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