4.6.1 Perturbations Between Bound States of Diatomic
Molecules
In this section, the perturbation examined in [31], which lead to large mixing of
states are discussed, namely:
1. Perturbations between states of the same symmetry;
2. Perturbations between electronic states of different symmetry due to interactions
between spin and angular momenta of the electrons ð b
H SO , spin–orbit operator)
as well as rotational perturbations;
Besides, hyperfine interaction, which has not been discussed in [31], will be
analyzed. Interactions between bound state rovibronic levels and the vibrational
continuum of another electronic state leading to predissociation of the former are
discussed in Sect. 4.7.
Selection rules for perturbations are as follows (see [23], p. 285 and Tables 4.1,
4.2):
1. Both states must have the same total angular momentum J; that is DJ = 0.
Table 4.1 Selection rules for the K, S, R, Ω and J angular momenta and various nature of the
coupling operator [39] (reproduced by permission of EDP Science)
Operator
a
|ΔK|
|ΔS|
|ΔR|
|ΔΩ|
|ΔJ|
Z, l,
J variation
b
Order of
magnitude for I 2 ,
cm
−1 c
b
T N
0
0
0
0
0
*l
−0,75
100
b
H SO
1
1
1
0
0
*Z
4
7•10
3
b
H SS
2
2
2
0
0
–
1
b
H OR
1
0
1
1
0
*J
10
–4
•J
b
H SR
1
1
1
1
0
*J
10
–4
•J
b
H G
1
0
1
1
0
*l
−1
•Z
0.06•J
b
H HFS
b
H MD
1
1
1
1
1
*Z
3
0.3
b
H EQ
2
0
0
2
2
*Z
3
0.1
b
H Z
1
0
1
1
1
–
0.5
b
H S
1
0
0
1
1
–
1
a b
T N is the nuclear kinetic energy operator [31] p. 168, b
H SO is the spin–orbit operator, b
H SS is the
spin–spin operator, b
H OR is the orbit-rotational operator, b
H SR is the spin-rotational operator, b
H G is
the gyroscopic operator, b
H HFS ¼ b
H MD þ b
H EQ is the hyperfine operator, b
H MD is the
magnetic-dipole operator, b
H EQ is the electric-quadrupole operator, b
H Z is Zeeman operator, b
H S
is Stark operator
b
The dependence of matrix elements on nuclear charge Z, reduced mass l and total angular
momentum J.
c A rough estimate of the order of magnitude for iodine molecules for the magnetic field 1 T, the
electric field 10
6 V/cm and dipole 1 Debye.
4.6 Intramolecular Perturbations …
107
Molecules
In this section, the perturbation examined in [31], which lead to large mixing of
states are discussed, namely:
1. Perturbations between states of the same symmetry;
2. Perturbations between electronic states of different symmetry due to interactions
between spin and angular momenta of the electrons ð b
H SO , spin–orbit operator)
as well as rotational perturbations;
Besides, hyperfine interaction, which has not been discussed in [31], will be
analyzed. Interactions between bound state rovibronic levels and the vibrational
continuum of another electronic state leading to predissociation of the former are
discussed in Sect. 4.7.
Selection rules for perturbations are as follows (see [23], p. 285 and Tables 4.1,
4.2):
1. Both states must have the same total angular momentum J; that is DJ = 0.
Table 4.1 Selection rules for the K, S, R, Ω and J angular momenta and various nature of the
coupling operator [39] (reproduced by permission of EDP Science)
Operator
a
|ΔK|
|ΔS|
|ΔR|
|ΔΩ|
|ΔJ|
Z, l,
J variation
b
Order of
magnitude for I 2 ,
cm
−1 c
b
T N
0
0
0
0
0
*l
−0,75
100
b
H SO
1
1
1
0
0
*Z
4
7•10
3
b
H SS
2
2
2
0
0
–
1
b
H OR
1
0
1
1
0
*J
10
–4
•J
b
H SR
1
1
1
1
0
*J
10
–4
•J
b
H G
1
0
1
1
0
*l
−1
•Z
0.06•J
b
H HFS
b
H MD
1
1
1
1
1
*Z
3
0.3
b
H EQ
2
0
0
2
2
*Z
3
0.1
b
H Z
1
0
1
1
1
–
0.5
b
H S
1
0
0
1
1
–
1
a b
T N is the nuclear kinetic energy operator [31] p. 168, b
H SO is the spin–orbit operator, b
H SS is the
spin–spin operator, b
H OR is the orbit-rotational operator, b
H SR is the spin-rotational operator, b
H G is
the gyroscopic operator, b
H HFS ¼ b
H MD þ b
H EQ is the hyperfine operator, b
H MD is the
magnetic-dipole operator, b
H EQ is the electric-quadrupole operator, b
H Z is Zeeman operator, b
H S
is Stark operator
b
The dependence of matrix elements on nuclear charge Z, reduced mass l and total angular
momentum J.
c A rough estimate of the order of magnitude for iodine molecules for the magnetic field 1 T, the
electric field 10
6 V/cm and dipole 1 Debye.
4.6 Intramolecular Perturbations …
107