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

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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

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 energy spectra of new double Λ hypernuclei

④

ΛΛ

Spectroscopic experiments

Emulsion experiment (KEK-E373)

by Nakazawa and his collaborators

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

Our few-body caluclational method

Gaussian Expansion Method (GEM) , since 1987

,

・A variational method using Gaussian basis functions

・Take all the sets of Jacobi coordinates

Developed by Kyushu Univ. Group,

Kamimura and his collaborators.

Review article :

E. Hiyama, M. Kamimura and Y. Kino,

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

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

Exsotic atoms / molecules ,

3- and 4-nucleon systems,

multi-cluster structure of light nuclei,

Light hypernuclei,

3-quark systems,

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.

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

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.

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

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

Λ

Λ

Λ

Λ

Λ

n

n

n

α

α

α

α

α

α

6He (1-)

9Be (1/2+)

5He (1/2-)

Λ

Λ

Λ

CAL : -3.12 MeV

EXP : -3.12 MeV

CAL : -3.29 MeV

EXP : -3.29 MeV

CAL : -6.64 MeV

EXP : -6.62 MeV

(The energy is measured from the full-breakup threshold

of each subsystem)

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

Phys. Rev. Lett.

ΛΛ

No Pauli principle

Between N and Λ

Λ particle can reach

deep inside, and

attract the

surrounding nucleons

towards the interior

of the nucleus.

Λ

Hypernucleus

Λ particle plays a ‘glue like role’ to produce a dynamical

contraction 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 calculation

E. Hiyama et al. Phys. Rev. C59 (1999), 2351.

KEK-E419

Λ

n

Λ

n

α

α

7Li

Rα-np

Λ

p

p

6Li

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

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 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 confirmationof Hida event, we expect to have more precise data at

J-PARC.

ΛΛ

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

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