Five and four-body structure of S=-2 hypernuclei

Five and four-body structure of S=-2 hypernuclei E. Hiyama (RIKEN)

Λ Λ n α α Outline of my talk ・Introduction ・Four-body structure of 7He, 7Li, 8Li, 9Li, 9Be, 10Be ΛΛ ΛΛ ΛΛ ΛΛ ΛΛ ΛΛ Λ Λ Λ Λ Λ Λ Λ ｎ Λ Λ Λ p d t 3He α α α α α ・ Five-body structure of 11Be ΛΛ ・ Four-body structure of 7H and 10Li Ξ- Ξ Ξ Ξ- n n α α α n 10Li 7H Ξ- Ξ-

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-strangeness systems Due to the difficulty of YN and YY 2-body scattering experiment for the study of baryon-baryon interaction, the systematic investigation of the structure oflight hypernuclei is essential.

Hypernuclear g-ray data since 1998 (figure by H.Tamura) ・Millener (p-shell model), ・Hiyama (few-body)

What is the structure when one or more Λs are added to a nucleus? + + + + ・・・・ Λ Λ Λ Λ Λ It is conjectured that extreme limit, which includes many Λs in nuclear matter, is the core of a neutron star. nucleus In this meaning, the sector of S=-2 nuclei , double Λhypernuclei and Ξhypernuclei is just the entrance to the multi-strangeness world. However, we have hardly any knowledge of the YY interaction because there exist no YY scattering data. Then, in order to understand the YY interaction, it is crucial to study the structure of double Λ hypernuclei and Ξ hypernuclei.

In 2001, the epoch-making data has been reported by the KEK-E373 experiment. Observation of 6He ΛΛ Uniquely identified without ambiguity forthe first time Λ Λ α+Λ+Λ α ６．９1±0.16 MeV 0+

Strategy of how to determine YY interaction from the study of light hypernuclear structure YY interaction Nijmegen model D 6He Suggest reducing the strength of spin-independent force by half ① use ③ ΛΛ Λ Λ Accurate structure calculation α compare between the theoretical result and the experimental data of the biding energy of 6He ② prediction of new double Λ hypernuclei ④ ΛΛ Spectroscopic experiments Emulsion experiment (KEK-E373) by Nakazawa and his collaborators

My theoretical contribution using few-body calculation KEK-E373 experiment analysis is still in progress. Approved proposal at J-PARC ・E07 “Systematic Study of double strangness systems at J-PARC” by Nakazawa and his collaborators It is difficult to determine (1) spin-parity (2) whether the observed state is the ground state or an excited state comparison Emulsion experiment Theoretical calculation input: ΛΛ interaction to reproduce the observed binding energy of 6He ΛΛ the identification of the state

Successful example to determine spin-parity of double Λhypernucleus --- Demachi-Yanagi event for 10Be ΛΛ Observation of 10Be --- KEK-E373 experiment ΛΛ Λ Λ 8Be+Λ+Λ α α 11.90±0.13 MeV 10Be ground state ? excited state ? ΛΛ 10Be ΛΛ Demachi-Yanagi event

Successful interpretation of spin-parity of Λ Λ α α E. Hiyama, M. Kamimura,T.Motoba, T. Yamada and Y. Yamamoto Phys. Rev. 66 (2002) , 024007 11.83 11.90 α+Λ+Λ 6.91 ±0.16 MeV Λ Λ Demachi-Yanagi event α -14.70

Hoping to observe newdouble Λ hypernuclei in future experiments, I predicted level structures of thesedouble Λ hypernuclei within the framework of the α+x+Λ+Λ 4-body model. E. Hiyama, M. Kamimura, T. Motoba, T.Yamada and Y. Yamamoto Phys. Rev. C66, 024007 (2002) Λ Λ 3He t x = p d n = = = = = α x 9Be 8Li 7Li 8Li 7He ΛΛ ΛΛ ΛΛ ΛΛ ΛΛ

Spectroscopy of ΛΛ-hypernuclei E. Hiyama, M. Kamimura,T.Motoba, T. Yamada and Y. Yamamoto Phys. Rev. 66 (2002) , 024007 > A 11 ΛΛhypernuclei new data (2009) I have been looking forward to having new data in this mass-number region.

Observation ofHida event KEK-E373 experiment Λ Λ Λ Λ n n n α α α α 11Be 12Be ΛΛ ΛΛ BΛΛ= 20.49±1.15 MeV BΛΛ= 22.06±1.15 MeV Important issue: Is the Hida event the observation of a ground state or an excited state? It is neccesary to perform 5-body calculation of this system. Why 5-body?

Core nucleus, 9Be is well described as α+α+ n three-cluster model. 11Be ΛΛ Λ Λ Then, 11Be is considered to be suited for studying with α+α+ n +Λ+Λ 5-body model. ΛΛ n α α Difficult 5-body calculation: 1) 3 kinds of particles (α, Λ, n) 2) 5 different kinds of interactions Λ Λ Λ n 3) Pauli principle between α and α, and between α and n α Λ α But, I have succeeded in performing this calculation. n α α

5-body calculation of 11Be ΛΛ 11Be ΛΛ Λ Λ n α α (γ～10000 MeV is sufficient.) rules out the Pauli-forbidden states from the 5-body wave unction. The Pauli-forbidden states (f ) arethe 0S, 1S and 0Dstates of theα αrelative motion, and the0S states of the α nrelative motion. This method for the Pauli principle is often employed in the study of light nuclei using microscopic cluster models.

11Be 5-body calculation of 11Be ΛΛ ΛΛ Λ Λ n α α A variational method: Gaussian Expansion Method (GEM) (review paper) E. H., Y. Kino and M. Kamimura, Prog. Part. Nucl. Phys., 51 (2003) 223. expansion coefficient specifies 5-body basis functions of each Jacobi-coordinate set specifies many sets of Jacobi coordinates

An example of 5-body basis function: 5-body spatial function spin function (a Jacobi coordinate set) spin specify radial dependence (shown below) specify angular momenta

Form of each basis function 5-body spatial function Gaussian for radial part : geometric progression for Gaussian ranges : Similarly for the other basis : Use of this type gaussian basis is known to be very suitable for describing simultaneously both the short-range correlations and long-range tail behaviour of few-body systems; This is precisely shown in Gaussian Expansion Method (GEM) (review paper) E. H., Y. Kino and M. Kamimura, Prog. Part. Nucl. Phys., 51 (2003) 223.

Some of important Jacobi corrdinates of theα+ α+ n + Λ+ Λsystem. Two αparticles are symmetrized. Two Λparticles are antisymmetrized. 120 sets of Jacobi corrdinates are employed.

Before doing full 5-body calculation, it is important and necessary to reproduce the observed binding energies of all the sets of subsystems in 11Be. In our calculation, this was successfully done using the same interactions for all subsystems: ΛΛ Λ Λ Λ Λ Λ Λ n n n α α α α α α 8Be (0+) 9Be (3/2-) 5He (3/2-) CAL : +0.80 MeV EXP : +0.80 MeV CAL : +0.09 MeV EXP : +0.09 MeV CAL : -1.57 MeV EXP : -1.57 MeV

adjusted predicted n Λ n Λ Λ Λ Λ Λ n α α α α α α ΛΛ ΛΛ ΛΛ 10Be (0+, 2+ ) 6He (0+ ) 10Be (1-) Λ Λ Λ Λ Λ CAL (0+): -6.93 MeV EXP (0+): -6.93 MeV CAL (2+): -10.96 MeV EXP (2+): -10.98 MeV CAL : -10.64 MeV EXP : -10.64 MeV CAL (0+): -14.74 MeV EXP (0+): -14.69 MeV All the potential parameters have been adjusted in the 2- and 3-body subsystems. Therefore, energies of these 4-body susbsystems and the 5-body system are predicted with no adjustable parameters. 11Be Λ Λ

Convergence of the ground-state energy of theα+α+ n +Λ+Λ5-body system ( ) 11Be ΛΛ J=3/2-

To be published in Phys. Rev. Lett.

As mentioned before, Hida event has another possibility, namely, observation of 12Be. ΛΛ Λ Λ BΛΛ= 22.06±1.15 MeV n n 12Be α α ΛΛ For this study, it is necessary to calculate 6-body problem. At present, it is difficult for me to perform 6-body calculation. However, I think, it is good chance to develop my method for 6-body problem. Within two years, I will try to do it. For the confirmationof Hida event, we expect to have more precise data at J-PARC.

Spectroscopy of ΛΛ-hypernuclei At J-PARC A=12, 13, …… 11Be , ΛΛ For the study of this massregion, we need to perform more of 5-body cluster-model calculation.

Therefore, we intend to calculate the following 5-body systems. Λ Λ Λ Λ Λ Λ Λ Λ t p 3He d α α α α α α α α 13B 11B 13C 12B ΛΛ ΛΛ ΛΛ ΛΛ Λ Λ To study 5-body structure of these hypernuclei is interesting and important as few-body problem. α α α 14C ΛΛ

Ξhypernuclei

Ξ- core nucleus For the study of ΞN interaction, it is important to study the structure of Ξ hypernuclei. However, so far there is no observed Ξ hypernucleus. Then, it is important to predict theoretically what kinds of Ξ hypernuclei will exist as bound states.

Approved proposal at J-PARC : Day-1 experiment ・E05 “Spectroscopic study of Ξ-Hypernucleus, 12Be, via the 12C(K-,K+) Reaction” by Nagaeand his collaborators Ξ- K+ K- p Ξ- 11B 11B 12C Ξ hypernucleus This will be the first observation of Ξ hypernucleus

12C(K-, K+) 12Be Day-1 experiment at J-PARC Ξ- What part’s information of the ΞN interaction do we extract? VΞN = V0 + σ・σ Vσ・σ ＋ τ・τ Vτ・τ＋(σ・σ)(τ・τ) Vσ・στ・τ All of the terms contribute to binding energy of 12Be ( 11B is not spin-, isospin- saturated). Ξ- t Then, even if we observethis system as a bound state, we shall get only information that VΞNitself is attractive. Ξ- α α Therefore, after the Day-1 experiment, next, we want to know desirable strength of V0, the spin-,isospin-independent term. 12Be Ξ- (T=1, J=1-)

VΞN = V0 + σ・σ Vσ・σ ＋ τ・τ Vτ・τ＋(σ・σ)(τ・τ) Vσ・στ・τ In order to obtain useful information about V0, the following systems are suited, because the (σ・σ), (τ・τ) and (σ・σ) (τ・τ)terms of VΞNvanish by folding them into the α-cluster wave function that are spin-, isospin-satulated. Ξ- Ξ- α α α problem : there is NO target to produce them by the (K-, K+) experiment . Because, ・・・

To produce αΞ- and ααΞ- systems by (K-, K+) reaction, K+ target K- These systems are unbound. Then, we cannot use them as targets. Ξ- p α α 5H 5Li Ξ- K+ K- p Ξ- α α α α 9B 9Li Ξ-

As the second best candidates to extract information about the spin-, isospin-independent term V0, we propose to perform… K+ K- p Ξ- n n α α n n 7H (T=3/2) 7Li (T=1/2) Why they are suited for investigating V0? Ξ- K+ K- Ξ- p n n α α α α 10Li (T=1) 10B (T=0) Ξ-

(more realistic illustration) Core nucleus 6He is known to be halo nucleus. Then, valence neutrons are located far away from α particle. n n α Ξ- Valence neutrons are located in p-orbit, whereas Ξparticle is located in 0s-orbit. Then, distance between Ξ andn is much larger than the interaction range of Ξ and n. n Ξ- 7H (T=3/2) Ξ- n α α Ξ- Then, αΞ potential, in which only V0term works, plays a dominant role in the binding energies of these system. 10Li (T=1) Ξ-

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

ΞN interaction Only one experimental information about ΞN interaction Y. Yamamoto, Gensikaku kenkyu 39, 23 (1996), T. Fukuda et al. Phys. Rev. C58, 1306, (1998); P.Khaustov et al., Phys. Rev. C61, 054603 (2000). Well-depth of the potential between Ξ and 11B: -14 MeV Among all of the Nijmegen model, ESC04 (Nijmegen soft core) and ND (Nijmegen Model D) reproduce the experimental value. OtherΞN interactions are repulsive or weak attractive. We employ ESC04 and ND. The properties of ESC04 and ND are quite different from each other.

Property of the spin- and isospin-components ofESC04 andND V(T,S) ESC04 ND T=0, S=1 strongly attractive T=0, S=0 weakly attractive T=1, S=1 T=1, S=0 (a bound state) weakly repulsive weakly attractive weakly repulsive 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, V0= [ V(0,0) + 3V(0,1) + 3V(1,0) + 9V(1,1) ] / 16, namely,strength of theV0- term is similar to each other.

Ξ- n α n 7H (T=3/2) Ξ- Ξ- n α α 10Li (T=1) Ξ- As mentioned before, αΞ potential, in which onlyV0term works, plays a dominant role in the binding energies of these system. Therefore, interestingly, we may expect to have similar binding energies between ESC04 and ND, although the spin- and isospin-components are very different between the two.

4-body calculation of 7H E. Hiyama et al., PRC78 (2008) 054316 Ξ- ESC04 MeV ND α+ n + n + Ξ- 1.71 MeV α+ n + n + Ξ- 0.96 6He + Ξ- 0.75 (αΞ- ) + n + n 0.39 0.0 0.0 (αΞ- ) + n + n 6He + Ξ- -1.35 1/2+ -1.56 1/2+ 7H 7H Ξ- Ξ- Ξ- n Similar binding energies using ND and ESC04. α n In experiments, we can expect a bound state. Independent on employed ΞN potential

4-body calculation of 10Li E. Hiyama et al., PRC78 (2008) 054316 In this way, the binding energies of Ξ hypernuclei with A=7 and 10 are dominated by αΞ potential, namely, spin-, andiso-spin independent ΞN interaction（Ｖ0）. Then, to get information about this part, we propose to perform the (K-,K+) experiment by using 7Li and 10B targets at J-PARC after the Day-1 experiment with 12C target. -Ξ ESC04d ND MeV α+ α+ n +Ξ- 5.17 MeV α+ α + n +Ξ- 9Be + Ξ- 3.60 2.86 9Be + Ξ- 1.32 (ααΞ- ) + n (ααΞ- ) + n 0.0 0.0 2- -2.96 -3.18 2- 10Li 10Li Ξ- Ξ- Ξ- n Similar binding energies using ND and ESC04d. α α In experiments, we can expect a bound state. Independent on employed ΞN potential

Concluding remark ・Four-body structure of 7He, 7Li, 8Li, 9Li, 9Be, 10Be ΛΛ ΛΛ ΛΛ ΛΛ ΛΛ ΛΛ ・ Five-body structure of 11Be ΛΛ ・ Four-body structure of 7H and 10Li Ξ Ξ In order to extract further information about YY interaction, observation of the above systems are necessary. We hope that we have many hypernuclei at J-PARC facility in the future.

Thank you!

Five and four-body structure of S=-2 hypernuclei