Unified Studies of the exotic structures in 12Beand the +8He slow scattering

Makoto Ito, Naoyuki Itagaki

Theoretical Nuclear Physics Lab., RIKEN Nishina Center

Department of Physics, Tokyo University

I. Introduction

II. Formulation : Extended microscopic cluster model

III. +8He scattering and exotic structures in 12Be

IV. Monopole transition of 12Be

V. Summary and Future perspectives

Cluster effects in reactions

1. Molecular Resonances (MRs) are typical examples : 12C+12C, 16O+16O, 12C+16O

Val. N : tight binding

Transfers of a valence neutron → No sharp resonances

Val. N : weak binding

Transfer of “active” neutrons→ Sharp resonances are generated ?

A (Cores) >> XN A (Cores) ～ XN

⇒ Collective excitation of individual nuclei is essential.

2. MR system + one valence neutron :12C+13C, 16O+17O, etc…

Transfer process is extensively investigated ⇒ NO clear resonances !!

Transfer effect in neutron-rich systems

Previous studies (12C+13C etc) Neutrons’ drip-line case

N ～ Z N >> Z

An additional neutron

Our interest : transfer reaction by a neutrons’ drip line nucleus

Ex.

ene

rgy

Orthogonality

Low-lying B.S. statesMolecular Orbitals (MOs): ― 、＋‥

Resonance formationSlow RI beam

Transfer channels

Today’s report

N

A BE ( A+B )

Unbound region

Bound region

+

8He + 4He (= 12Be)

4He + 4N + 4He

Scattering and structure

⇒ Transfer effects shall be strong !!

We should combine MO and asymptotic channels.

( )

( Exp. at GANIL )

12Be (experiments)

12Be+ → (6He+6He)+A. Saito et al.

6He + 6He (Atomic)

Moleculue

Structural changes

Low-lying (Breaking of N=8 Magicity) High-lying states (Atomic)

(Important system before proceeding systematic studies)

E(sd-0p)～ 1MeV

Def. Length ～ 2fm

1/2+ (sd)

-

+

-

+ 3/2+ (sd)

1/2- (0p)

3/2- (0p)

1/2+ (sd)

1/2- (pf)

＋

―

―

＋

Formulation ( I ) : Single particle motion in two centers

( s.p.) =(L) ± (R) : LCAO L(0p) ± R(0p)

Y(1,0)

Y(1,±1)

(0p)

S

Z

Config. MixingDistance : S(0s)4

(10Be=++N+N )

(+)2 = ( Pz(L) ― Pz(R) )2

Formulation (II)

+ 6He6He + 5He + 5He

Linear Combination of Atomic Orbital (LCAO)

+6He(0+)

= Pz(L) ・ Pz(L) + Pz(R) ・ Pz(R) － 2Pz(L) ・ Pz(R)

= Px(R) ・ Px(R) + Py(R) ・ Py(R) +Pz(R) ・ Pz(R)

Total wave function

S

SC,

),(

Pm(a) ・ Pn(b) (m,n)=x,y,z (a,b) = L,R

Variational PRM S

Z

General MO: (C(L)Pi(L) + C(R)Pj(R))2

Energy surfaces in 12Be = ++4N

(0p3/2)2(sd) 2

(-)2 (+)2

(0p)6

(-)4

Adiabatic Energy surfaces

2 MeV

Atomic-MolecularHybrid configuration

6He 6He

Covalent SD

S ～ 5fm

VNN : Volkov No.2+G3RS

J= 0+

+ 8He

6He + 6He

6He + 6He

5He + 7He

+ 8He

Continuum Energy

R() ～ 1.4fm

Coupling to open channels in continuum

0)(,

)( Kb

Open channels Compound states (Closed)

0)( 0 KEH

)(,,

)()(,

LLR

uSu

Bound state approximation with Atomic Orbital Basis

Scattering B.C.

Rearrangement channels : + 8Heg.s. 、 6Heg.s. + 6Heg.s. 、 5Heg.s. + 7Heg.s.

Closed states method : Prof. Kamimura, Prog. Part. Nucl. Phys. 51 (2003)

400 ～ 500 S.D. with J projection

+ 8He ⇒ 6He + 6He

Cro

ss s

ectio

ns (

mb

)

Ec.m. ( MeV )

Cross sections of neutron transfers

Ec.m. ( MeV )

+ 8He ⇒ xHe + yHe (J=0+)

Elastic

6He + 6He

5He + 7He

Dotted curves : Three open channels only

Solid curves: Open + closed chanels

This is a prediction for recent experiments at GANIL.

Effects of the transfer coupling : Minimum coupling

+ 8Heg.s.

+ 8He(21+)

6Heg.s.+ 6He(21+)

6He(21+) + 6He(21

+)

5He(3/2 － ) + 7He(3/21－ )

5He(3/2 － ) + 7He(1/21－ )

5He(3/2 － ) + 7He(5/21－ )

5He(1/2 － ) + 7He(3/21－ )

6Heg.s.+ 6Heg.s.

Dotted curves

Sharp resonant structures are generated by Transfer Coupling → New aspects !!

+8He ⇒ xHe+yHe

Elastic

6He+6He

5He+7He I=0

5He+7He I=2

Solid : Full calculation

Schematic picture of excitation modes

Excitation modes in 12Be 7He5He

6He

8He

6He

Excitation from the 02

+ state.

Excitation from the 01

+ state.

Cluster + S. P. Excitation

01+

02+

Cluster’s relative Motion is excited.

Single particleExcitation

(-)2(-)2

(-)2 (+)2

(0pR)(0pL) (+)2

05+

03+

04+

06+

+8He ⇒ 6He+6He

Covalent SD- REL. + S.P. of 4N

6He + 6He

+ 8He

Coexistence in A=12 systems : Coexistence phenomena

+ 8Heg.s.

6Heg.s.+ 6Heg.s.

5Heg.s.+ 7Heg.s.

12C

12B+ 8Beg.s.

5Heg.s.+ 7Beg.s.

6Heg.s.+ 6Beg.s.

+ 8Lig.s.

6Heg.s.+ 6Lig.s.

5Heg.s.+ 7Lig.s.

12Be

02+

Hoyle state

03+

04+

05+

06+

19.8 MeV

8.8 MeV

5.4 MeV

2.9 MeV

～ 4 MeV

Coexistence becomes prominent.

Vn-n 、 V-n is Weak.

Comparison of 12Be and 12C

12Be + → (6He+6He) +

12C + → (++) +

There appear many resonances !!

( A. Saito et al. at Tokyo Univ. )

( M. Itoh et al. at Tohoku Univ. )

0+

No decays to +8He

7.5 12

Rotational bands : Coexistence of MRs and covalent SD Exp. at RIKEN (Saito)

Red : Covalent SD

Pink : 5He + 7He Green : 6He + 6He

Blue : + 8He

Green squares: (-)2(+)2

White square: (-)2(-)2

Exp. by Freer Exp. at RIKEN (Shimoura)

Bou

nd r

egio

nS

catt

erin

g re

gion

Monopole Transition

Pioneering work on monopole transition

Simple shell model (1p-1h, 2hw) ： No strength around low-lying region, Ex<10MeV

Cluster correlation in a ground state (Yamada et al., PTP, inpress)

There is a possibility that monopole transitions are enhanced If cluster structures are developed. ( Ex < 10MeV )

ex

A

iirISEM 00),0(

1

21

ClusterASGM rel )2(..

..SG

Excitation of clusters’ relative motion (2hw)

Cluster structure

If has large cluster components, the monopole matrix elements

will be enhanced !

Large cluster components in G.S. can be always justified by Bayman-Bohr Theorem

Why monopole ?

Adiabatic energy surfaces in 12Be

Adiabatic Energy surfaces

VNN : Volkov No.2+G3RS

+ 8He

8He

(-)2 (+)2

– Distance

3rd 0+

1st 0+

GCM (01+)

GCM (03+)

Cluster Excitation

– Distance

Monopole transition of 12Be

(-)2 (+)2

8He

11

2 00),0(A

iif rISEM 2

),0( ISEM

01+

03+

Adiabatic connection enhances theMonopole transition !

01+ → 03

+ is enhanced.

– distance ( fm )

( a.u. )

Adiabatic surfaces (J= 0+) Energy spectra ( J= 0+ )

ｰ i W(R)

+6He(21+)

10Be case : M.I., PLB636, 236 (2006)

Cluster

Contents

Unified description of the +8He reactions and the exotic structures in 12Be

Results

New features

2. Exited (resonance) states are characterized in terms of the excitation degree of freedoms included in the ground state. (Val. neutrons or cluster relative motion)

1. Comparison with the recent experiment of the +8He scattering (GANIL)

Future studies

M. I., N. Itagaki, H.Sakurai, K. Ikeda, PRL 100, 182502 (2008).

M. I., N. Itagaki, PRC78, 011602(R) (2008).

1. Transfer coupling is important for the formation of the sharp resonances.

2. Systematic studies on the resonant scattering of neutrons’ drip-line nuclei

M. I., N. Itagaki, Phys. Rev. Focus Vol.22, Story4 (2008).

(Resonance formation by neutron transfers )

3. The energy spacing of the resonances becomes quite small.

4. The monopole transition is enhanced with a development of the cluster.

Coverage by APS

American Phys. SocietyWEB JournalPhys. Rev. Focus

See also, RIKEN RESEARCH5 September (2008)

(http://focus.aps.org/story/v22/st4)

http://www.rikenresearch.riken.jp/research/517/

Extension of Cluster Concept

Rigid cluster

8He

6He

7He5He

0+ 0S

0+ 1S

～ 3MeV

02+

03+

12Be = + + 4N

0+

12C = (+) + 16O = + 12C

0S

2+0D

～ 7MeV

02+

05+

・・

・・

Excitation : 8Be-Rel. motion

6He

5He 5He

Excitation :12C-Rel. +12C Rot.

～ 4 MeV

Loose cluster

Clusters are rigid.

Neutron rearrangements with small energy increasing

Clusters are loose !!

dE ～ 2 MeV

dE ～ 1 MeV

(N ～ Z : dE>10 MeV)

Generalized Two-center Cluster Model (GTCM)

Combined model of mol. orbit and asymptotic channels

+ + ...

C1 C2 C3

0Pi (i=x,y,z) coupled channel with atomic basis

Mol. Orbit 8He

Resonance PRMPTP113 (05)

+8He ScatteringPRC78(R) (08)

12Be=++4N

ｰ i W(R)

S, Ci : Variational PRM

S

Combine

Absorbing BC Scattering BC Tr. Density

12Be(01+)→12Be(0ex

+)Monopole Transition

<f | | i>

7He5He6He6He

M. Ito et al., PLB588(04), PLB636(06), PRL100(08)

Molecular structures will appear close to the respective cluster threshold.

α-Particle ⇒ Stable

Systematic Appearanceof cluster structures

3H+p ～ 20 MeV

Cluster structures in 4N nuclei IKEDA Diagram

Ikeda’s Threshold rules

Be isotopes

Molecular Orbital : Itagaki et al.

―

+

PRC61,62 (2000)

Studies on Exotic Nuclear Systems in (Ex,N, Z) Space

( N,Z ) : Two Dimensions

Ex.

ene

rgy

StructuralChange

Low-lyingMolecular Orbital : ― 、＋‥

Unbound Nuclear SystemsSlow RI beam

Decays inContinuum

Is Threshold Rule valid ??

N

H. Voit et al.,NPA476,491 (1988)E. Almqvist et al., PRL4, 515 (1960)

Molecular resonance phenomena in stable systems

12C+12C at Coulomb barrier⇒Sharp resonances

13C+12C at Coulomb barrier⇒NO clear resonances

(+)2 = ( Pz(L) ― Pz(R) )2

Formulation :10Be=++N+N

+ 6He6He + 5He + 5He

Linear Combination of Atomic Orbital (LCAO)

+6He(0+)

= Pz(L) ・ Pz(L) + Pz(R) ・ Pz(R) － 2Pz(L) ・ Pz(R)

= Px(R) ・ Px(R) + Py(R) ・ Py(R) +Pz(R) ・ Pz(R)

Total wave function : Fully anti-symmetrized

S

SC,

),(

Pm(a) ・ Pn(b) (m,n)=x,y,z (a,b) = L,R

Variational PRM S

Z

( 12Be=++4N: 38 AOs,K=0 )

: (0s)4

Enhancement of the two neutron transfer

Unitary condition of S-matrix

128

HeS

)()().( 7566 HeHeHeHeSDCov

Open Closed

5He +

7He

6He +

6He

4He +

6He

Covalent SD, | Sf,i |2=1

+

8 He

⇒

6 He+

6 He

Strong decay into 6He+6He

J= 0+

12866 HeHeHeS

Large part of the flux flows to 6He+6He.

本研究の背景

単極遷移とクラスター構造に関する先行研究

下浦 ： 単純な殻模型の場合、 Ex<10MeV に単極遷移の強度はない

基底状態におけるクラスター相関 ( 山田 )

クラスター構造の発達に伴い、低励起領域に強い単極遷移強度が現れることが指摘されている。

ex

A

iirISEM 00),0(

1

21

ClusterASGM rel )2(..

..SG

クラスターの相対運動を 2hw 励起

( N : クラスター相対運動の量子 )

殻模型 + クラスター

基底状態にクラスターの種があり、それが 2hw 励起する

クラスター基底　　　　　　　　　　　　 = N ( 最低許容数 ) + N ( 高節数 )

クラスター構造

+ +

N = N low N > N low

Why monopole ?

Pioneering work on monopole transition

Simple shell model (1p-1h, 2hw) ： No strength around low-lying region, Ex<10MeV

Cluster correlation in a ground state (Yamada et al., PTP, inpress)

There is a possibility that monopole transitions are enhanced If cluster structures are developed. ( Ex < 10MeV )

ex

A

iirISEM 00),0(

1

21

ClusterASGM rel )2(..

..SG

Excitation of clusters’ relative motion (2hw)

( N : Quanta for relative motions )

Shell model + Cluster

2hw excitation of the seed of clusters in a ground state

Cluster basis

　　　　　　　　　　　　 = N (Lowest arrowed) + N (Higher quanta)

Cluster structure

+ +

N = N low N > N low