1. Cluster aspect of light unstable nuclei
Y. Kanada-En’yo (YITP, Kyoto Univ.)
M. Kimura (Tsukuba)
Y. Taniguchi (Kyoto Univ.)
Today I will report our activities on nuclear structure studies.

2. 1. Introduction

3. Cluster physics 1949 1930’s 1960’s 1970-80’s 1990’s- a-particles
Meyer & Jensen, shell structure, mean-field
1949
coexistence of
　　cluster &　
　　mean-field
innovative models (GCM,MO.SVM,AMD,..)
sd, pf-shell
Unstable nuclei
Let me briefly review a history of cluster physics.
In old days, a nucleus is interpreted as composite of alpha particles. Later, shell model picture was proposed by Meyer and Jensen in 1949.
Needless to say, mean-field aspect is actually an essential feature, and mean-field approaches have been major current in nuclear structure studies.
In spite of the importance of mean-field, also cluster pictures have been indispensable to understand features of light nuclei, not only scattering problems
but also properties of nuclear structure in light nuclear region. In these decades, from 1960’s to 1980’s
microscopic cluster models developed and were applied to light nuclei.
Recently, physics of unstable nuclei induced the remarkable progress of cluster physics
involving the development of innovative theoretical models.
In exotic phenomena of unstable nuclei, various new-types of cluster structure have been discovered.
Following these development in unstable nuclei, extension of the conventional cluster picture was required.
What is important is that cluster is an essential nature as well as mean-field aspect, and the coexistence of
These two natures provide a variety of structure of nuclear many-body systems.
1930’s
1960’s ’s
1990’s-
Bethe et al.
Weakly
Interacting
a-particles
Cluster & scattering
microscopic cluster models
(RGM,OCM,GCM)
multi a
non-a(N, t, 12C, 16O) clusters
Clustering in
unstable nuclei
new-type
clustering
p-shell, sd-shell
nuclei
Very light nuclei
(A<8)
molecular resonances
16O+16O etc.

4. structure in light nuclei
Exotic
Exploring concept of cluster:
Spatial correlation of multi nucleons
triangle α
sd-shell α α
3-2 in 14C α n 2H 1H
3He
4He 3H
6Li
7Li
9Be
6He
8Li
8He
8Be
7Be
10Be
9Li
11Be
12Be
11Li
10B
11B
12B
13B
14B
15B
14Be 9B 8B
12C
13C
14C
15C
16C
17C
18C
19C
20C
17B
19B
11C
10C 9C 8C
14N
15N
16N
17N
18N
19N
20N
21N
13N
12N
11N
12O
13O
14O
15O
16O
17O
18O
19O
20O
21O
22O α α
dilute gas C
0+2 in 12C
In the recent progress of unstable nuclear physics, various exotic structure has been discovered.
Neutron halo, skin, and molecular states, and so on. Many of these phenomena in light unstable nuclei are related to
dynamics of valence nuetrons and a tight core, or in case of Be, two cluster cores.
Recently, also in stable nuclei, new types of cluster structure has been suggested, and found in excited states.
For example, dilute gas-like 3-alpha state in the excited state of 12C, and triangle shape with 3 alpha core in
14C.Discovery of these exotic phenomena indicate that there still remain unknown states and unknown properties
even in stable nuclei as well as unstable nuclei. B
Decoupling of
Proton and neutrons Be
10C, 16C Li He α α H
excited states
core α α
core
neutron skin
Be isotopes
8He,C
molecular
neutron halo
vanishing of
magic number
6He,11Li,11Be

5. Conventional cluster structure
Weak coupling picture:
Cluters are formed by tightly bound nucleons.
Weakly coupled inter-cluster motion is considered.
The conventional cluster structure is based on weak coupling picture. Clusters are formed by tightly bound nucleons, and
weak coupling inter-cluster motion is considered.
Typical clustering in stable nuclei α
16O α α α
12C α α α
8Be
12C
20Ne
16O*

6. Exploring concept of clustering (1)
A.Tosaka et al.,
S. Aoyama et al.
halo nuclei:　6He, 11Li
Molecular structures
K.Varga et al.,
Esbensen et al.,
Hagino et al.
Descouvemont et al.
neutron-rich Be isotopes
T-type
6He+6He
in 12Be
V-type α α 2n
Now, the concept of cluster is exploring. The keys are decoupling of scales and spatial multi-nucleon correlation. In the halo nuclei, where the
Loosely bound valence neutron behavior is important, the di-neutron correlation is an attractive feature.
Of cource, the di-neutron correlation is regarded as a kind of cluster, and this physics may lead to BEC-BCS phenomena in neutron matter.
In case of Be isotopes, two alpha cores are formed. In the low-lying states, the surrounding neutrons are moving in the mean-field of two alpha.
It means the coexistence of alpha cluster cores and mean-field-like valence neutrons. These phenomena arise from the decoupling of scales.
2a-core
neutron orbit α α
core-n
di-neutron
Seya, Von Oerzten,
Descouvemont et al.,
Itagaki et al.,
K-E et al.
M. Ito et al.
correlation
Ne, O isotopes
16O a
Valence neutrons play important roles
Yoshida et al.,
Kimura et al.
Furutachi et al.

7. Exploring concept of clustering (2)
a-cluster gas
cluster crystalization
Dilute 3a gas α
12C(02 ) +
14C*(3-2) α
triangle
16O*
Tohsaki et al., Yamada et al.,
Funaki et al. Wakasa et al.,
Itagaki et al.,
Von Oertzen et al.
Price et al.
Recently, further novel cluster structure has been proposed. A gas of weakly interaction alpha particle and cluster crystalization
in the excited states of 12C by Tohsaki et al. and Funaki et al. and 14C by Itagaki et al, respectively.
Then, one can usually speculate a alpha cluster gas or cluster crystalization in phases of nuclear matter. α
Nuclear matter
12,14,15,16C*
linear chain
a-condensation
dineutron-cond.
Roepche et al.
BEC-BCS
matsuo et al.

8. Exploring concept of clustering (3)
Heavier nuclear region α
Coexistence of
cluster & mean-field
Itagaki et al.
nucleon correlation at surface
Superdeformation & cluster
In heavier mass number regions, although the mean-field nature becomes more and more important in general, we will still find further rich cluster phenomena.
For example, it is challenging to study possible existence of di-neutron correlations or alpha correlations at the surface region.
In sd-shell nuclei, molecular states are built upon the low-lying deformed states because of the excitation of inter-cluster coordinates.
In case of Ne isotopes, the ground state of 20Ne is described by the mixing of deformed Nilsson-like structure and cluster structure.
When we add neutrons, it is suggested that deformed state and cluster state appear independently due to the additional neutrons.
Molecular states.
16O
16O
Cluster excitation
16O
16O
32S + SD
Z=N nuclei: 32S, 40Ca
Kimura et al., taniguchi et al.

9. Contribution of cluster aspects
Cluster is one of the essential features in nuclear many-body system.
Contribution to recent developments
Physics:
Halo nuclei,
Breaking of magicity
Molecular, deformation,
new cluster states
Methods:
less assumption, ab-initio calc. ,
tensor force, effective nuclear force
resonances & continuum
Systematic study focusing on cluster phenomena.
Question: what is the mechanism of appearance of clusters ?

10. 2. Topics 2-1. Molecular states: 12Be ,13B
2-2. Cluster gas-like states: 12C, 11B(11C), 8He

11. 2-1. Molecular states: 12Be ,13B

12. 2-1. Molecular states in 12Be,13B
Breaking of magicity (N=8) in 12Be
Formation of 2a+molecular orbitals + 2
(2.24MeV) + 1
intruder state + - α
2.24 MeV
s-orbital s2
12Be
Deformed ground state
with d-wave components α α
Experiments: Iwasaki et al.,
Navin et al., Pain et all.
Bond role

13. 12Be + + Success of AMD for 12Be VAP calculation with AMD method Exp.
positive parity states with normal spins
Exp. + 2
(2.24MeV) α
(c) + +
AMD + 1
(b)
(a)
intruder α α
Breaking of N=8 magicity
Y.Kanada-En’yo et al., PRC 68, (2003)
Formation of 2a+molecular orbitals

14. Search for MO states of 13B
Experimental report
4He(12Be,13Bg)
S. Ota et al. jps meetring, Mar 2007
proton intruder configuration α
MO states ? α
12Be
13B
one proton

15. Excited states of 13B studied with AMD
VAP calc. of AMD
MV1(m=0.65)+G3RS(ls=3000)
13B(-)
13B(+)

16. - + + 13B(1/2+1) Present calc. Hyper deformation ?
Proton intruder state
in neutron-rich nuclei
neutron
proton
4He(12Be,13Bg) Experiments
By Ota et al. + - + α α

17. deformed bands with MO structure in 13B
Deformed bands in Ex < 10 MeV
MO structure in 13B
Proton intruder state
one proton
12Be
13B

18. 2-2. Cluster gas-like states:
12C*, 11B*(11C*), 8He*

19. 2-2. Cluster gas-like states
Tohsaki et al., Yamada et al.,
Funaki et al. Wakasa et al.,
12C
16O
A.Tohsaki et al., (2001)
Funaki et al.(2003) α α
chain ?
16O(0+5) ? α α
Dilute cluster gas α
Bosonic behavior
03, 4 +
11C, 11B
K-E. , Kawabata et α
10.3 MeV α 02 +
7.65 MeV α t
8Be+a
13C ,14C
Itagaki, K-E. ,
Kawabata et 01 + α α +
p3/2 α α α α
3a+p3/2closed

20. - - - - 11B(11C) 12C A candidate in 11B(11C)
three-center cluster states in 11B and 11C
Y. K-E. PRC(2006)
11B(11C)
12C
AMD by Y.K-E.
Mysterious 3/2-3 state:
Weak beta & M1 transitions
Dilute 3a gas
Dilute 2a+t α
3/24 -
2a+t α
We have studied the structure of 11B, and proposed that the third 3/2- state at 8.5 MeV has
a dilute state with a 2alpha+t cluster structure.
We succeeded to reproduce the properties of this state, such as weak M1 transitions and beta decays.
Moreover, we found that it has a remarkable strength of iso-scalar monopole transitions into the ground state.
It is in good agreement with the recent observation of the strong monopole transitions in the inelastic scattering (d,d’)
What is interesting is that the features of this cluster state are very similar to those of the second 0+ state of 12C. Namely,
this state is a dilute cluster state of 2alpha+t.
3/23 -
10.3 02 +
7Li+a α t
7.65 MeV
8.5
3/22 -
8Be+a t α α
Strong
E0 transition
3/21 -
Kawabata et al. by (d,d’) 01 + α +
p3/2
p3/2 α α
3a+p3/2closed

21. Dineutron gas ? + 12C(02 ) 16O* a-condensation
di-neutron in dilute neutron matter
Roepche et al.(1998)
Matsuo et al.(2006)
The next question is where we can discover such a variation of phase in low-density. Of course, one can usually speculate in
stars such as neutron stars. But, it is very important to search for some signals or precursors in the phenomena of nuclei.
One of the success to link the BEC phase of the nuclear matter to the practical phenomena in nuclei is the idea of
3 alpha BEC in the excited state of 12C proposed by Tohsaki et al. They suggested alpha condensate in heavier nuclei
such as 16O and 20Ne.
Let me turn to di-neutron condensate of di-neutron correlation in low density matter.
As you know, di-neutron correlation has been discussed in halo nuclei in three-body models, where
di-neutron correlation is important in the region far from the core. Recently, very neutron-rich systems 10He and 7H
have observed. Then, possible multi di-neutron correlation is a hot subject.
Dilute 3a gas
di-neutrons in halo nuclei (6He, 11Li)
12C(02 ) + α
T-type
16O*
V-type
Tohsaki et al., Yamada et al.,
Funaki et al.
5, 7H ?
Aoyama, et al.

22. a a a a 12C 8He Two dineutrons in 8He 6He(01+) = + = α + α α
Dilute cluster gas
Excited
States ?
12C(02+)
6He(01+) = a a + a
12C(01+)
8He(01+) a
V-type
T-type = α +
p3/2
p3/2 α α

23. Possible dineutron gas-like state of 8He
AMD+GCM calc. suggests
dineutron gas-like state
8He
8He(02+)
r.m.s.n.r.=3.1 fm
4He+4n
6He+2n
01+
p3/2
Volkov No.2
MV1
MV1
r.m.s.n.r.=2.6 fm
m=0.58
b=h=0
m=0.62
b=h=0
m=0.56
b=h=0.15
AMD+GCM
with effective N-N interactions(MV1, Volkov)

24. Dineutron structure: analogy to 12C(0+2)
8He(0+2)
12C(0+2)
SU(3)-limit
Dineutron component
at large distance a a a a
SU(3)-limit
(C)
12C(02+)
g.s.
g.s.
8He(02+)
S-fac=0.47
r (fm)
r (fm)

25. 3. Summary 1. Molecular states: 13B* AMD(VAP)
2. Dineutron gas-like state: 8He*
AMD(VAP)
AMD(GCM)

26. Variation in the energy-isospin plane
Systematic study covering a wide region of the
energy-isospin plane is essential to understand
nuclear many-body systems α
αcondensation
12C
p3/2
8He
Dineutron
Condensation ?
Breaking of
N=8 magicity MO
intruder
12Be
13B
Excitation energy
Stable
Unstable
Isospin symmetry