nuclei Y KanadaEnyo Kyoto Univ Collaborators Y HidakaRIKEN T IchikawaYITP M KimuraHokkaido F KobayashiKyoto T Suhara Matsue Y TaniguchiTsukuba ID: 914129
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Slide1
Cluster formation and breaking, and cluster excitation in light nuclei
Y.
Kanada-En’yo
(Kyoto Univ.)
Collaborators:
Y
.
Hidaka(RIKEN),
T. Ichikawa(YITP),
M
.
Kimura(Hokkaido), F. Kobayashi(Kyoto),
T.
Suhara
(Matsue)
,
Y. Taniguchi(Tsukuba)
Slide21.Introduction
Slide3Cluster & Mean field
Single-particle motion
v.s
.
Many-body correlation
Rich phenomena
in ground and excited states
Energy/nucleon～constant
1. Independent-particle feature in self-consistent mean-field2.Strong nucleon-nucleon correlations 3.Saturation properties
Nuclear system
orbit, shell
s.p
. in mean field
rotation
deformation
1p-1h, vibration
r
elative motion
c
luster
Excitations
cluster
Slide4Cluster states in low energy
12
C
Liquid drop
6 protons
6 neutrons
0 MeV
100 MeV
Nucleon gas
Energy
10
MeV
3
a
-cluster
a
a
a
a
a
a
triangle
c
hain ?
Cluster gas
Saturation
density
a
a
a
Shell & cluster
formation(correlation)
l
ow
density
cluster
excitation
+
n
ucleon breakup
12
C(0
+
2
)
Hoyle state
Impact to nuclear
synthesis
Slide5Coexistence of cluster and MF features
Fermions in MF
12
C
developed
3
a
Cluster excitation
Shell structure
・MFCluster
Cluster formation
m
any-body correlation
3
a
12
C
12
C ground state
12
C excited states
No
fermi
surface
fermi
surface
Slide6Cluster structures
in stable and unstable nuclei
Typical
cluster structures known in
s
table nuclei
8
Be
12
C
20
Ne
a
+
a
3
a
16
O +
a
16
O*
12
C +
a
7
Li
a
+ t
a
-cluster
40
Ca
*,
28
Si*,
32
S*
36
Ar-
a
,
24
Mg-
a
,
28
Si-
a
Si-C, O-C, O-O
Molecular
orbital
Be, C, O, Ne, F
a
-cluster
excitation
14
C*
3
a
linear chain
Unstable nuclei
Heavier nuclei
a
Slide7History of cluster physics with development of theoretical framework
coexistence of
cluster &
mean-field
1930’s
Weakly
Interacting
a
-particles
shell model,
mean-field1949
1960’s
1970-80’s
microscopic cluster models
(
RGM,OCM,GCM)
cluster
&
scatteringi
n very light nuclei
(A<8
)
a
+(n,d,t,a)clusters in p-shell, sd-shell
nuclei3a,16O+a,12C+a
1990’s-
c
lusters in
unstable nuclei
cluster
formation
valence
neutrons
2
a (3a
)+Xn,16O+a+2n
Unstable nuclei
sd
,
pf
-shell
Models with no(less) cluster assumption
(
GCM,FMD,SVM,AMD,.)
New-type
cluster structures
Ab
initio calculations
GFMC, NCSM, SVM, UCOM,
EFT
2000’s-
A<10
cluster & scattering
a+(
n,d,t,a)
Slide8Models and ab initio calculations
1960’s: cluster models (RGM)
a
+
a
,
a
+(
N,d,t
)
scattering
2
a in
8Be2000’s: ab initio calculationsStructure
GFMC : 2
a formation in the 8-body system
FMD(UCOM),NCSM, EFT... clusters in A~10
Scattering GFMC:
a+N scattering
NCSM+RGM: a+(N,d,t
) scattering SVM: d+d scattering
FMD(UCOM
)+RGM
by
wiringa
et al. PRC (2000)
VMC
calc.
Slide9An approach for nuclear structure to study
cluster and mean-field aspects
Stable and unstable nuclei
Ground and excited states
2.
A theoretical
model: AMD
Slide10Model wave fn.
Effective nuclear force
phenomenological)
Energy Variation
AMD wave fn.
Variational
parameters:
Gauss centers, spin orientations
spatial
isospin
Intrinsic spins
Slater
d
et.
Gaussian
det
Gaussian wave packet
AMD method for structure study
Similar to FMD wave fn.
Slide11AMD
model space
A variety of cluster
st.
Shell
structure
Energy variation
Model space
(Z plane)
Randomly chosen
Initial states
Energy minimum
states
det
det
Energy
s
urface
Cluster and MF
formation/breaking
Slide123. Some topics of cluster phenomena
Slide13Topics of cluster phenomena
Cluster gas, chain states
in C and B isotopes
Cluster structures in Be isotopes
Slide14Topics of cluster phenomena
Cluster gas,
chain states
in C and B isotopes
Cluster structures in Be isotopes
Slide15Cluster gas states in excited states
a
condensation
12
C
Tohsaki
et
al
.(2001)
0
1
+
02+
7.65 MeV
8
Be+a
2
2
+
0
3
+
cluster gas
3
a
Dilute cluster gas
Bosonic behavior:a particles condensate in the same orbit.
BEC
in nuclear matter
Roepke et al., PRL(1998)+
4a condensation in 16Osuggested by Funaki et al.
(2008,2010)cluster excitation
+
Hoyle
st.
Funaki et al. (2003)
Uegaki
et al. (1977)
Slide162a+t cluster in 11
B
(
3/2
-3)
11
B,
11C
7
Li+a2a+t
3/2
1
-
3/22-
3/23
-
8.5
AMD
by Y.K-E., Suhara
Strong E0
Weak M1,GT
0
1
+
0
2
+7.65 MeV12C
8
Be+
a
Kawabata et al.PLB646, 6 (2007) cluster gas of 3a
2
a
+t gas
PRC75, 024302 (2007)
PRC85, 054320 (2012)
2
2
+
0
3
+
triangle
？
2
a
+t chain?
3
1
-
+
Slide17Rotational
band from
cluster gas
s
pin J(J+1)
s
pin J(J+1)
Excitation energy (MeV)
a
a
a
a
Spherical gas
d
eformation
rotation
a
a
Itoh
et al.(2011)
2
2
+
4
+
Freer et al.(2011)
0
2+
9/22
-
3/23-
Yamaguchi et al.(2011) 12C
11B
Non-geometric
geometric
s
pin
r
otation of 3a
, 4a gasOhkubo et al., PLB684(2010)
Funaki et al. PTPS196 (2012)
discussed in D3 session
Slide18Linear chain state in
14
C*
14
C
AMD
by
T.Suhara and Y.K-E,Phys.Rev.C82:044301,2010.
3a linear chain
proton
neutron
Neutron-rich
14C
Energy (Mev)
14,16
C
Linear chain?
v
on
Oertzen
et al.
Itagaki
et al.
Y.K-E.et a.
Suhara
et al.
12
C
g.s
.
14
C
g.s
.
+
12
C*
n
ot linear
12
C
14
C*,
16
C
*
0
2
+
0
3
+
Y.K-E.et al.,
T. Neff et al.
Slide19Topics of cluster phenomena
Cluster gas, chain states
in C and B isotopes
Cluster structures in Be isotopes
Slide20Excitation
energy
0
3
+
Cluster structures
in neutron-rich Be
0
1
+
0
2
+
Normal state
Molecular orbital
(MO bond)
Exp
:
Millin
et al.
’05,
Freer
et al. ’06
10
Be: energy levels
J(J+1)
0+
2+
4+
0+(
g.s
.)
2+
4+
10
Be
6
He+
4
He
Ito et al
.
Kobayashi
et al.
Kuchera
et al
.
MeV
AMD
exp
Slide21+
-
+
-
+
s
-orbital
α
α
α
α
±
p
-
orbital
Molecular orbital(MO) structure
in Be
MO state
Normal state
2
a
-core formation
MO formation
Low-lying MO states
in
11,12,13
Be
Gain kinetic energy
in developed 2α syste
m
vanishing of magic number in
11
Be,
12
Be,
13
Be
MO formation
Seya et al. Von
Oertzen
et al.,
N.
Itagaki
et al., Y. K-E. et al. Ito et al.
Recent exp. for
13
Be
Kondo et al. PLB690(2010)
Slide22N
Excitation
energy
0
1
+
0
2
+
10
Be
11
Be,
12Be, 13
BeVanishing of N=8 magic number in neutron-rich Be
0
1
+
0
2
+
Normal state
Normal state
8
Be
2
a
MO
d
eformed
g.s
.
Intruder
vanishing
of
neutron magic number
Inversion
Y.K-E.PRC85
(2012) ;
68
(2003
)
12
Be
g.s
. 0+
13
Be
g.s
. 1/2-
p
s
s
p
Slide234. Discussion
Slide24Cluster formation, breaking, excitation, and MO
+
12
C*
n
ot linear
0
2
+
0
3
+
MO
6
He+
4
He
10
Be
12
C
14
C
10
Be+
4
He
linear
c
luster
breaking
2
a
system
+
-
+
α
α
+
-
α
α
s
-orbital
p
-orbital
0
2
+
0
1
+
0
1
+
4-body
(a)
correlation
a
correlation
2
a
-cluster
breaking
2
a
cluster
weakening
p
-orbital
Slide25Cluster & shapes: symmetry breaking(SB) and restoration
nucleons in MF
12
C
developed
3
a
Cluster excitation
MF
Cluster
Cluster formation
m
any-body correlation at surface
3
a
12
C
No
fermi
surface
fermi
surface
Triangle
Spherical
Oblate
Spherical
a
gas
12
C*(0
+
2
)
12
C
gs
(0
+
),
12
C
gs
(3
-
)
O(3)
O(2)
No
correlation
D3h
O(3)
Strong
a
correlation
Slide26Cluster correlation and SB
Density wave(DW)
F
ermi gas
Triangle
Spherical
Oblate
Spherical
a
gas
Strong
a
correlation
Y. K-E. and Y. Hidaka, PRC
84, 014313 (2011)
BEC: alpha cond.
Infinite matter
k=0
2k periodicity
r
otational/axial symmetry
broken
restored
Translational symmetry
b
roken phase
restored
Angular DW
(
low dimension, Z=N light nuclei)
2L
z
+1
periodicity
Slide27SummaryTopics of cluster phenomena
Light nuclei: cluster
gas,
chain, molecular orbital in Be, B, C
Heavier system:
studied by Kimura et al., Taniguchi et al.shape coexistence, superdeformation in Si-Cr isotopes
breaking of neutron Magic number around 30Ne, 32
Mg, molecular orbital structure in Be, F, NeCoexistence of cluster and MF features brings
rich phenomena as functions of proton/neutron numbers and excitation energy.Cluster and symmetry breaking
analogy with other quantum many-fermion systems (cold atoms, quark systems)
Slide28Rich phenomena in
unstable nuclei
Excitation energy
neutron
N
proton
Z
*
proton number
* neutron number
* excitation energy
Unbalanced proton-neutron ratioNew RI F
acility
Slide29Many-body correlations at low density
a
-cond.
in low density
12
C(0
2
)
+
16O*Dilute a
-cluster gas
BEC-BCS
BCS
Unbound
α
α
α
Neutron matter
N
uclear matter
Dineutron
at surface of
neutron-rich nuclei
Itagaki et al.,
Von Oertzen et al.
α
α
α
14-16
C*
α
α
α
Price et al.
Geometric
（
crystal
？）
Matsuo
et al
.
PRC73 044309 (‘06)
Cluster
gas, chain ?
Dineutron
correlation ?
Slide30Ground
state
Resonances, cluster decay
α-
caputure
Liquid-gas
phase
Fusion/fission
cluster
Heavy-ion
collision
Threshold
a
condensation
Nuclear matter
deformation
High spin
vibration
Giant resonance
Weak-binding
Stable
nuclei
Super-heavy
element
Particle-hole
neutron
halo/skin
2
neutron
Resonance
, continuum
Shell
evolution
Rich phenomena in nuclear many-body system
s
Temperature/Excitation
energy
neutron-rich
proton-rich
Nucleon number
Slide31Slide32Rotational
band from
cluster gas
s
pin J(J+1)
s
pin J(J+1)
Excitation energy (MeV)
a
a
a
a
Spherical
gas
deformation
rotation
a
a
Itoh
et al.(2011)
2
2
+
4
+
Freer et al.(2011)
0
2+
9/22
-
3/23-
Yamaguchi et al.(2011) 12C
11B
geometric
s
pin
r
otation of 3
a, 4a gas
Ohkubo et al., PLB684(2010)Funaki et al. PTPS196 (2012)
discussed in D3 session
0
3
+
a
a
a
bending
chain
03
+
02
+
Slide33Deformation
b
Energy
16
O-
16
O
d
iabatic
path
adiabatic path
SD
Deformtions
and cluster resonances
MR
R
h
igher nodal
R
R
32
S:SD
32
S:ND
Slide34DW on the edge of the oblate state
Pentagon in
28
Si
due to 7
a
-cluster
SSB from axial symmetric
oblate shape
to axial asymmetric shape
D5h symmetry
constructs
K=0+, K=5- bands
DW in nuclear matter
is a SSB(spontaneous symmetry breaking)
for translational invariance
i.e. transition from uniform matter
to
non-uniform matter
Origin of DW: Instability of Fermi surface due to correlation
k
Correlation between particle (k) and hole (-k)
has non-zero expectation value
wave number 2k periodicity (non-uniform)
Other kinds of two-body correlation(condensation)
are translational invariant
BCS
exciton
DW
in
28
Si
?
-k
Slide35Energy levels of
13
Be with
12
Be+n calculation
1/2-
5/2+
3/2+
3p-2h
1p-0h
2p-1h
AMD+”RGM”
Density distribution of
VAP calculations
Slide36