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Cluster Phenomena in Stable and Unstable 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(NIMS), Y. Yoshida (Kyoto)
1.Introduction
Cluster structuresin stable and unstable nuclei
Typical cluster structures known in stable nuclei
8Be 12C 20Ne
a + a 3 a 16O + a
16O*
12C + a
7Li
a + t
a-cluster
40Ca*, 28Si*, 32S*
36Ar-a, 24Mg-a, 28Si-a
Si-Si, Si-C, O-C, O-O
Molecularorbital Be, C, O, Ne, F
a-clusterexcitation
14C*
3a linear chain
Unstable nuclei Heavier nuclei
a
Cluster & Mean field
Mean field, shell structureIndependent single-particle
v.s.
Cluster:Many-body correlation
Independent particle in MF
Developed cluster
Cluster excitation
Shell structure ・ MF Cluster
Cluster formation
many-body correlation
g.s. correlation excited statesno correlation
Cluster structures
12C
Nucleon liquid
0 MeV 100 MeV
Nucleon gas
Energy10 MeV
r0
Shell & cluster corr.
low density
cluster excitation
+
r0/3~ r0/5
Cluster gas, crystal
high density
Nuclear structure
Cluster enhancement
Cluster phenomena in low density
Heavy Ion collision
Liquid-gas phase
Multi fragmentation AMD cal.: 129Xe+Sn E/A 50 MeV
by A. Ono PRC66 (2002)
QMD cal. by Watanabe PRL109 (2009)
Supernova,Neutron star crust
Nuclear pasta
Cluster structuresin n-rich nuclei
Molecularorbital
n-rich Be, F, Ne
a-clusterexcitation
n-rich C
linear chain
gs clustercorrelation
clusterweakening/melting
Clusteringin deformedNeutron density
in C*
n-skin suppression large deformation breaking of magic
number N=8, N=20
stable nuclei
n-rich nuclei
cluster gas
16O
Roles of excess neutronsin cluster structures of n-rich nuclei
Ne, F, O isotopes
a a
Seya, Von Oerzten, Descouvemont et al.,Itagaki et al., Dote et al., K-E et al. Arai et al., M. Ito et al.
Be isotopes
a a
a a
Molecular Orbital:bonded clusters
Atomic:Cluster resonance
10Be
shell model-like
a
16O a6He+He
18O+a
Strongcoupling
Weakcoupling
Normal states
Scholz et al., Rogachev et al., Goldberg et al.,Ashwood et al., Yildiz et al., Descouvemont, Kimura,
Soic et al., Freer et al., Saito et al., Curtis et al., Milin et al., Bohlen et al.,
MO bond and Cluster res. in 22Ne
16O a
16O a
MO-bond
Cluster res.
22Ne 18O+aAMD study by Kimura, PRC75 (2007)
Exp Scholz et al., Rogachev et al., Goldberg et al.,Ashwood et al., Yildiz et al., Theor: Descouvemont, Kimura,
EXP
AMD
MO structures in F isotopes
a
MO bond with15N+ a core
AMD study by Kimura et al., PRC83 (2011)
0hw2hw3hw
1hwplay an important role in lowering intruder statesin N~20 region
also in Ne isotopes
19-29F
21F 23F 25F 27F 29F19F
3hw
2hw
a-cluster states in n-rich nuclei
a
Cluster resonances
6,8He+a in Be
10Be+a in 14C
14C+a in 18O
18O+a in 22Ne
Ex = several ~ 20 MeVNew states discovered and suggested at
-> information of nucleus-nucleus potential and valence neutron effects there.
Theor: Seya, von Oerzten, Descouvemont et al.,Itagaki et al., K-E et al. Arai et al., M. Ito et al.
Exp: Soic et al., Freer et al., Saito et al., Curtis et al., Milin et al., Bohlen et al.,
in a-decay, a-transfer, a-scattering
Exp Scholz ‘72, Rogachev ‘01, Goldberg ‘04, Ashwood ‘06, Yildiz et al., Theor: Descouvemont ’88, Kimura ‘07
Exp Scholz et al., Rogachev et al., Goldberg et al.,Ashwood et al., Yildiz et al., Theor: Descouvemont, Kimura,
Exp Soic 04, von Oertzen ‘04, Price 07, Haigh 08,Theor: Suhara ‘10
Rich cluster phenomena in nuclear systems
Cluster formation/breaking in low-lying states
Cluster excitation and resonances
Molecular Bond in neutron-rich nuclei
Many clusters : cluster gas, chain
New types of cluster
as functions of proton&neutron numbers and excitation energy
6,8He+He in Be, 10Be+a in 14C,14C+a in 18O, 18O+a in 22Ne
A theoretical method: AMD (antisymmetrized molecular dynamics)
An approach for nuclear structure to study• cluster and mean-field aspects• Stable and unstable nuclei• Ground and excited states
2. A theoretical model: AMD
kjiijk
jiij
ii vvtH effeff
1
eff '
Effective nuclear forcephenomenological)
0 H
Energy Variation
AMD wave fn.
np
ccc
A
or
21
21
2
2AMD
AMDAMDAMD
)(exp)(
,,,det
''''''
i
ii
ijiΖ
iiΖi
Zrr
spatial
isospinIntrinsic spins
Slater det.
Gaussian
,...),,,( 21AMD AZZZ
det
Gaussian wave packet
AMD method for structure study
iZ
Similar to FMD wave fn. A variety of cluster st.
Shell-modellike st.
3. Some topics of cluster phenomena
3-1. MO bond in n-rich Be & vanishing of magic number
3-2. Cluster resonances
3-3. Linear chain in n-rich C
3-1. MO bond in n-rich Be & vanishing of magic number
3-2. Cluster resonances
3-3. Linear chain in n-rich C
0 2 4 6 8 10 12 14 16 18 200
5
10
Cluster structures in neutron-rich Be
01+
Exp: Milin et al. ’05, Freer et al. ’06
10Be: energy levels
J(J+1)
0+
2+
4+
2+
4+
10Be
6He+4He
Ito et al.Kobayashi et al.Kuchera et al.
MeV
AMD
exp
clusterres.
MO bond
Normal
02+
03+
AMD calc. Y. K-E, et al. PRC (98)
+
-
+ - +s-orbital
αα
α α
±
p-orbital
Molecular orbital(MO) structure in Be
MO state
Normal state
2a-core formation
MO formation
Level inversion in 11,12,13Be
Gain kinetic energyin developed 2α system
vanishing of magic number in 11Be, 12Be, 13Be
MO formation
Seya PTP65(81), von Oertzen ZPA354(96) N. Itagaki PRC61(00), Y. K-E.. Ito PLB588(04)
n-rich
Energy
01+
02+
10Be 12Be, 11,13Be
Vanishing of N=8 magic number in neutron-rich Be
01+
02+
Normal state
Normal 0hw
MO bond
deformation in 12Be(gs)
Intruder 2hw
Y.K-E.PRC (03),(12) , Ito PRL(08) Dufour NPA(10)
12Be g.s. 0+ 13Be g.s. 1/2-
p
s
s
p
Inelastic scat. life time: Iwasaki PLB481(00), Imai PLB673(09)
Inversion
Kondo et al. PLB690 (10)
abnormal parity of 13Be(gs)
B(GT) with charge ex.: Meharchand PRL108 (12)
intruder config. in 12Be(gs)
12Be(02+) with p-shell config.
1n-knockout reac.: Navin PRL85(00), Pain PRL96(06)
Fortune PRC(06), Blanchon PRC(10)
Shimoura PLB654 (07)
Breaking of magic number in 13Be
12Be+n
Er(MeV)
0
1
2 2.0
(5/2+)
(1/2-)3.04
Simon07
1/2+ virtual st.
Kondo10
(1/2-)0.51
2.39
(5/2+)
1/2- ?
13Be: unbound13Be spectra measured by 1n knock-out reactionsat GSI(Simon et al. 2007) and RIKEN(Kondo et al.,2010)
13Be
p1/2
s1/2
p3/2
d5/2
s1/2
1/2- is lowest in 13Be
intruder
EXP.
AMD calc. Y. K-E. PRC(12)
Kondo10 Simon07AMD12Be+n
3-1. MO bond in n-rich Be & vanishing of magic number
3-2. Cluster resonances
3-3. Linear chain in n-rich C
a a
0+2
K=0+1
a0+
3,4?
6He+4He
Kuchera et al.Ito et al.Kobayashi et al.
a a
Normal
MO bond
Exotic cluster res. also suggested
a
a a
aa
03+
6,8He+6,4He
0+2
0+1
Freer PRL.82(99)(06)Saito NPA738 (04)Yang PRL112 (14 )
aa
a t
t
6He+3H
MO bond ?
Cluster res. ?
9Li10Be 12Be
Cluster resonances
8He+6He in 14Be9Li+6He in 15B
a
Ito et al. Y. K-E et al.
a t
a t
6He+3H resonance
9Li(3/23-)
9Li(gs)
6He+3H cluster resonances in 9Li9Li: energy levels(calculation)
-10
-5
0
5
1/2- 3/2-
5/2- 7/2-
6He+3H threshold
3/2- g.s.
J(J+1)
9Li
MeV
K=1/2- band
Y. K-E. et al PRC.85(12)
a
aMO bond
a t
a t
6He
NO MO bonda
a
10Be 9Li
t decoupling
K=0+2
a aK=0+
1 at3/2-
1
K=0+3,4?
g.s(3/2-1)
K=1/2-
(3/2-3)
a a a t
Cluster resonances
6He
Cluster structures in 10Be and 9Li
3-1. MO bond in n-rich Be & vanishing of magic number
3-2. Cluster resonances
3-3. Linear chain in n-rich C
Linear chain state in 14C*14C AMD by T.Suhara and Y.K-E,
Phys.Rev.C82:044301,2010.
3a linear chainproton neutron
Neutron-rich
14C
Energ
y (
Mev)
14,16C
Linear chain?
von Oertzen ZPA354(96) EPJA21(04),PR 432(06)Itagaki PRC64(01)Suhara PRC82(10)Maruhn NPA833(10)
12C g.s. 14C g.s.
+
12C* not linear
12C14C*,16C*
02
+
03+ Y.K-E.et al.,
T. Neff et al.
Tohsaki et al., Funaki et al.
Linear chain in n-rich C
Stretching effect in rotation
15C*(19/2-)b=0.78
suggested to be ayrast state
11Be+a
Largely deformed 11Be with MO-bond
AMD by Y.K-E,PR432(2006)
Meta stablefor bending motion
MO model for 14,16C Itagaki et al. PRC64(01) HF calc. for 16,20C by Maruhn et al. NPA833(10)
4. Summary
SummaryRich cluster phenomena in n-rich nuclei MO bond & breaking of N=8 shell Cluster resonances Linear chainCluster formation, development, and valence neutrons play important roles in nuclear structure.
Ikeda et al.PTP464-S (1968)
Extended Ikeda diagram?by von Oertzen et al
Taken from Phys. Report 432 (2006)
Many-body correlations at low density
a-cond.in low density
12C(02 )+
16O*
Dilute a-cluster gas
BEC-BCS BCSUnboundα
α
α
Neutron matterNuclear matter
Dineutron at surface of neutron-rich nuclei
Itagaki et al.,Von Oertzen et al.
α
α
α
14-20C*
αα α
Price et al.
Geometric( crystal ?)
Matsuo et al. PRC73 044309 (‘06)
Cluster gas, chain ? Dineutron correlation ?
Information of many-body correlations in low density, in isospin asymmetric systems.
Excitation energy multidimension * proton number* neutron number* excitation energy* density
Neutron number
proton numberLow density
Systematic study in a wide region