Download - 軽い不安定核における 共鳴状態の構造
11
軽い不安定核における
共鳴状態の構造
KEK 理論セミナー 2010.10.07
明 孝之
大阪工業大学
Outline
1. Structures of He isotopes2. “core+valence neutrons” with complex scaling 3. Results
• 7He (+3n) , 8He (+4n)4. Tensor correlation in 4,5,6He using “TOSM”
TM, K. Kato, K. Ikeda PRC76 (2007) 054309TM, K. Kato, H. Toki, K. Ikeda, PRC76 (2007) 024305TM, R. Ando, K. Kato PRC80 (2009) 014315TM, R. Ando, K. Kato PLB691(2010)150 TM, H. Toki, K. Ikeda PTP121(2009)511
3
Nuclear Chart
Observation of halo structure in 11LiI.Tanihata et al. PRL55(1985)2676.
11Li
44
Characteristics of He isotopes (expt.)
Halo
Skin
4-body resonance
5-body resonance3-body
resonance
4Cf. TUNL Nuclear Data Evaluation Golovkov et al., PLB672(2009)22
• Cluster Orbital Shell Model (COSM)Open channel effect is included. – 8He : 7He+n, 6He+2n, 5He+3n, ...
• Complex Scaling Method
Resonances with correct boundary condition as “Gamow states”
Give continuum level density (resonance+continuum)
5Y. Suzuki, K. Ikeda, PRC38(1988)410, H. Masui, K. Kato, K. Ikeda, PRC73(2006)034318
(4He)
S. Aoyama, T. Myo, K. Kato, K. Ikeda, PTP116(2006)1 (review)
i ie , e r r k k
Method
E=Eri/2
6
Cluster Orbital Shell Model• System is obtained based on RGM equation
1
4 4( He) ( ) ( He) ( He) ( ) 0N
V Vji
Ai iN n H E N n C
A
4rel( He) ( He) ( )V
AH H H N n 1
4( He) ( He) ( )V
N
i ii
A C N n
A
44( He) : (0s)
• Orthogonarity Condition Model (OCM) is applied.
c
4
4He1
( )VNN
i jnncnklk
i k k lj i i jk
p pV C E E CT V
A m
PF =0 : i
1 2 3( ) : 2 Vi ii i in LN A{
i : configuration index
No explicit tensor correlation
, Gaussian expansion
Remove Pauli Forbidden states (PF)
valence neutron number
7
Hamiltonian
• V4He-n : microscopic KKNN potential
• phase shifts of 4He+n scattering
• Vn-n : Minnesota potential with slightly strengthened
A. Csoto, PRC48(1993)165. K. Arai, Y. Suzuki and R.G. Lovas, PRC59(1999)1432.TM et al. PTP113(2005)763.TM, S. Aoyama, K. Kato, K. Ikeda, PRC63(2001)054313
(4He)
Fit 6He(0+)
8
Complex scaling for 3-body case( ) : exp( ) , exp( ) , U i i r r k k
1 B B SSB
S
10 9
1
( Li+n , Li+n )
+
n
C
R
B
C
BB
R
C
R
T. Berggren, NPA109(’68)265.J.Aguilar and J.M.Combes, Commun. Math. Phys.,22(’71)269.E.Balslev and J.M.Combes, Commun. Math. Phys.,22(’71)280.
B.G. Giraud, K. Kato, A. Ohnishi
J. Phys. A 37 (‘04)11575
Completeness relation
9
Schrödinger Eq. and Wave Func. in CSM1( ) ( )U HU H T V 2 , ( )i iT e T V V e
r3/ 2 , ( ) ( )i iH E H E e e
r r
Asymptotic Condition in CSM ( ) r
( )
r
r
resr r
resr r
r r r r
exp( ) exp( )
exp( ) exp( )
exp cos( ) exp sin( )
i
iik r i e r
ik r i r e
i r r
rr r r, 0ik e
State No scaling ScalingBound
Resonance
Continuum
0 0
ie k r ie k r0
10
Treatments of the unbound states in CSM
• Exact asymptotic condition for resonances• Discretize continuum states.
1 2( )nn A{
cf. Continuum Discretized Coupled Channel (CDCC) calculation by Kyusyu Group
11 9
1( Li) ( Li) ( )
N
i ii
nn
A
2 ( )
Nnl
n lmn
a rC r Y re
Gaussian expansioni: configuration index
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Spectrum of 6He with 4He+n+n model
A. Csoto, PRC49 (‘94) 3035, S. Aoyama et al. PTP94(’95)343, T. Myo et al. PRC63(’01)054313
Eth(4He+n+n)
4He+n+n
6He(*)
5He+n
12121212TM, K.Kato, K.Ikeda PRC76(’07)054309TM, R.Ando, K.Kato PRC80(’09)014315
4-bodyresonance
5-body resonance
3-bodyresonance
TUNL Nuclear Data Evaluation
He isotopes : Expt vs. COSM (4He:(0s)4)
TM, R.Ando, K.Kato, PLB691(‘10)150
13
Matter & Charge radii of 6,8He
[fm]
I. Tanihata et al., PLB289(‘92)261 G. D. Alkhazov et al., PRL78(‘97)2313O. A. Kiselev et al., EPJA 25, Suppl. 1(‘05)215. P. Mueller et al., PRL99(2007)252501
TheorExptRm
Rch
14
6He=4He+n+n with ACCC+CSM
S. Aoyama (Niigata) PRC68(’03)034313
Eth(4He+n+n)
ACCC: Analytical Continuation in Coupling Constant (Niigata group)
Large decay width is obtained.
H H V
soft dipole resonance in 6He (1−). E=(3.02i15.6) MeV
15
0 (0)(0)
†
1 1Im Tr ( ) ( ) , ,
1 Tr ( ) ( ) 1 (single channel case 2
)
E G E G E GE H
dE S E S E ddEi dE
Continuum Level Density in CSM
S. Shlomo, NPA539(’92)17K. Arai and A. Kruppa, PRC60(’99)064315R. Suzuki, T. Myo and K. Kato, PTP113(’05)1273.
• CLD in CSM
00
1
1 (asymptotic)
GE H
GE H
01 Im Tr ( ) ( )E G E G E
(Kinetic)
16
4He+n scattering with complex scaling
Energy eigenvalues P3/2 scattering phase shift
30 Gaussian basis functions
17
4He+n scattering with discretized continuum
Energy eigenvaluesmeasured from Eth(4He+n)
Phase shifts(s,p-waves)
R. Suzuki, T. Myo and K. Kato, PTP113(’05)1273.
18
Strength function in CSM( )S E
† 1ˆ ˆ( ) ( ) Im ( )IIS E O O E E R E
• Strength function
• Green’s function and Response function
1( ) CB R CB RC
B B CB R C
dEE E E
G EE H E E E
( ) ( ) ( ) ( )B R CS E S E S E S E T. Berggren, NPA109(’68)265, T. Myo, A. Ohnishi and K. Kato, PTP99(’98)801
†
† †
†
ˆ( )
ˆ ˆ ˆ
ˆ ˆ
(ˆ
) II
B B I R R II I
B RB R
IC CIC
C C
R E O O
O O O OE E E E
O OdEE E
G E
Bi-orthogonal relation
19
Energy eigenvalues E1 transition
E1 of 6He into 4He+n+n(3-body breakup)
20
Coulomb breakup strength of 6He
6He : 240MeV/A, Pb Target (T. Aumann et.al, PRC59(1999)1252)
TM, K.Kato, S. Aoyama and K.IkedaPRC63(2001)054313.
6 4He (G.S.) He n n
Kikuchi, TM, Takashina, Kato, IkedaPTP122(2009)499PRC81 (2010) 044308
E1+E2Equivalent photon method
Coulomb breakup strength of 11Li
E1 strength by using the Green’s function method
+Complex scaling method+Equivalent photon method (TM et al., PRC63(’01))
• Expt: T. Nakamura et al. , PRL96,252502(2006) • Energy resolution with =0.17 MeV.E
11 9Li (G.S.) Li n n
No three-body resonance
T.Myo, K.Kato, H.Toki, K.IkedaPRC76(2007)024305
22222222
7He (unbound) : Expt vs. Complex Scaling
1.50
1.95
Experiments TM, K.Kato, K.Ikeda PRC76(’07)054309
n n n 4(0 )s
complex scaling4-body resonance
23
Experiments of 7Hea) RIKEN p(8He,d)7He
A. A. Korsheninnikov et al., PRL82(1999)3581.
b) Berlin 9Be(15N,17F)7He G. Bohlen et al. ,PRC64(2001)024312.
c) GSI 8He breakup M. Meister et al., PRL88(2002)102501.
d) ANL 2H(6He, p)7He at 11.5 MeV/u A. H. Wuosmaa et al., PRC72(2005) 061301.
e) SPIRAL p(8He,d)7He F. Skaza et al., PRC73(2006)044301.
f) KVI, 7Li(d,2He)7He N. Ryezayeva et al., PLB639(2006)623.
2424
S-factor of 6He-n component in 7He
,'6 ' 7 2He HeJJ nlj
nlj
J JS a Bi-orthogonal relationT. Berggren,
NPA109(1968)265
TM, K.Kato, K.Ikeda, PRC76(2007)054309
7He(J)
Weak coupling of 6He(0+)+n(p1/2)
6He(halo)
2525
One-neutron removal strength in CSM( )S E
† 11
† 1 1
( ) ( )
1 Im ( )
( )
AAA A
A AA A
i
i i
i
iii
i
a a
S E a a E E
R E
R EE E
• Strength function and response function
• Complex scaled-Green’s function
1( ) i i
i iG E
E H E E
T. Berggren, NPA109(’68)265, T. Myo, A. Ohnishi and K. Kato, PTP99(’98)801
Bi-orthogonal relation
S.Aoyama, TM, K.Kato, K.Ikeda, PTP116(2006)1 (review)
complete set of (A-1) SYSTEM
Response function
energy of (A-1) SYSTEM
2626
', '
6 7 2( ) He ( ) HeJ
J J nljnlj
JS E E a
7He(3/2−)
” 4He+n+n” complete set using CSM
4He+n+n
6He(*)
5He+n
n−1
One-neutron removal strength of 7HeGSTM, Ando, KatoPRC80(2009)014315
2+1
4He+2n
27
32000 dim. Full diagonalization of complex matrix @ SX8R of NEC
Energy spectrum 8He with complex scaling
TM, R.Ando, K.Kato, PLB691(‘10)150
28
8He : 0+1 & 0+
2 states
0+1
0+2
sum=4
†lj lja a
0+1 : (p3/2)4 ~ 87%
0+2 : (p3/2)2(p1/2)2 ~ 96%
lj
8He : 0+1 & 0+
2 states
29
0+1
0+2
sum=4C2=6
J
†π πJ J(αβ) (αβ)A A
: orbit
(p3/2)4
0+ : 2+ = 1 : 5(p3/2)2(p1/2)2
0+ : 1+ : 2+ = 2 : 1.5 : 2.5
Cf. AMD by Kanada-En’yo
Monopole Strength of 8He (Isoscalar)
30
6He+2n
0+2
4He+4n7He+n
Spin flip : p3/2 → p1/2
CSM=20 deg.
Monopole Strength of 8He (Isoscalar)
31
CSM=20 deg.
6He+2n4He+4n7He+n
7He+n
2r
0+2
Spin flip : p3/2 → p1/2
32
Summary• Cluster Orbital Shell Model
+ Complex Scaling (Level density)• Coulomb breakups of 6He and 11Li
• 7He : Importance of 6He(2+1) resonance
• 8He : Five-body resonances– Differences between 0+
1 and 0+2
– Monopole strength : 8He → 7He+n → 6He+n+nCf: Coulomb breakup, Iwata et al. PRC62 (2000) 064311
2n density in 6He
33
Dineutron
Cigar
Y. Kikuchi
Lowest config.
6He(t,p)8He reaction (2n transfer)• PLB672(2009)22, JINR, Dubna
0+2