Y. Kanada-En’yo (YITP, Kyoto Univ.)M. Kimura (Tsukuba)Y. Taniguchi (Kyoto Univ.)

Cluster aspect of light unstable nucleiCluster aspect of light unstable nuclei

1. Introduction

new-typeclustering

coexistence of　　 cluster & 　　　 mean-field

Cluster physics

1930’sBethe et al.

Weakly Interacting

-particles

Meyer & Jensen, shell structure, mean-field

1949

1960’s 1970-80’sCluster & scattering

microscopic cluster models

(RGM,OCM,GCM)

Very light nuclei (A<8)

multi

non-(N, t, 12C, 16O) clusters

p-shell, sd-shellnuclei

molecular resonances16O+16O etc.

1990’s-Clustering in

unstable nuclei

Unstable nuclei

sd, pf-shellinnovative models (GCM,MO.SVM,AMD,..)

n

2H1H

3He 4He3H

6Li 7Li

9Be

6He

8Li8He

8Be7Be 10Be9Li

11Be12Be11Li

10B 11B 12B 13B 14B 15B14Be

9B8B

12C 13C 14C 15C 16C 17C 18C 19C 20C17B 19B

11C10C9C8C

14N 15N 16N 17N 18N 19N 20N 21N13N12N11N

12O 13O 14O 15O 16O 17O 18O 19O 20O 21O 22O

core

core

neutron halo

neutron skin

Decoupling of Proton and neutrons

α α

α α

molecular

α

α

α

dilute gas

α

α α

0+2 in 12C

6He,11Li,11Be

8He,CBe isotopes

10C, 16C

3-2 in 14C

triangle

excited states

He

Li

Be

B

C

H

structure in light nuclei

vanishing of magic number

sd-shellExploring concept of cluster:

Spatial correlation of multi nucleons

Typical clustering in stable nuclei

α α8Be

ααα

12C

16O α20Ne

12C α16O*

Conventional cluster structure

Weak coupling picture: Cluters are formed by tightly bound nucleons.

Weakly coupled inter-cluster motion is considered.

Exploring concept of clustering (1)

halo nuclei: 　 6He, 11LiA.Tosaka et al.,S. Aoyama et al.

correlation

K.Varga et al.,

2n

di-neutron core-n

V-type T-type

Ne, O isotopes

6He+6He in 12Be

2-coreneutron orbit

α α

α α

Seya, Von Oerzten, Descouvemont et al.,Itagaki et al., K-E et al.M. Ito et al.

16O

Molecular structures

neutron-rich Be isotopesEsbensen et al.,Hagino et al.Descouvemont et al.

Valence neutrons play important roles Yoshida et al.,

Kimura et al.Furutachi et al.

-cluster gas

Tohsaki et al., Yamada et al.,Funaki et al. Wakasa et al.,

12C(02 )+

α

α

α

Dilute 3Dilute 3gas gas

16O*

Exploring concept of clustering (2)

Itagaki et al.,Von Oertzen et al.

α

α

α

14C*(3-2)

cluster crystalization

-condensation

BEC-BCS

dineutron-cond.

αα α

Price et al.

12,14,15,16C* linear chain

triangle

Roepche et al.

Nuclear matter

matsuo et al.

Exploring concept of clustering (3)

Superdeformation & cluster

16O 16O 32S+ SD

Cluster excitation

Molecular states.16O 16O

Coexistence of cluster & mean-field

Heavier nuclear region

α

α

α

Z=N nuclei: 32S, 40Ca

nucleon correlation at surface

Itagaki et al.

Kimura et al., taniguchi et al.

Contribution of cluster aspects

Physics:

Halo nuclei,

Breaking of magicity

Molecular, deformation,

new cluster states

Methods:

less assumption, ab-initio calc. ,

tensor force, effective nuclear force

resonances & continuum

Contribution to recent developments

Cluster is one of the essential features in nuclear many-body system.

Systematic study focusing on cluster phenomena.Question: what is the mechanism of appearance of clusters ?

2-1. Molecular states: 12Be ,13B

2-2. Cluster gas-like states: 12C, 11B(11C), 8He

2. Topics

2-1. Molecular states: 12Be ,13B

2-1. Molecular states in 12Be,13B

Breaking of magicity (N=8) in 12Be

0+2 (2.24MeV)

+10 intruder state

0

2

Formation of 2+molecular orbitals

--orbitalorbital

±

Deformed ground statewith d-wave componentsExperiments: Iwasaki et al., Navin et al., Pain et all.

20

12Be

+ - +αα2.24 MeV

αα

Bond role

Breaking of N=8 magicityY.Kanada-En’yo et al., PRC 68, 014319 (2003)

Exp.

AMD

positive parity states with normal spins

(a)(b)

(c)

++

Success of AMD for 12Be

Formation of 2+molecular orbitals

VAP calculation with AMD method

0+2 (2.24MeV)

+10 intruder

0

2

α α

12Be

αα

2

0

12Be 13Bone proton

0

2

3

MO states ?

Search for MO states of 13B

α α

Experimental report 4He(12Be,13B)

MeV 5xE12/1

αα

proton intruder configuration

S. Ota et al. jps meetring, Mar 2007

Excited states of 13B studied with AMD

VAP calc. of AMDMV1(m=0.65)+G3RS(ls=3000)

0

5

10

15

20

0 20 40

J (J +1)

Excitation

　energy　(MeV)

0

5

10

15

20

0 20 40

J (J +1)

Excitation

　energy　(MeV)

13B(-) 13B(+)

22/3K 12/1K

0

2

3

3

2

12/1

2)()(3 sdsd

+ - +αα

13B(1/2+1)

Present calc.

MeV 8xE73.0

Hyper deformation ?

protonneutron4He(12Be,13B) ExperimentsBy Ota et al.

MeV 5xE12/1

Proton intruder statein neutron-rich nuclei

2

0

0

2

12Be 13B

one proton

22/3K

12/1K

deformed bands with MO structure in 13B

Deformed bands in Ex < 10 MeVMO structure in 13B

Proton intruder state

2-2. Cluster gas-like states: 12C*, 11B*(11C*), 8He*

01+

02+

03, 4+

10.3 MeV

7.65 MeV

3+p3/2closed

+ααα

α α α

12C

8Be+

p3/2

chain ?

α

α

α

Dilute clusterDilute clustergas gas

A.Tohsaki et al., (2001)Funaki et al.(2003)

11C, 11B

13C ,14C

α

α

α

α

16O

αα

αα 16O(0+

5) ?

Bosonic behaviorBosonic behavior

2-2. Cluster gas-like states

Tohsaki et al., Yamada et al.,Funaki et al. Wakasa et al.,

K-E. , Kawabata et

Itagaki, K-E. , Kawabata et

t

11B(11C)

7Li+

2+t

3/21

-

3/22

-

3/23

-3/24

-

8.5

10.3

ααt

α

α

Dilute 2Dilute 2+t+t

p3/2

AMD by Y.K-E.

Mysterious 3/2-3 state:

Weak beta & M1 transitions

Strong E0 transition

01+

02+

7.65 MeV

3+p3/2closed

+ααα

12C

8Be+

p3/2

α

α

α

Dilute 3Dilute 3gas gas

three-center cluster states in three-center cluster states in 1111B and B and 1111CCA candidate in 1111B(B(1111CC)

Kawabata et al. by (d,d’)

Y. K-E. PRC(2006)

t

-condensation

Tohsaki et al., Yamada et al.,Funaki et al.

12C(02 )+

α

α

α

Dilute 3Dilute 3gas gas

16O*

di-neutron in dilute neutron matter

di-neutrons in halo nuclei (6He, 11Li)

V-typeT-type

Aoyama, et al.5, 7H ?

Roepche et al.(1998)

Dineutron gas ?

Matsuo et al.(2006)

T-type

Two dineutrons in 8He

12C

Dilute clusterDilute clustergas gas

8He

8He(01+)

p3/2

ExcitedStates ?

12C(01+)

12C(02+)

V-type

+

6He(01+)

+ααα p3/2

=

=

Possible dineutron gas-like state of 8He

01+

p3/2

8He(02+)

8He AMD+GCM calc. suggestsdineutron gas-like state

AMD+GCMwith effective N-N interactions(MV1, Volkov)

6He+2n

4He+4n

r.m.s.n.r.=3.1 fm

r.m.s.n.r.=2.6 fmMV1 MV1Volkov No.2m=0.58b=h=0

m=0.62b=h=0

m=0.56b=h=0.15

Dineutron structure: analogy to 12C(0Dineutron structure: analogy to 12C(0++22))

(C)

8He(02+)

g.s.

8He(0+2)

nn 2-2-He)0(He 48

)0()0( LL

)(rry

S-fac=0.47

SU(3)-limit

r

r (fm)

12C(02+)g.s.

)0()0(Be8 L

)0(Be)0(C 812

12C(0+2)

)(rry SU(3)-limit

r

r (fm)

Dineutron component at large distance

)0(He6

1. Molecular states: 13B*

2. Dineutron gas-like state: 8He*

AMD(VAP)

AMD(GCM)

3. Summary

Variation in the energy-isospin plane

Unstable

Isospin symmetry

Ex

cita

tio

n e

ne

rgy

Stable

α

α

α

αcondensation

12C

p3/2

p3/2

8He

α

α

DineutronCondensation ?

Breaking of N=8 magicity

α α

MO

α αintruder

12Be13B

αα

Systematic study covering a wide region of the energy-isospin plane is essential to understand nuclear many-body systems