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Jost 関数法と共鳴部分幅および仮想状態. Jost 関数法 (Jost Function Method) 共鳴部分幅 （ Partial Widths) 仮想状態 (Virtual States). Table I. Values of the resonant poles of the Noro-Taylor model. pole E r (a.u.) Γ (a.u.) 14.768197 1.420192 × 10 -3 27.241200 1.511912 - PowerPoint PPT Presentation
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Jost 関数法と共鳴部分幅および仮想状態
(1) Jost 関数法 (Jost Function Method)
(2)共鳴部分幅 （ Partial Widths)
(3)仮想状態 (Virtual States)
Table I. Values of the resonant poles of the Noro-Taylor model.
pole Er (a.u.) Γ (a.u.)
1 4.768197 1.420192 ×10 -3
2 7.241200 1.511912
3 8.171216 6.508332
4 8.440526 12.56299
5 8.072642 19.14563
6 7.123813 26.02534
7 5.641023 33.07014
8 3.662702 40.19467
9 1.220763 47.33935
10 -1.658115 54.46087
11 -4.950418 61.52509
12 -8.635939 68.50621
Partial Decay Widths
Channel radius dependence
Definition of partial widths
2
2
1
2
12
21
1
2
c
c
cc
cc
c
c
A
A
k
k
)()(lim )( rkHAr ccc
cresr
N
n n1
N. Moiseyv and U. Peskin; Phys. Rev. A42(1990) 255.
Partial widths of resonant states
Jost Function Method; S.A. Sofianos and S.A. Rakityansky J. Phys. A: Math. Gen. 30(1997), 3725, J. Phys. A: Math. Gen. 31(1998), 5149.
}{),( )('
)('
)('
)('
1''
)(2
)(
mnnmnnN
nnnn
n
nnmr FHFHVH
kirEF
: Homogeneous solutions ),()( rkH nn
0),(det )( EF : Resonances
Partial Width
|||)()(
lim|''''' nn
nn
nnres
nnres
resEEn
n
SS
SEESEE
m resmnresmn
m resmnresnm
resE
nn
resE
nn
EGEF
EGEF
FF
FF
)()(
)()(
'
)(
'
)(
'')(
)(
)(
)(
)},(det{)(
),()(
1)(
EFEG
EF nm
nm
2/iEEi)E(S)E(S
r
'nn'nn
Bn'nn
),(1
rn nres
N. Moiseyev and U. Peskin; Phys. Rev. A42(1990) 255.
Current density method for partial widths
),()( rjAr nnrn
),()( )( rkHrj nnkn
n
Partial Width:2
''
'
' n
n
nn
nn
n
n
A
A
k
k
T-matrix scheme
2
res)f(
n
res)f(
n
n
n |)|V|(
)|V|(|
''
n
nres )r()r(
)rk(Hk)r( n)(
nn
n)f(n
'n'n'nnn
)(
n
nres
)f(n )r(V)rk(drHk)|V|(
'nm'n
mm'nnn
)(
n
n )r(cV)rk(drHk
m 'nm'n'nnn
)(m
n
n )r(V)rk(drHck
),E(Fcki res)(
nmm
mn
n
)r(a)r( )f(nnrn
),E(Fck2
1
)rk(Hk
)}r,E(F)rk(H)r,E(F)rk(H{c21
lim
)r(
)r(clima
r)(
nmm
mn
n
n)(
nn
n
mr
)(nmn
)(nr
)(nmn
)(nm
r
)f(n
mnmm
rn
)r,E(Fc)rk(Hlim
)rk(HAlim)r(lim
n mres
)(nmmn
)(n
r
nn
)(nn
rres
r
),E(FcNA resm
)(nmmn
N
n n1
Jost Function Method
+ Complex Scaling Method
Complex Scaled Jost Function Method; (CSJFM)
Application to a three body resonance
5He: 4He+n
H. Masui, S. Aoyama, T. Myo, K. Kato and K. Ikeda, Nucl. Phys. A673 (2000), 207
10Li: 9Li+n
