Geoscience Reference
In-Depth Information
Rydberg series with the dissociative continuum. The coupling between Rydberg and
dissociative channels (
1.22
) is determined analogously. The direct coupling among
dissociative channels dominates the inelastic transitions. The diagonal elements
t
ˇƒ;ˇ
0
ƒ
0
related to the elastic scattering in the dissociative channels have second-
order smallness with respect to the configuration coupling
V
CI
and are absent here.
1.3.4
Matrix Elements of Configuration Coupling
The explicit form of these elements depends significantly on the relative part played
by the XY
C
ion rotation and spin-orbit interaction. So long as the role of nucleus
rotation is characterized by the distance between the nearest rotation levels, there are
two limiting cases only. The first one (Hund's case
a
) takes place when the energy
of the spin-axis interaction is large in comparison with this distance. The second
one (Hund's case
b
) corresponds to their reverse relation. This case takes place for
light molecular ions only, which are the most interesting for us. Taking into account
the connection between the
q
-channel (Eq.
1.16
) and the adiabatic (Eq.
1.19
)basis
of states, we put the elements of configuration coupling into the form of two terms
lN
v
;ˇƒ
D
X
ƒ
0
V
CI
U
Jl
Nƒ
0
V
CI
lƒ
0
v
;ˇƒ
lƒ
v
;ˇƒ
C
X
ƒ
0
D
U
Jl
Nƒ
0
V
rad
U
Jl
Nƒ
0
V
cor
lƒ
v
;ˇƒ
:
(1.24)
The first term describes a nonadiabatic coupling of the intermediate Rydberg
complex with the dissociative continuum by means of nuclear radial motion. In the
case of weak dependence of the radial part of the CI on the internuclear distance
R
, the Frank-Condon representation V
rad
lƒ
.R
e
/
˝
v
ˇ
ˇ
ˇƒ
E
for the matrix
elements is equitable, where
ˇƒ
is the nuclear wave function of the dissociative
channel. The electron part of the matrix elements V
rad
lƒ
lƒ
v
;ˇƒ
D
V
rad
complies with the rigorous
selection rules:
ƒ
D
0:
(1.25)
The second term in Eq.
1.25
is caused by the nonadiabatic coupling of electron
motion with the internuclear axis rotation (Coriolis coupling) and can be written as
(Golubkov et al.
1997
)
n
Jƒ
D
J
ƒ
0
j
L
j
J
ƒ
E
ı
ƒ
0
;ƒ1
Q
v
;ˇƒ
2M
c
X
a
Jƒ
0
l
V
cor
lƒ
0
;ˇƒ
D
D
J
ƒ
0
j
L
C
j
J
ƒ
E
ı
ƒ
0
;ƒC1
o
;
C
Jƒ
C
(1.26)
