction Be+ 9 0 MeV

9 0 MeV B+ Exp: -8.89 0.12 MeV Exp: -9.11 0.22 MeV Cal: 8.84 MeV n Be 10 Cal: 8.67 MeV Exp: 0.22 0.25 MeV In good agreement Cal: 0.17 MeV with the data p 10 B 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 3 -1.24 He+ 0 MeV 3 H+ -1.00 1+ 0.24 MeV -2.39 1+ -2.04 0+ 0+ 0.35 MeV n p p 4 He Exp. n

n p 4 H SB) p n SB) C t u o h t 5.21 (wi B) S C h t i w 5.44( rt CSB) u o h it w (

5.28 MeV it h C W ( V e M 5.29 B) 5.16(with CS CS B ) t u o h it w ( 6 5.3 30.22 .0 0 8 6 . 5 = B EXP With CSB Inconsistent with the data With CSB interaction Be+ 9 0 MeV

Recently, 10B(e,eK+) 10 Be has been done at JLab. Analysis is in progress. Exp: -9.11 0.22 MeV Cal: 8.84 MeV (without CSB) Cal: 8.76 MeV (with CSB) n 10 Be 0 MeV 9 B+ No plan Propose to measure binding energy at J-PARC Exp: -8.89 0.12 MeV Cal: 8.67 MeV (without CSB) Cal: 8.77 MeV (with CSB) Exp: 0.22 0.25 MeV Cal: 0.17 MeV (without CSB) Cal: 0.01 MeV (With CSB) Error bar is large to discuss CSB interaction. We can extract information on CSB interaction, if they provide new data of A=10 hypernuclei 10 B within 100 keV accuracy.

p Summary 10 (1) We calculated spin-doublet states of 1-- 2- in B. The calculated splitting energy is 0.04 MeV which is consistent with the experimental fact of no observed -ray. For the detailed investigation of spin doublet state in 10B, 10 I propose to measure weak decay from 10B as well as Be. (2)The CSB effects in A=10 hypernuclei are investigated quantitatively on the basis of the phenomenological CSB interaction, which describe the experimental energy difference between 4H and 4 He. However, the error bars of energies in A=10 hypernuclei are too large to discuss the CSB effect in these hypernuclei. Then, we propose to measure 10B by (,K) or (K,) at J-PARC in the future.