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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