Geoscience Reference

In-Depth Information

where
M
c
is the reduced mass of the quasi-molecule XY
**
,

D
Œ.J
ƒ/.J
˙
ƒ
C
1/
1
=
2
; L
˙
D
L
˙
iL
:

Jƒ

˙

The quantity Q
v
;ˇƒ
is defined as the radial part of the nuclear matrix element and

equal to

D
v
ˇ
ˇ
ˇ
ˇ

ˇ
ˇ
ˇ
ˇ

ˇƒ
E
:

1

R
2

Q
v
;ˇƒ
D

The projections
L
˙
of the electron angular momentum operator
L
are defined

in the molecular frame system and affect the wave functions of the dissociative

channels
ˇƒ
at construction by the common quantum chemical rules. From

Eq.
1.26
it implies that unlike Eq.
1.25
the selection rule for Coriolis communication

is defined as

ƒ
D˙
1:

(1.27)

For homoatomic quasi-molecules X
2
the selection rules (
1.25
)and(
1.27
)are

provided by the condition: g
$
g;
u

$

u
. Note also that the part of the Coriolis

coupling proportional to
˝
L
2
˛
ƒ
ı
ƒƒ
0
is included in the definition of the first term in

Eq.
1.24
because the selection rules for this interaction are the same as in Eq.
1.25
.

Thus, the formal construction of solutions of the AI problem is completed.

Nevertheless, to visualize the physical picture of phenomena is appropriate to turn

to the energy spectrum of the intermediate Rydberg quasi-molecule states and, for

clarity, to analyze the structure of its adiabatic terms.

Rydberg States of the XY
**
Quasi-Molecule

1.3.5

From the integral equation (
1.15
) in the operator form, it follows that the eigenvalue

spectrum of the Rydberg energy of the intermediate complex XY
**
is determined

by the poles of the collision
T
matrix, which satisfy the matrix equation

8

<

9

=

l;
v
;N
j
Jl
v
N
ih
Jl
v
N
j
cot
"

#

X

i
X

ˇ

p
2.E
v
E
N
E/

t

j
Jˇ
ih
Jˇ
j

D
1
;

:

;

(1.28)

where
E
v
and
E
N
are the energies of vibrational and rotational motions. Matrix rank

for the given value of J equals the total number of channels taken into account

in e
C
XY
C

and X
*

C
Y configurations. Solutions of the transcendental equation

(
1.28
) represent a complicated set of complex spectral energy values, the imaginary

parts of which depend on the sign and the magnitude of the total energy
E
of the

system.