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
2
7.241200
1.511912
3
8.171216
6.508332
4
8.440526
12.56299
5
8.072642
19.14563
6
7.123813
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
1.420192 ×10 -3
26.02534
Partial Decay Widths
Channel radius dependence
Definition of partial widths
lim res (r)   Ac H (kc r)
r 
( )
c
c
c2 c1 kc2 A

c1 c2 kc1 A
2
c2
2
c1
  n
N

n1
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.
( )
r Fnm
( E, r )  
n
i2kn
Hn() (kn , r )
det F
( )
() N
Hn  Vnn'{Hn(' ) Fn('m)
n'1
: Homogeneous solutions
( E, )  0 : Resonances
 Hn(' ) Fn('m)}
Partial Width
Snn' (E)  S (E)nn'
B
n
n n '
i
E  E r  i / 2
n
( E  Eres )Snn
Snn
| Elim
|

|
|
n' Eres ( E  Eres )Sn'n' Sn'n'
F


F
()
()


Eres
F
( )
F
( )
nn
Eres
n 'n '
()
nm
F ( Eres )Gmn ( Eres )
 ()
F
(
E
)
G
(
E
)
n
'
m
res
mn
'
res
m

m
Gnm ( E)
F ( E, ) nm 
( )
det{F ( E, )}
( )
1
Current density method for partial widths
N. Moiseyev and U. Peskin; Phys. Rev. A42(1990) 255.
 res  n1n (r ),
 n (r ) 
A
j
(
r
),
r 
n n
jn (r ) 
n
( )
H
(
k
,
r
)
n
kn
Partial Width: n   n ' kn An
n '
 n kn ' An '
2
T-matrix scheme
n ( | V | res) 2
|
|
n' ( | V | res)
(f )
n
(f )
n'
res(r)  n (r)
n

 (r)  n k H(n) (k n r)
n
(f )
n
((nf ) | V | res)  n k  drH( ) (k n r) Vnn'n ' (r)
n
n'
 n k  drH( ) (k n r) Vnn'  cmn 'm (r)
n
n'
m


 n k  cm  drH( ) (k n r) Vnn'n 'm (r)
n m
n'


()
 i n k  cmFnm
(Eres, )
n m
n (r) r
a  (r)

(f )
n n
  cmnm(r) 

a n  lim  m (f )
r  
n (r) 


1

()
()
( )
( )
c
{
H
(
k
r
)
F
(
E
,
r
)

H
(
k
r
)
F
(
E
,
r
)}
n
n
nm
r
 2  m n n nm r

 lim  m

r 
n
()


H
(
k
r
)
k n n n


1 k n
()

c
F
(
E
,

)

m
nm
r
n m
2
lim res(r)  lim  An H (k n r)
r 
r 
()
n
n
 lim  H (k n r) c F (Eres, r)
r 

( )
n
n
( )
m nm
m
An  Nc F (Eres, )
( )
m nm
m
  n
N

n1
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

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