Unified Studies of the exotic structures in 12Be

1
Unified Studies of the exotic structures in
12Be and the a8He 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. a8He scattering and exotic structures in
12Be
IV. Monopole transition of 12Be
V. Summary and Future perspectives
2
Cluster effects in reactions
1. Molecular Resonances (MRs) are typical
examples 12C12C, 16O16O, 12C16O
? Collective excitation of individual nuclei is
essential.
An additional neutron
2. MR system one valence neutron 12C13C,
16O17O, etc
Transfer process is extensively investigated ? NO
clear resonances !!
Transfer effect in neutron-rich systems
Previous studies (12C13C etc)
Neutrons drip-line case
A (Cores) gtgt XN
A (Cores) XN
NZ
N gtgt Z
Val. N tight binding
Val. N weak binding
Transfer of active neutrons ? Sharp resonances
are generated ?
Transfers of a valence neutron ? No sharp
resonances
3
Our interest transfer reaction by a neutrons
drip line nucleus
N
Resonance formation
Slow RI beam
A
B

Unbound region
E ( AB )
Transfer channels
Todays report
Bound region
Scattering and structure
8He 4He ( 12Be)
Orthogonality
Ex. energy
( )
4He 4N 4He
? Transfer effects shall be strong !!
( Exp. at GANIL )
Low-lying B.S. states Molecular Orbitals (MOs)
p ??s?
We should combine MO and asymptotic channels.
4
12Be (experiments)
(Important system before proceeding systematic
studies)
Low-lying (Breaking of N8 Magicity)
High-lying states (Atomic)
12Bea ? (6He6He)a A. Saito et al.
E(sd-0p) 1MeV
Def. Length2fm
Structural changes
Moleculue
6He 6He (Atomic)
5
j(0p)
Formulation ( I ) Single particle motion in two
centers
F ( s.p.) j(L) j(R) LCAO
jL(0p) jR(0p)
Y(1,1)
s-

1/2- (pf)
1/2 (sd)
Y(1,0)
p
?
3/2 (sd)
Z
1/2- (0p)
s
?
1/2 (sd)
3/2- (0p)
(10BeaaNN )
a
a
p-

S
Config. Mixing Distance S
a (0s)4
6
Linear Combination of Atomic Orbital (LCAO)
Formulation (II)
Z
(s)2 ( Pz(L) ? Pz(R) )2
a
a
Pz(L)Pz(L) Pz(R)Pz(R) - 2Pz(L)Pz(R)
a 6He
6He a
5He 5He
Px(R)Px(R) Py(R)Py(R) Pz(R)Pz(R)
a
a
a6He(0)
General MO (C(L)Pi(L) C(R)Pj(R))2
Total wave function
(m,n)x,y,z
(a,b) L,R
Pm(a)Pn(b)
S
Variational PRM
7
Energy surfaces in 12Be aa4N
VNN Volkov No.2G3RS
6He
6He
Adiabatic Energy surfaces
n(0p)6
Jp 0
Continuum Energy
5He 7He
(p-)4
6He 6He
a 8He
6He 6He
R(a)1.4fm
a 8He
Covalent SD
n(0p3/2)2(sd) 2
2 MeV
S5fm
Atomic-Molecular Hybrid configuration
(p-)2 (s)2
8
Coupling to open channels in continuum
Closed states method Prof. Kamimura, Prog.
Part. Nucl. Phys. 51 (2003)
Compound states (Closed)
Open channels
Bound state approximation with Atomic Orbital
Basis
Scattering B.C.
400500 S.D. with Jp projection
Rearrangement channels a 8Heg.s.? 6Heg.s.
6Heg.s.?5Heg.s. 7Heg.s.
9
Cross sections of neutron transfers
a 8He ? xHe yHe (Jp0)
a 8He ? 6He 6He
Elastic
Cross sections ( mb )
6He 6He
5He 7He
Ec.m. ( MeV )
Ec.m. ( MeV )
Dotted curves Three open channels only
This is a prediction for recent experiments at
GANIL.
Solid curves Open closed chanels
10
Effects of the transfer coupling Minimum
coupling
Solid Full calculation
Dotted curves
a8He ? xHeyHe
a 8Heg.s.
a 8He(21)
Elastic
5He(3/2-) 7He(3/21-)
6He6He
5He(3/2-) 7He(1/21-)
5He7He I0
5He(3/2-) 7He(5/21-)
5He(1/2-) 7He(3/21-)
5He7He I2
6Heg.s. 6Heg.s.
6Heg.s. 6He(21)
6He(21) 6He(21)
Sharp resonant structures are generated by
Transfer Coupling ? New aspects !!
11
Schematic picture of excitation modes
12
Excitation from the 02 state.
Excitation modes in 12Be
7He
5He
Covalent SD
(0pR)(0pL) (s)2
a-a REL. S.P. of 4N
a8He ? 6He6He
06
6He
6He
05
Cluster S. P. Excitation
04
Single particle Excitation
6He 6He
03
a 8He
Clusters relative Motion is excited.
8He
(p-)2(p-)2
Excitation from the 01 state.
02
01
(p-)2 (s)2
13
Coexistence in A12 systems Coexistence
phenomena
6Heg.s. 6Beg.s.
Coexistence becomes prominent.
8.8 MeV
a
a
5Heg.s. 7Beg.s.
6Heg.s. 6Lig.s.
Vn-n?Va-n is Weak.
5.4 MeV
19.8 MeV
4 MeV
5Heg.s. 7Lig.s.
5Heg.s. 7Heg.s.
06
Hoyle state
05
2.9 MeV
6Heg.s. 6Heg.s.
04
02
a 8Lig.s.
03
a 8Heg.s.
a 8Beg.s.
12C
12B
12Be
14
Comparison of 12Be and 12C
12C a ? (aaa) a
( M. Itoh et al. at Tohoku Univ. )
12Be a ? (6He6He) a
( A. Saito et al. at Tokyo Univ. )
There appear many resonances !!
0
7.5
12
No decays to a8He
15
Rotational bands Coexistence of MRs and
covalent SD
Exp. at RIKEN (Saito)
Exp. at RIKEN (Shimoura)
Exp. by Freer
Scattering region
Bound region
Green squares (p-)2(s)2
Green 6He 6He
Pink 5He 7He
Red Covalent SD
Blue a 8He
White square (p-)2(p-)2
16
Monopole Transition
Why monopole ?
Cluster structure
There is a possibility that monopole transitions
are enhanced If cluster structures are
developed. ( Ex lt 10MeV )
Pioneering work on monopole transition
Cluster correlation in a ground state (Yamada et
al., PTP, inpress)
Excitation of clusters relative motion (2hw)
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
Simple shell model (1p-1h, 2hw) No strength
around low-lying region, Exlt10MeV
17
Adiabatic energy surfaces in 12Be
3rd 0
VNN Volkov No.2G3RS
Adiabatic Energy surfaces
8He
GCM (03)
Cluster Excitation
1st 0
a 8He
(p-)2 (s)2
GCM (01)
a a Distance
a a Distance
18
Monopole transition of 12Be
Adiabatic connection enhances the Monopole
transition !
( a.u. )
8He
03
01 ? 03 is enhanced.
(p-)2 (s)2
01
a a distance ( fm )
19
10Be case M.I., PLB636, 236 (2006)
Energy spectra ( Jp 0 )
Adiabatic surfaces (Jp 0)
a6He(21)
Cluster
?i W(R)
20
Contents
Unified description of the a8He reactions and
the exotic structures in 12Be
M. I., N. Itagaki, H.Sakurai, K. Ikeda, PRL 100,
182502 (2008).
M. I., N. Itagaki, PRC78, 011602(R) (2008).
Results
M. I., N. Itagaki, Phys. Rev. Focus Vol.22,
Story4 (2008).
New features
1. Transfer coupling is important for the
formation of the sharp resonances.
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)
3. The energy spacing of the resonances becomes
quite small.
4. The monopole transition is enhanced with a
development of the cluster.
Future studies
1. Comparison with the recent experiment of the
a8He scattering (GANIL)
2. Systematic studies on the resonant scattering
of neutrons drip-line nuclei
(Resonance formation by neutron transfers )
21
Coverage by APS
American Phys. Society WEB Journal Phys. Rev.
Focus
(http//focus.aps.org/story/v22/st4)
See also, RIKEN RESEARCH 5 September (2008)
http//www.rikenresearch .riken.jp/research/517/
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(NZ dEgt10 MeV)
Extension of Cluster Concept
Rigid cluster
Loose cluster
dE1 MeV
dE2 MeV
05
7He
5He

03
1S
0
7MeV
5He
5He
0D
2
4 MeV
3MeV
6He
6He
0S
0S
0
0
8He
02
02
12C (aa) a
16O a 12C
12Be a a 4N
Excitation 8Be-a Rel. motion
Excitation 12C-a Rel. 12C Rot.
Neutron rearrangements with small energy
increasing
Clusters are rigid.
Clusters are loose !!
24
Generalized Two-center Cluster Model (GTCM)
M. Ito et al., PLB588(04), PLB636(06), PRL100(08)
12Beaa4N
a
8He
7He
5He
6He
6He
Mol. Orbit
Combine
Combined model of mol. orbit and asymptotic
channels
...
S


Y
C2
C3
C1
0Pi (ix,y,z) coupled channel with atomic basis
S, Ci Variational PRM
Absorbing BC
Scattering BC
Tr. Density
ltYf r Yigt
Resonance PRM PTP113 (05)
12Be(01) ?12Be(0ex) Monopole Transition
a8He Scattering PRC78(R) (08)
?i W(R)
25
IKEDA Diagram
Cluster structures in 4N nuclei
Ikedas Threshold rules
Molecular structures will appear close to the
respective cluster threshold.
Be isotopes
Molecular Orbital Itagaki et al.
a-Particle ? Stable
p?
3Hp 20 MeV
Systematic Appearance of a cluster structures
s
PRC61,62 (2000)
26
Studies on Exotic Nuclear Systems in (Ex,N, Z)
Space
Slow RI beam
Unbound Nuclear Systems
Decays in Continuum
Is Threshold Rule valid ??
Ex. energy
Structural Change
Low-lying Molecular Orbital p ??s?
N
( N,Z ) Two Dimensions
27
Molecular resonance phenomena in stable systems
12C12C at Coulomb barrier ?Sharp resonances
13C12C at Coulomb barrier ?NO clear resonances
H. Voit et al.,NPA476,491 (1988)
E. Almqvist et al., PRL4, 515 (1960)
28
Linear Combination of Atomic Orbital (LCAO)
Formulation 10BeaaNN
Z
(s)2 ( Pz(L) ? Pz(R) )2
a (0s)4
a
a
Pz(L)Pz(L) Pz(R)Pz(R) - 2Pz(L)Pz(R)
a 6He
6He a
5He 5He
Px(R)Px(R) Py(R)Py(R) Pz(R)Pz(R)
a
a
a6He(0)
( 12Beaa4N 38 AOs,K0 )
Total wave function Fully anti-symmetrized
(m,n)x,y,z
(a,b) L,R
Pm(a)Pn(b)
S
Variational PRM
29
Enhancement of the two neutron transfer
Strong decay into 6He6He
Open
Closed
Covalent SD, Sf,i 21
Unitary condition of S-matrix
5He 7He
6He 6He
4He 6He
a8He ? 6He6He
Jp 0
Large part of the flux flows to 6He6He.
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???????????????????????????? ???????????????
????????????????????
??????????????? (??)
???????????2hw??
( N ???????????? )
???????
N (?????) N (???)
??? ?????


N N low
N gt N low
???????????????????2hw????
?? ??????????Exlt10MeV???????????
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Why monopole ?
Cluster structure
There is a possibility that monopole transitions
are enhanced If cluster structures are
developed. ( Ex lt 10MeV )
Pioneering work on monopole transition
Cluster correlation in a ground state (Yamada et
al., PTP, inpress)
Excitation of clusters relative motion (2hw)
( N Quanta for relative motions )
Cluster basis
N (Lowest arrowed) N
(Higher quanta)
Shell model Cluster


N N low
N gt N low
2hw excitation of the seed of clusters in a
ground state
Simple shell model (1p-1h, 2hw) No strength
around low-lying region, Exlt10MeV