Structure of light hypernuclei Emiko Hiyama Kyushu Univ

Structure of light hypernuclei Emiko Hiyama (Kyushu Univ. /RIKEN)

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, twobody 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. For this purpose, we have much knowledge about YN (especially, ΛN interaction) so far. As for YN interaction, as a next step, we should study ΛN-ΣN coupling. For this purpose, it might be good idea to produce neutron-rich　Λ　hypernuclei. Search a resonant state in nnΛ system at JLab is one of the project.

Another interesting subject is nnnnΛ system. n n n Λ 5 Λn should be bound! n Why do we think to have a bound state of 5Λn?

n n published in PRL, as mentioned by Shimoura san n n

4 n breakup threshold Exp. ～-1. 0 Me. V ～ 3 Me. V E(Me. V) Theoretical issue: ・Can we describe observed 4 n system using realistic NN interaction and T=3/2 three-body force? ・If we reproduce the observed 4 n system theoretically, can we also reproduce 　other A=4 nuclei, 4 He and 4 Li, which are mirror nuclei?

Published in PRC.

To answer these issues, We employ AV 8 NN potential + a phenomenological three-body force. These parameters (W 1, W 2, b 1, b 2) are determined so as to reproduce the binding energies of the ground states of 3 H, 3 He and 4 He. For 4 n system, we need T=3/2 three-body force. We use the same potential with T=1/2, but, different parameter of W 1(T=3/2)= free b 1=4. 0 fm => W 1 should be fixed so as to reproduce the observed 4 n system W 2(T=3/2) = +35 Me. V b 2=0. 75

The observed 4 n system was reported from the bound region to resonant region. In order to obtain energy position (Er) and decay width (Γ), we use complex scaling method. The energy pole is stable with respect to θ. Re(E) corresponds to energy With respect to 4 n breakup threshold. Im(E) corresponds to Γ/2. 4 n breakup threshold

energy trajectory of J=0+ state changing W 1

In order to reproduce the data of 4 n system, We need W 1= -36 Me. V～-30 Me. V. Attraction is 15 times Stronger. It should be noted that W 1=-2. 04 Me. V to reproduce the observed binding energy of 4 He, 3 He and 3 H. Exp. Question: W 1 value for T=3/2 is reasonable? To check the validity of three-body force, we calculate the energies of 4 H, 4 He(T=1), 4 Li.

Exp. 4 H (-5. 29 Me. V) If we use W 1=-36 Me. V～-30 Me. V to reproduce the observed data of 4 n, We have strong binding energies of 4 H, 4 He (T=1) and 4 Li. This result is inconsistent with the data of A=4 nuclei. The J=2 - state of A=4 nuclei should be resonant states.

How do we consider this inconsistency? ・The T=3/2 force is just a phenomenological. Should we consider spin-dependent term in three-body force? Tensor force, spin-orbit force? ? ? The confirmation experiment for 4 n was performed last year at RIBF. Two weeks ago, they reported that there is still a peak near the threshold. We should think what is missing part in our calculation. If the experiment is true, let’s add a Λ particle to 4 n.

n n Λ 5 Λn should be bound! This is important to study ΛN-ΣN coupling. Then, I hope that production of 5Λn will be performed at ALICE or GSI?

Next step, we should study about ΛΛ interaction and ΞN interaction! Currently, in the case of ΛΛ interaction, we obtain information on strength of attraction of 1 S 0. What about p-wave? Spin-dependent force? We have no information. ΞN interaction: so far we have not known whether or not ΞN interaction should be attractive.

Ξ- core nucleus For the study of ΞN interaction, it is important to study the structure of Ξ hypernuclei. However, so far there was no observed Ξ hypernucleus without ambiguity.

Approved proposal at J-PARC : Day-1 experiment ・E 05 “Spectroscopic study of Ξ-Hypernucleus, 12 Be, Ξ - via the 12 C(K-, K+) Reaction” by Nagae　and his collaborators K+ K- Ξ- p 11 B 12 C 11 B Ξ hypernucleus Now, theoretically, it is time to analyze that what kind of spin-parities they observed.

14 N-Ξ- 0 Me. V -4. 38 ± 0. 25 ～-1. 10 ± 0. 25 Me. V Ξ- 14 N Kiso event Furthermore, we observed bound Ξ hypernucleus, for the first time in the world. Now, we understood that ΞN interaction should be attractive. Also, it is important to interpret spin-parity to comparing theory and experimental data.

Physical Review C 94, 064319 (2016) Using RMF theory, we interpret that Kiso event is observation of 14 N(g. s) +Ξ(0 p) state. Weak point: RMF theory focus on the only ground state of 14 N, not the excited state of 14 N. It is planning to take into account of the excited state of 14 N for further analysis of Kiso event using α+α+α+d+Ξ 5 -body cluster model.

For the analysis of 11 B+Ξ system, we should calculate energy spectra of this system within the framework of α+α+t+Ξ four-body model. This is also future plan. 12 Be Ξ- Ξ- t α α Now, we have a question: What part’s information of the ΞN interaction do we extract?

VΞN = V 0 + σ・σ Vσ・σ ＋ τ・τ Vτ・τ＋ (σ・σ)(τ・τ) Vσ・σ　τ・τ 15 α α α d 12 Be Ξ- Ξ- α t α ΞC All of the terms contribute to binding energy of 12 Be and 15 C ( 11 B and 14 N is not spin-, isospinΞ Ξ saturated). - Then, even if we observe　this system as a bound state, we shall get only information that VΞN　itself is attractive. Therefore, after the Day-1 experiment, next, we want to know desirable strength of V 0, the spin-, isospin-independent term.

VΞN = V 0 + σ・σ Vσ・σ ＋ τ・τ Vτ・τ＋ (σ・σ)(τ・τ) Vσ・σ　τ・τ In order to obtain useful information about V 0, the following systems are suited, because the (σ・σ), (τ・τ) and (σ・σ) (τ・τ) terms of VΞN　vanish by folding them into the α-cluster wave function that are Ξ- α spin-, isospin-satulated. problem : there is NO target to produce them by the (K-, K+) experiment. Because, ・・・ α

To produce αΞ- and ααΞ- systems by (K-, K+) reaction, K- These systems are unbound. Then, we cannot use them as targets. Also, it might be difficult to Produce these Ξ hypernuclei at Aiice. K+ target p Ξ- α α 5 Li Ξ- 5 H K+ KΞ- p α α 9 B α Ξ- α 9 Li

As the second best candidates to extract information about the spin-, isospin-independent term V 0, we propose to perform… K+ K- p n Ξ- n α n 7 Li (T=1/2) (T=3/2) 7 H Ξ- Why they are suited K+ K- p α 10 B n α (T=0) Ξ- α n α 10 Li Ξ- (T=1) for investigating V 0?

(more realistic illustration) n n α Ξ- Core nucleus 6 He is known to be halo nucleus. Then, valence neutrons are located far away from α particle. Valence neutrons n are located in p-orbit, whereas Ξparticle Ξ- is located in 0 s-orbit. 7 H Ξ- (T=3/2) n Then, distance between Ξ and n is much larger than the interaction range of Ξ and n. α Ξ- α 10 Li Ξ- (T=1) Then, αΞ potential, in which only V 0 term works, plays a dominant role in the binding energies of these system.

Before the experiments will be done, we should predict whether these Ξhypernuclei will be observed as bound states or not. Ξ- n α n 7 H Ξ- (T=3/2) Ξ- n α α 10 Li Ξ- (T=1) Namely, we calculate the binding energies of these hypernuclei.

ΞN interaction Only one experimental information about ΞN interaction Y. Yamamoto, Gensikaku kenkyu 39, 23 (1996), T. Fukuda et al. Phys. Rev. C 58, 1306, (1998); P. Khaustov et al. , Phys. Rev. C 61, 054603 (2000). Well-depth of the potential between Ξ and 11 B: -14 Me. V Among all of the Nijmegen model, ESC 04 (Nijmegen soft core) and ND (Nijmegen Model D) reproduce the experimental value. OtherΞN interaction are repulsive or weak attractive. We employ ESC 04 and ND. The properties of ESC 04 and ND are quite different from each other.

Property of the spin- and isospin-components of ESC 04 and ND V(T, S) ESC 04 T=0, S=1 　　strongly attractive T=0, S=0 weakly repulsive T=1, S=1 weakly attractive T=1, S=0 weakly repulsive ND (a bound state) weakly attractive Although the spin- and isospin-components of these two models are very different between them (due to the different meson contributions), we find that the spin- and isospin-averaged property, V 0 = [ V(0, 0) + 3 V(0, 1) + 3 V(1, 0) + 9 V(1, 1) ] / 16, namely, strength of the V 0 - term is similar to each other.

The characteristic property of ESC 04 potential V(T=0, S=1): strongly attractive n Ξ 0 -0. 60 Me. V V(T=0, S=0), V(T=1, S=1) Not so strong attractive or weak repulsive T=0, L=0, 2 , S=1, J=1+ p Ξ- T=0, L=0, 2 , S=1, J=1+ UΞ=-12. 1 Me. V -1. 60 Me. V attractive Coulomb force Ξ- : 1321. 3 Me. V Ξ 0: 1314. 9 Me. V If it is true, They might be produced at ALICE. strength of ΛΛーΞN－ΣΣ is large.

ESC potential leads to give bound states in s-shell Ξ hypernuclei such as NNΞ and NNNΞ. N N Ξ N

ESC 04 Results 0 Me. V (np)-Ξ 1/2+ -0. 15 Me. V N N Ξ NNΞ No bound using ND

T=1/2、Tz=1/2 K- n p p T=1/2, Tz=-1/2 p n Ξ- 3 He Using 3 He target, it might be produced this Ξ hypernucleus. Also, at ALICE, it might be possible to produce this Ξ hypernucleus. K+

Results ESC 04 No bound using ND 0 Me. V (3 N)+Ξ 1+ -0. 86 0+ -2. 3 T=0 repulsive strongly attractive = T, S 1+: [12 V(1, 1)+V(1, 0)+10 V(0, 1)+3 V(0, 0)]/25 0+: [V(1, 0)+V(0, 1)]/2 weakly repulsive strongly attractive N N N Ξ

K- n p n p n Ξ- 4 He(T=0) K+ T=1 We have no bound state using both of ESC 04 and ND. It is difficult to produce NNNΞ hypernucleus with T=0 experimentally at J-JPARC. However, it might be possible to produce at ALICE.

In this way, I would say that it is dependent on the ΞN interaction employed whether the ground-state of　s-shell Ξ hypernuclei is bound or not. Therefore, to determine ΞN spin-isospin part, I would suggest the experimentalists to perform the search experiment of s-shell at ALICE. On the other hand, it would be necessary to predict theoretically bound state of Ξ hypernuclei without depending on ΞN interaction employed.

As mentioned before, αΞ potential, in which only V 0 term works, Ξ- n α n 7 H plays a dominant role in the binding energies of these system. (T=3/2) Ξ- Ξ- α n α 10 Li Ξ- (T=1) Therefore, interestingly, we may expect to have similar binding energies between ESC 04 and ND, although the spin- and isospin-components are very different between the two.

4 -body calculation of E. Hiyama et al. , 7 H Ξ- PRC 78 (2008) 054316 ESC 04 Me. V 1. 71 ND α+ n + Ξ 6 He 0. 75 0. 0 Me. V 0. 96 0. 39 + Ξ- 1/2+ 6 He 7 H + Ξ- 1/2+ -1. 56 7 H Ξ- In experiments, we can expect a bound state. (αΞ- ) + n 0. 0 (αΞ- ) + n -1. 35 α+ n + Ξ- Ξ- n α n Ξ- Similar binding energies using ND and ESC 04. Independent on employed ΞN potential

In this way, we predict to have bound state in 7ΞH. However, we have one ambiguity for this system. => decay width Decay width comes from ΛΛ-ΞN　interaction.

4 -body calculation of E. Hiyama et al. , 7 H Ξ- PRC 78 (2008) 054316 ESC 04 Me. V 1. 71 ND α+ n + Ξ 6 He 0. 75 0. 0 Me. V 0. 96 0. 39 + Ξ- 1/2+ Γ=2. 64 Me. V 6 He -1. 56 Γ=0. 27 Me. V 7 H + Ξ- 1/2+ 7 H Ξ- In experiments, we can expect a bound state. (αΞ- ) + n 0. 0 (αΞ- ) + n -1. 35 α+ n + Ξ- Ξ- n α n Ξ- Similar binding energies using ND and ESC 04. However, decay width is dependent on on employed ΞN potential

4 -body calculation of -Ξ Me. V 5. 17 ESC 04 d 3. 60 Me. V 2. 86 1. 32 + Ξ- (ααΞ- ) + n 0. 0 Li In experiments, we can expect a bound state. 9 Be + Ξ- (ααΞ- ) + n -2. 96 Γ=5. 87 Me. V 10 Ξ- α+ α + n +Ξ- 0. 0 2 - -3. 18 PRC 78 (2008) 054316 ND α+ α+ n +Ξ 9 Be E. Hiyama et al. , 10 Li 2 Γ=0. 75 Me. V 10 Li Similar binding energies using ND and ESC 04 d. Independent on employed ΞN potential Ξ- Ξ- n α α But, decay width is dependent on employed ΞN interaction.

In this way, the binding energies of Ξ hypernuclei with A=7 and 10 are dominated by αΞ potential, namely, spin-, and　iso-spin independent ΞN interaction（Ｖ 0）. Then, to get information about this part, we propose to perform the (K-, K+) experiment by using 7 Li and 10 B targets at J-PARC after the Day-1 experiment with 12 C target. However, as mentioned by the previous slide, the decay width is dependent on the employed ΞN interaction. Question: How do we obtain this information. Answer: we should obtain the binding energy of s-shell double Λ hypernuclei such as 4ΛΛH and 5ΛΛH, which have not been observed yet.

(1) ΛΛ－ΞN coupling One of the major goals in hypernuclear physics : To study structure of multi-strangeness systems (extreme limit : neutron star) N N N N Multi-strangeness systems Λ Λ Λ ΞN 25 Me. V ΛΛ Threshold energy difference is very small ! It is considered that ΛΛ→ΞN particle conversion is strong in multi-strangeness systems.

Effect of ΛΛ－ΞN coupling is small in 　 6ΛΛHe which was observed as NAGARA event. Pauli Forbidden V ΛΛ--ΞN P 3/2 S 1/2 n n p p 6 He ΛΛ Λ Λ Ξ- p (3 protons in S 1/2) 　・ I. R. Afnan and B. F. Gibson, Phys. Rev. C 67, 017001 (2003). ・ Khin Swe Myint, S. Shinmura and Y. Akaishi, nucl-th/029090. ・T. Yamada and C. Nakamoto, Phys. Rev. C 62, 034319 (2000).

For the study of ΛΛ－ΞN coupling interaction, s-shell double Λ hypernuclei such as 4 H ΛΛ and 5 H ΛΛ ( ΛΛ 5 He) are very suitable. Λ n Λ p 4 H ΛΛ Λ n p 5 H ΛΛ ( ΛΛ 5 He) ・I. N. Filikhin and A. Gal, Phys. Rev. Lett. 89, 172502　(2002) ・Khin Swe Myint, S. Shinmura and Y. Akaishi, Eur. Phys. J. 　A 16, 21　(2003). ・D. E. Lanscoy and Y. Yamamoto, Phys. Rev. C 69, 014303　(2004). ・H. Nemura, S. Shinmura, Y. Akaishi and Khin Swe Myint, 　 Phys. Rev. Lett. 94, 202502 (2005).

Λ n 5 H ΛΛ p V ΛΛ－ΞN P 3/2 S 1/2 n n Λ p Λ 5 H ΛΛ Due to NO Pauli plocking, the ΛΛ－ΞN coupling can be large in ΛΛ 5 H B. F. Gibson, I. R. Afnan, J. A. Carlson and D. R. Lehman, Prog. Theor. Phys. Suppl. 117, 339 (1994). Ξ- p (2 protons in S 1/2)

I would suggest the experimentalist to perform search experiment of A=5 double Λ hypernuclei than A=4 double Λ hypernuclei. Because, I can say that A=5 double Λ hypenuclei are surely obtained as a bound state. But, how do we perform experiment to obtain A=5 double Λ hypernuclei? To produce 5ΛΛH, it is use 7 Li target to produce A=7 Ξ hypernucleus, first.

4 -body calculation of E. Hiyama et al. , 7 H Ξ- PRC 78 (2008) 054316 ESC 04 Me. V 1. 71 ND α+ n + Ξ 6 He 0. 75 0. 0 Me. V 0. 96 0. 39 + Ξ- 1/2+ 7 H I. Fuse and Y. Akaishi , Phys. Rev. C 54, R 24 (1996) 6 He + Ξ- 1/2+ -1. 56 7 H Ξ- Decay in to 5ΛΛH+n+n (αΞ- ) + n 0. 0 (αΞ- ) + n -1. 35 α+ n + Ξ- Ξ- n α n Ξ- Similar binding energies using ND and ESC 04. Independent on employed ΞN potential

Summary 1. In Λ　hypernuclei, if possible, it is interesting to produce nnnnΛ system at ALICE or GSI. 2. Now, we found that ΞN interaction is attractive. 3. At Alice, it might be good idea to produce s-shell Ξ hypernuclei to determine Spin-isospin term of ΞN inyteraction. 5. Next, we should know the information on spin- and isospin-independent force. For this purpose, I would like to suggest to produce A=7 and 10 Ξ Hypernuclei using 7 Li and 10 B targets at J-PARC. 6. ΛΛ-ΞN interaction is also important. For this purpose, I suggest to produce 5 H using 7 Li target at J-PARC. And it might be good to produce 4 H at ALICE. ΛΛ ΛΛ