Five-body Cluster Structure of the double Λ hypernucleus 11Be

Emiko Hiyama (RIKEN)

ΛΛ

・ Four-body structure of 　 7He, 7Li, 8Li, 9Li, 9Be, 10BeΛΛ

・ Five-body structure of 　 11Be ΛΛ

ΛΛ ΛΛ ΛΛ ΛΛ ΛΛ

α

ｎΛ Λ

α

pΛ Λ

α

dΛ Λ

α

tΛ Λ

α

3HeΛ Λ

αα

Λ Λn

Outline of my talk

・ Introduction

Introduction

Λ+ ・・・・

It is conjectured that extreme limit, which includes many Λs in nuclear matter, is the core of a neutron star.

In this meaning, the sector of S=-2 nuclei ,

double Λ hypernuclei and Ξ hypernuclei 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.

What is the structure when one or more Λs are added to a nucleus?

nucleus

ΛΛΛΛ

+ + +

Uniquely 　 identified 　 without 　 ambiguity

for　 the first time

α+Λ+Λ

0+

　　　 In 2001, the epoch-making data

　　 has been reported by the 　　　 KEK-E373 experiment.

Observation of 　 6HeΛΛ

α

ΛΛ

６．９ 1±0.16 MeV

useSuggest reducing the strength of

spin-independent force by half

compare between the theoretical resultand the experimental data of the biding energy of 6He

①

②

③

prediction of energy spectra of new double Λ hypernuclei

Strategy of how to determine YY interaction from the study of light hypernuclear structure

YY interaction Nijmegen model D　

Λ Λ

αAccurate structure calculation

Spectroscopic experiments Emulsion experiment (KEK-E373) by Nakazawa and his collaborators

6HeΛΛ

④ ΛΛ

comparison

My theoretical contributionusing few-body calculation

・ E07 “Systematic Study of double strangness systems at J-PARC” by Nakazawa and his collaborators

Approved proposal at J-PARC

Emulsion experimentTheoretical calculation input: ΛΛ interaction to reproduce the observed binding energy of 　 6HeΛΛ

the identification of the state

It is difficult to determine (1) spin-parity

(2) whether the observed state is the ground state or an excited state

KEK-E373 experiment analysis is still in progress.

・ A variational method using Gaussian basis functions

・ Take all the sets of Jacobi coordinates

High-precision calculations of various 3- and 4-body systems:

Our few-body caluclational method

Gaussian Expansion Method (GEM) , since 1987

Review article : E. Hiyama, M. Kamimura and Y. Kino,Prog. Part. Nucl. Phys. 51 (2003), 223.

Developed by Kyushu Univ. Group, Kamimura and his collaborators.

,

Light hypernuclei,

3-quark systems,

Exsotic atoms / molecules ,

3- and 4-nucleon systems,

multi-cluster structure of light nuclei,

comparison

My theoretical contributionusing few-body calculation

・ E07 “Systematic Study of double strangness systems at J-PARC” by Nakazawa and his collaborators

Approved proposal at J-PARC

Emulsion experimentTheoretical calculation input: ΛΛ interaction to reproduce the observed binding energy of 　 6HeΛΛ

the identification of the state

It is difficult to determine (1) spin-parity

(2) whether the observed state is the ground state or an excited state

KEK-E373 experiment analysis is still in progress.

Successful example to determine spin-parity ofdouble Λ hypernucleus --- Demachi-Yanagi event for 10Be

Demachi-Yanagi event

8Be+Λ+Λ

ground state ?excited state ?

Observation of 　 10Be --- KEK-E373 experiment

ΛΛ

ΛΛ

αα

Λ Λ

10BeΛΛ

10BeΛΛ

11.90±0.13 MeV

Successful interpretation of spin-parity of

E. Hiyama, M. Kamimura,T.Motoba, T. Yamada and Y. YamamotoPhys. Rev. 66 (2002) , 024007

Demachi-Yanagi event

αα

Λ Λ

11.9

0

11.8

3

-14.70

α+Λ+Λ

6.91 ±0.16 MeV

α

ΛΛ

α x

Λ Λ x = n p d t 3He= = = = =

7He 7Li 8LiΛΛ ΛΛ ΛΛ

8Li 9BeΛΛ ΛΛ

Hoping to observe new 　 double Λ hypernuclei in future

experiments, I predicted level structures of

these 　 double 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)

Spectroscopy of ΛΛ-hypernuclei E. Hiyama, M. Kamimura,T.Motoba, T. Yamada and Y. YamamotoPhys. Rev. 66 (2002) , 024007

A 11ΛΛ hypernuclei >

I have been looking forward to having

new data in this mass-number region.

new data

(2009)

αα

Λ Λ

n

11BeΛΛ

BΛΛ= 20.49±1.15 MeV

Important issue: Is the Hida event the observation of a ground stateor an excited state?

Observation of 　 Hida eve

nt

αα

Λ Λ

n n

12BeΛΛ

BΛΛ= 22.06±1.15 MeV

KEK-E373 experiment

It is neccesary to perform 5-body calculation of this system.Why 5-body?

α

Λ Λ

n

11BeΛΛ

α

Core nucleus, 9Be is well described as

α+α+ n three-cluster model.

Then, 11Be is considered to be suited for

studying with α+α+ n +Λ+Λ 5-body model.

ΛΛ

Difficult 5-body calculation:

1) 3 kinds of particles (α, Λ, n)

2) 5 different kinds of interactionsΛ Λ

Λ n

αΛ

αn

αα

3) Pauli principle between α and α,

and between α and n

But, I have succeeded in performing this calculation.

α

Λ Λ

n

11BeΛΛ

α

rules out the Pauli-forbidden states from the 5-body wave unction.

The Pauli-forbidden states (f ) are the 0S, 1S and 0D states of the α α

relative motion, and the 0S states of the α n relative motion.

This method for the Pauli principle is often employed in the study of light

nuclei using microscopic cluster models.

(γ ～ 10000 MeV is sufficient.)

5-body calculation of 11BeΛΛ

α

Λ Λ

n

11BeΛΛ

α

5-body calculation of 11BeΛΛ

specifies many sets of Jacobi coordinates

specifies 5-body basis functions of each Jacobi-coordinate set

expansion coefficient

A variational method:

Gaussian Expansion Method (GEM)

(review paper) E. H., Y. Kino and M. Kamimura,

Prog. Part. Nucl. Phys., 51 (2003) 223.

Two αparticles are symmetrized.

Two Λparticles are antisymmetrized.

Some of important Jacobi corrdinates of the α+ α+ n + Λ+ Λ system.

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:

CAL : +0.80 MeV

EXP : +0.80 MeV

5He (3/2-)

ΛΛ

8Be (0+)

CAL : +0.09 MeV

EXP : +0.09 MeV

9Be (3/2-)

CAL : -1.57 MeV

EXP : -1.57 MeV

αα

Λ Λn

αα

Λ Λn

αα

Λ Λ

n

αα

Λ Λn

CAL : -3.12 MeV

EXP : -3.12 MeV

5He (1/2-)6He (1-)Λ

CAL : -3.29 MeV

EXP : -3.29 MeV

αα

Λ Λn

Λ

αα

Λ Λn

9Be (1/2+)Λ

CAL : -6.64 MeV

EXP : -6.62 MeV

(The energy is measured from the full-breakup threshold

of each subsystem)

ΛΛαα

Λ Λ

n

10Be (0+, 2+ )Λ Λ

CAL (2+): -10.96 MeV

EXP (2+): -10.98 MeV

CAL (0+): -14.74 MeV

EXP (0+): -14.69 MeV

ΛΛαα

Λ Λ

n

6He (0+ )Λ Λ

CAL (0+): -6.93 MeV

EXP (0+): -6.93 MeV

ΛΛαα

Λ

Λ

n

10Be (1-)

CAL : -10.64 MeV

EXP : -10.64 MeV

Λ

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

adjusted predicted

Convergence of the ground-state energy of the α+α+ n +Λ+Λ 5-body system ( ) 11Be

ΛΛ

J=3/2-

To be published inPhys. Rev. Lett.

What is structure of 11Be 　 ?ΛΛ

Λ

Hypernucleus

Λ particle can reachdeep inside, and attract the surrounding nucleonstowards the interiorof the nucleus.

No Pauli principleBetween N and Λ

Λ particle plays a ‘glue like role’ to produce a dynamicalcontraction of the core nucleus.

By reduction of B(E2) due to the addition of

Λ particle to the core nucleus, we can find the

contraction of nucleus by glue-like role of Λ particle.

Theoretical calculationE. Hiyama et al. Phys. Rev. C59 (1999), 2351.KEK-E419

α

n

pRα-np

6Li

α

n

p

Λ

Λ

7LiΛ

Rα-np(6Li) > Rα-np(7Li)Reduced by about 20 %

B(E2: 3+→1+:6Li)=9.3 ±0.5e2fm4 →B(E2:5/2+→1/2+:7Li)= 3.6 ±2.1 e2fm4

20% reduction

8% reduction

α

n

αα

Λ

Λ

n

α α

Λ Λ

n

α

9Be 10BeΛ

11BeΛΛ

Λ

α α

11BeΛΛ

ΛΛ

n

As mentioned before, Hida event has another possibility, namely, observation of 12Be.ΛΛ

αα

Λ Λ

n n12BeΛΛ

BΛΛ= 22.06±1.15 MeV

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 methodfor 6-body problem.Fortunately, we will have much more powerful supercomputer (HITACHI SR16000) at KEK in June in 2011. This supercomputer enable me to make six-body calculation.

For the confirmation 　 of Hida event, we expect to have more precise data at J-PARC.

ΛΛ

Spectroscopy of ΛΛ-hypernuclei

11Be ,ΛΛ

At J-PARC

A=12, 13, ……

For the study of this mass region,

we need to perform more of5-body cluster-model calculation.

Therefore, we intend to calculate the following 5-body systems.

αα

Λ Λ

α

14CΛΛ

To study 5-body structure of these hypernuclei is interesting and important as few-body problem.

αα

Λ Λp

11BΛΛ

αα

Λ Λd

12BΛΛ

αα

Λ Λt

αα

Λ Λ3He

13BΛΛ

13CΛΛ

Multi-strangeness systemsuch as Neutron star

J-PARC

Concluding remark

GSI

JLAB

DAΦN EJ-PARC

Thank you!