Geoscience Reference
In-Depth Information
So long as the adiabatic basis
j
JMlƒ
v
i
and channel basis (
1.16
) are connected
by the unitary transformation (Golubkov et al.
1997
)
j
JMlƒ
v
i D
X
N
U
Jl
Nƒ
j
JMlN
v
i
(1.19)
t
lN
v
;l
0
N
0
v
0
for
elements we have
t
lN
v
;l
0
N
0
v
0
D
X
ƒ
Nƒ
˝
v
ˇ
ˇ
tan
ƒ
.R/
ˇ
ˇ
v
0
˛
a
Jƒ
l
0
U
Jl
0
a
Jƒ
l
U
Jl
ƒN
0
;
(1.20)
where U
Jl
Nƒ
is the Fano's rotation submatrix. Therefore, taking the pattern of
Rydberg terms and the information about the adiabatic wave functions (
1.17
)as
a basis, one can define by Eq.
1.20
a complete set of the
t
matrix elements.
According to Eqs.
1.12
and
1.18
, the reaction matrix
t
satisfies the operator
equation
P
Z
j
ˇƒ
ih
ˇƒ
j
E
E
ˇ
X
ˇ
t
D
t
C
t
1
t
dE
ˇ
:
From this equation with regard to the smallness of the configuration coupling,
we can obtain the following expressions for the matrix elements:
t
lN
v
;l
0
N
0
v
0
D
t
lN
v
;l
0
N
0
v
0
P
Z
V
CI
X
ˇ
lN
v
;ˇƒ
V
CI
1
ˇƒ;l
0
N
0
v
0
E
E
ˇ
C
dE
ˇ
;
(1.21)
t
lN
v
;ˇƒ
D
V
CI
lN
v
;ˇƒ
P
Z
t
lN
v
;l
0
N
0
v
0
V
CI
X
l
0
N
0
v
0
1
l
0
N
0
v
0
;ˇƒ
E
E
ˇ
C
dE
ˇ
P
Z
V
lN
v
;ˇ
0
ƒ
0
V
CI
X
1
ˇ
0
ƒ
0
;ˇƒ
E
E
ˇ
C
dE
ˇ
;
(1.22)
ˇ
0
¤
ˇ;ƒ
0
t
ˇƒ;ˇ
0
ƒ
0
D
V
CI
ˇƒ;ˇ
0
ƒ
0
:
(1.23)
The value of the CI is defined by specific peculiarities of the quasimolecule
electron structure. The examples of well-known e
C
XY
C
systems show that it is
really small, i.e., the values
ˇ
ˇ
ˇ
lN
v
;ˇƒ
ˇ
ˇ
ˇ
2
V
CI
are small in comparison with unity. Elements
t
lN
v
;l
0
N
0
v
0
in (
1.21
) are presented in the form of two terms, where the first one
is caused by the interaction with the ion core and the second by the mixing of
