Recent status in Hypernuclear Physics E. Hiyama (Nara Women’s Univ.)

The discussion about the recent progress in the hypernuclear physics by introducing my studies performed so far. My study nucleus Λ Λ Λ Single Λ hypernucleus Double Λ hypernucleus

In 2008 (next year), the construction of J-PARC facility is complete. And the experiment about hypernuclear physics will be run since So, we expect to have a lot of data of hypernuclei in the future. What are interesting and important to study Hypernuclear physics?

Before answering this question, firstly I intoruduce the obtained hypernuclear experimental data so far. Before 1995 (1)hyperon(Y)-nucleon(N) and hyperon(Y)-hyperon(Y) scattering data

Hyperon-nucleon scattering experimental data obtained so far Total number of data:40 NN:4,000 No YY scattering data (Due to the difficulty of the YN and YY scattering experiment)

(2) How many single Λ hypernuclei and double Λ hypernuclei were observed so far?

(2) いくつハイパー核は見つかっているの？ Λ ハイパー核について 全部で 30 個くらい Nuclear chart of a single Λ hypernuclei About 30 events

Double Λ hypernuclei 6 He, 10 Be, 13 B ΛΛ There are ambiguities in identifying these double Λ hypernuclei.

(3) How many γ transitions were measured? /2 + 1/ H4H Λ 7 Li Λ 9 Be Λ 13 C Λ γ γ γ γ Only excitation energies were measured. B(E2) and B(M1) values NEVER have been observed.

Since 1995 We have been obtaining epoch-making experimental data continuously because of development of experimental method, especially, development of high resolution γ-ray spectroscopy method with Ge detector. Some of the recent epoch-making experimental data

(1)For the first time, the B(E2) value in 7 Li was successfully observed by KEK-E Li Λ 7 Li Λ As a consequence, we could extract the hypernuclear size for the first time. Λ

(2) γ-ray spectroscopic experiments of 9 Be and 13 C were successfully performed at BNL-E929 and E930. Λ Λ 8 Be Λ 12 C Λ 9 Be 13 C Λ Λ As a result, we could determine the strength of ΛN spin-orbit force.

(3) At KEK-E373 experiment, a double Λ hypernucleus was observed and was identified uniquely 6 He. ΛΛ α ΛΛ 6 He ΛΛ This is the first observation of double Λ hypernuclei with NO ambiguity.

Furthermore, At J-PARC, we are planning to have many single Λ hypernuclei and double Λ hypernuclei in the future. Why is it important to produce many single Λ hypernuclei and double Λ hypernuclei?

Major goal of hypernuclear physics (1)To understand the hyperon(Y)-nucleon(N) and hyperon(Y)-hyperon(Y) interaction (2) To study new dynamics of many body systems consisting of nucleons and hyperons The J-PARC facility is the key facility to provide the data necessary to attain the goal of hypernuclear physics. But since the scattering YN scattering data is limited, then it is necessary to obtain information on YN and YY interactions from the hypernuclear structure study. For this purpose, we need to have many hypernuclei and double Λ hypernuclei.

The J-PARC facility is the key facility to provide the data necessary to attain the goal of hypernuclear physics. My role To use high precision calculational method of few-body systems to carry out the goal (1) and (2).

Gaussian Expansion Method Developed by Kyushu Univ. group Kamimura (1) 3-cluster structure of light nuclei (2) Coulomb 3-body muonic molecular ions appearing in the muon-catalyzed fusion cycles (1987 ～ ) (3) 3-nucleon bound states with realistic NN and 3N forces (1988) (4)Metastable antiprotonic helium atom (He + +p+e)(1995 ～ ) E. Hiyama, M. Kamimura and Y. Kino, Prog. Part. Nucl. Phys. 51 (2003), 223. Applied to

This method also successfully applied to four-body problems. The merit of this method: (1)To calculate the energy of bound state very accurately (2) To calculate the wavefunction very precisely One example

Benchmark test of 4 He Phys. Rev.C64, (2001) n n p p NN:AV8 4 He 4 nucleon bound state

Good agreement among 7different method In the binding energy, r.m.s, and two-body correlation function

Our method → hypernuclear structure Major goal of hypernuclear physics (1)To understand the hyperon(Y)-nucleon(N) and hyperon(Y)-hyperon(Y) interaction Since YN scattering experiment are difficult to perform, the existing data is very limited. So far proposed YN interactions have a large degree of ambiguity. Nijmegen model, Julich model Quark model based potential

It is necessary to obtain useful information on YN and YY interaction from hypernuclear structure study.

Our calculation of few-body systems play essential role in this connection between the basic models and the experimental data. This theoretical component is our calculational contribution from few-body systems.

Discussion on γ-ray spectroscopy experiment and theoretical structure calculations of 9 Be and 13 C related to the YN spin-orbit interaction Λ Λ 8 Be Λ 12 C Λ 9 Be 13 C Λ Λ Strong NN spin-orbit force which leads to magic number nuclei How large is the YN spin-orbit force compared with the NN spin-orbit force?

Meson theory Nijmegen model « Constituent quark model Proposed by Fujiwara et al. If we use these types of spin-orbit forces in hypernuclear structure calculation, then how is the spin-orbit energy splitting?

Why is the spin-orbit force is small based on the constituent quark model ? The strength of Antisymmetric LS(ALS) is opposite sigh with the symmetric LS(SLS). And that of ALS is cancelled that of SLS. ALS : σ ー σ ΛN 2 V ALS SLS: V SLS σ ＋ σ ΛN 2 O.Morimatsu et al. Nucl. Phys. A420,573 (1984) Thus, quark model leads to small spin-orbit splitting energy in hypernuclear structure, xL

Be Λ 1/2 + 5/2 + 3/2 + ΔE Ls splitting γ γ 9 Be Λ BNL-E C 13 C Λ γ γ 1/2 + 3/2 - 1/2 - ΔE Λ 0+0+ BNL-E929

E. Hiyama et al. Phys. Rev. Lett. 85, 270 (2000) 8 Be = αα 12 C = α αα 9 Be= Λ 13 C= Λ αα Λ α αα Λ

ΛN spin orbit force and 9 Be and 13 C Λ Λ 5/2 + 3/ keV ～ 5/2 + 3/ keV Meson Quark 9 Be Λ 3/2 - 1/ keV ～ keV Meson Quark 13 C Λ 1/2 - 3/2 - Exp. 5/2 + 3/ Exp keV BNL-E930 H. Akikawa et al. Phys. Rev. Lett. 88,(2002) /2 - 3/2 - BNL-E929 ± 54 ± 36 keV S.Ajimura et al. Phys. Rev. Lett. 86,(2001) 4255

When any new types of YN interaction are proposed in the future, it is desirable to pay attention to having a reasonable strength of YN spin-orbit force by testing it in the structure calculation of 9 Be and 13 C. Λ Λ

Where do we go from here? How large are the ΣN and ΛΛ spin-orbit forces? ・ ΣN scattering experiments at J-PARC facility ・ γ-ray spectroscopy experiments of double Λ hypernuclei nucleus ΛΛ

We are extracting novel information about YN interaction because of the cooperation analysis involving the γ-ray spectroscopy experiment and highly accurate calculations. Once the Hamiltonian is determined, we can calculated precisely the structure of many-body systems consisting of neutron, proton and hyperon. Furthermore, we can predict with understanding new phenomena such as we have never imagined before.

Major goal of hypernuclear physics (1)To understand the hyperon(Y)-nucleon(N) and hyperon(Y)-hyperon(Y) interaction (2) To study new dynamics of many body systems consisting of nucleons and hyperons The J-PARC facility is the key facility to provide the data necessary to attain the goal of hypernuclear physics.

(2) To study new dynamics of many body systems consisting of only nucleons One of the major goal in neutron rich nuclear physics (to my knowledge) In unstable nuclear physics stable nucleus n n When many nucleons are added to the stable nucleus, how is structure?

nucleus Hyperon(Λ 、 Ξ ・・ ) In hypernuclear physics How is structure, when hyperons are added to the nucleus? In this view point, we have the same interest both in studying unstable nuclear physics and hypernuclear physics.

What is interesting in unstable nuclear physics? cluster N Nucleus consisting of 2 clusters one nucleon is added to the nucleus Pauli principle The valence nucleon is located outside the nucleus.

What is interesting in unstable nuclear physics? cluster N Nucleus consisting of 2 clusters N N More nucleons are added to the nucleus ・・・ ・ where are additional nucleons are located in the nucleus? ・ Do additional nucleons contribute to the dynamical change of structure of 2 clusters? ・ Do additional nucleons affect to the critical stability of the nucleus?

Hypernuclear physics Λ Λ Nucleus Hypernucleus There is no Pauli Pricliple between N and Λ. Λ particle can reach deep inside, and attract the surrounding nucleons towards the interior of the nucleus. Λ γ nucleus hypernucleus As a results, if a Λ particle is added to the nucleus, the resultant hypernucleus will become more stable against the neutron decay. Glue-like role of Λ particle

Glue-like role of Λ particle play a crucial role in binding energy mechanism, critical stability. From the view point of the ‘critical stability’, α Λ n n N N N ΛΛ N N Λ 7 He Λ 4H4H Λ 4H ΛΛ α Λ n 6 He Λ

Hypernuclear physics Λ Λ Nucleus Hypernucleus There is no Pauli Pricliple between N and Λ. Λ particle can reach deep inside, and attract the surrounding nucleons towards the interior of the nucleus. Λ γ nucleus hypernucleus As a results, if a Λ particle is added to the nucleus, the resultant hypernucleus will become more stable against the neutron decay. Glue-like role of Λ particle

Example α n + Λ 5 He:ground state is unbound α Λ n 6 He Λ ground state is bound. α nn 6 He:famous halo nucleus + Λ α Λ n n 7 He Λ

α +n 0.89 MeV P 3/2 Λ 5 He+n Λ MeV 1-1- α +n+Λ 0 MeV 5 He 6 He Λ α Λ L=0 5 He Λ 0.17 MeV α Λ n 6 He Λ How do the 3 particle locate to each other ? Is there neutron halo in 6 He hypernucleus? Λ n halo ?

密度 ρ n (r) = ∫|Ψ( 6 He)| 2 dRdr ^ r Λ α Λ n r.m.s α-Λ 2.8 fm α-n 5.0 fm Halo nucleus 6 He α-n 4.5 fm Larger than 6 He

Example: 7 He α N N 6 He : One of the lightest n-rich nuclei α NN Λ 7 He: One of the lightest n-rich hypernuclei Λ Λ No data

Phys. Rev. C53, 2075 (1996) γ α+n+n MeV B Λ =5.44 MeV (cal.) γ 1/2 + 5/2 + 7/2 + 5 He+n+n Λ α+Λ+n+n 0 MeV Halo state No data 6 He 7 He Λ E. Hiyama et al. Prompt particle decay

γ α+n+n MeV B Λ =5.44 MeV (cal.) γ 1/2 + 5/2 + 7/2 + 5 He+n+n Λ α+Λ+n+n 0 MeV Halo state No data 6 He 7 He Λ Prompt particle decay 5/2 + →1/2 + 3/2 + →1/2 + ・ Useful for the study of the excitation mechanism in n-rich hypernuclei ・ Helpful to the study of the excitation mechanism of the halo nucleus In n-rich nuclei and n-rich hypernuclei, there will be many examples such as Combination of 6 He and 7 He. I hope that γ-ray spectroscopy of n-rich hypernuclei will be performed at J-PARC. Λ

S=0 N N S=-1 Schematic illustration of the nuclear chart S=0 Most of the n-rich or p-rich nuclei near the drip line have halo- or skin-structure. Outside the drip line, there must be many nucleon-unbound states. What will happen, if we inject a Λ hyperon to those nuclei near the drip line? S=-1 We can expect that the glue-like role of Λ extends the nucleon drip line to more outside.

N N N ΛΛ N N Λ 4 He Λ 4H ΛΛ Particle-conversion such as ΛN → ΣN is very important in critical stability of few-body hypernuclear systems.

In non-strangeness nuclei NN N⊿N⊿ 250 MeV N NN NN ⊿ + 3 H, 3 He It is well known that the ground state of 3 H and 3 He are deeply Bound without ⊿ contribution.

Single Λ hypernuclei NN N⊿N⊿ 250 MeV 80 MeV Λ Σ N N N Λ 4 He Λ N N N Σ + If NNNΣ channel is neglected, then the ground state of 4 He is bound or unbound? Λ

From view point of “critical stability”, the particle-conversion such as ΛN→ΣN is very important in the binding mechanism of few-body hypernuclear systems. N N N Λ 4 He N N N Σ +

80 MeV Λ Σ N N N Λ 4 He Λ N N N Σ + ・ Y.Akaishi et al., Phys. Rev. Lett. 84, 3539(2000). ・ E. Hiyama et al., Phys. Rev. C65, (R) (2001). ・ H. Nemura et al., Phys. Rev. Lett. 89, (2002). ・ A. Nogga et al., Phys. Rev. Lett. 88, (2002).

Ψ JM (A=4)=ΣΦ c (r c,R c,ρ c ) N=1 8

4 He, 4 H Λ Λ V NN : AV8 potential V YN : Nijmegen soft-core ’97f potential

P Σ =2.21% P Σ =1.12 % N N N Λ 4 He Λ N N N Σ +

N N N Λ Λ N N N Σ + Therefore, by solving the coupled 4-body problem of A=4 hypernuclei, we found that the Σ-channel components play an essential role in the binding mechanism of the A=4 hypernuclei.

NN N⊿N⊿ 250 MeV 80 MeV Λ Σ ΞN ΛΛ 28 MeV S=-2 nuclei ΛΛ-ΞN particle conversion must be more important.

(1) Observation of 6 He Uniquely identified without ambiguity for the first time ΛΛ α+Λ+Λ 7.25 ±0.1 MeV 0+0+ α ΛΛ NAGARA Event 2 epoch-making experimental data on double Λ hypernuclei At KEK-E373 and BNL-E906. KEK-E373

[2] Observation of 4 H ΛΛ n p Λ Λ 4H4H They observed the sequential weak decay from 4 H. However, they could not determine the binding energy of 4 H. BNL-E906 ΛΛ

n p Λ Λ 4H4H The important issue: Does the YY interaction which designed to reproduce the binding energy of 6 He make 4 H bound? And how does the effect of ΛΛ ー ΞN coupling play important role in the binding energy of 6 He and 4 H? ΛΛ

1)I.N. Filikhin and A. Gal, Phys. Rev. Lett. 89, (2002) 2)H. Nemura, Y. Akaishi et al., Phys. Rev. C67, (2002) n p Λ Λ V ΛΛ α Λ Λ NOT BOUND ! 4H4H ΛΛ 6 He ΛΛ NAGARA event α+Λ+Λ 7.25±0.1 MeV 0+0+

Did not include ΛΛ-ΞN coupling ΛΛ-ΞN coupling => ・ significant in 4 H ΛΛ np ΛΛ 4H4H ・ Not so important in 6 He ΛΛ α ΛΛ 6 He ΛΛ

S 1/2 P 3/2 6 He ΛΛ nnpp ΛΛ Ξ０Ξ０ n Forbidden The effect of ΛΛ-ΞN coupling is small in 6 He and the p-shell double Λ hypernuclei ・ I.R. Afnan and B.F. Gibson, Phys. Rev. C67, (2003). ・ Khin Swe Myint, S. Shinmura and Y. Akaishi, nucl-th/ ・ T. Yamada and C. Nakamoto, Phys. Rev.C62, (2000). ΛΛ V ΛΛ ー ΞN

S 1/2 np ΛΛ Ξ０Ξ０ n 4H4H ΛΛ P 3/2 allowed (Ξ- p) There is NO Pauli blocking and the ΛΛ ー ΞN effect can be large.

np Λ Λ N N N Ξ + 4H4H ΛΛ One of the most numerically difficult 4-body problem E. Hiyama Dr. Nemura n n ΛΣ nn Σ Σ

E(MeV) Exp. (KEK-E373) CAL. 5 He+Λ Λ α+Λ+Λ 6 He ΛΛ with Pauli blocking E(MeV) n+p+Λ+Λ 3 H+Λ Λ No Exp. unbound NNΛΛ channel only NNΛΛ + NNNΞ P Ξ =1.6% 0.1MeV P Ξ =3.2% 4 H with no Pauli blocking ΛΛ α 0MeV

np Λ Λ N N N Ξ + 4H4H ΛΛ From this fact, we found that ΛΛ-ΞN coupling is very important in “critical stability” of this 4-body system. I hope that search-experiment of this system will be done at J-PARC in the future.

Conclusion In the terms of my single Λ and double Λ hypernuclear studies, I shall discuss the status of the recent progress in hypernuclear physics. I hope that the hypernuclear experiment at J-PARC will be performed. J-PARC facility is the key facility to develop the hypernuclar physics.

At the end of next year (2008), first beam at J-PARC will be run. And they are planning to perform the experiment about hypernuclei in So, it is expected that all experimentalists might be so busy. If man-power of such experiments is not enough, I am ready for joining those experiments.

In 2002, KEK-E509 I had 7 shifts for this experiments. Film badge

12 / 2008 I shall be happy if I could join the future experiments at the J-PARC facility with this new film badge. New film badge

Thank you!