levels with parity þ À1
ð Þ
JÀ1=2 is called e levels; and
levels with parity À À1
ð Þ
JÀ1=2 is called f levels:
ð4:6:2Þ
The e/f labels are independent of the coupling case; they depend on the total
angular momentum and the state parity.
If one uses e/f labels [31], p. 145, [40], perturbations are governed by the
DJ ¼ 0; e $ e; f $ f ; g $ g; u $ u
ð4:6:3Þ
selection rules. The g $ g, u $ u selection rules are valid for all types of perturbation except hyperfine and Stark perturbations.
Rovibronic wave functions of the isolated (free) diatomic molecules are
described in a Hund’s (a) case as follows [41]:
JMXeKv
j
i¼ 2
À
1
2 JMX
j
i
½
KR
j iþ e J; M; ÀX
j
iÀK; ÀR
j
iv j i:
ð4:6:4Þ
Here:
J denotes the total angular momentum with projection along space- and
molecule-fixed axes of M and X, respectively;
K; R
j
i denotes the electronic wave function with projections K and R, respectively, of the electronic orbital and spin angular momenta along the molecular axis;
v
j i denotes the vibrational wave function with quantum number v.
The symmetry index is e = ±1, and the total parity I of the molecular wave
function of the
2 R states is e(–1)
J−1/2−s where s = 0 and 1 for the R
+ and R
− states,
respectively, and zero otherwise. For P and R
+ states, the e = +1 levels are labeled
e, and the e = −1 levels are labeled f. This assignment is reversed for R
− states [41].
The assignment of quantum numbers, indices, labels, and parity to the P and R
molecular states in (4.6.2) are clarified in Table 4.3.
For the gerade (g) states
e ¼ À1
ð Þ
J
ð4:6:5Þ
For the ungerade (u) states
e ¼ À1
ð Þ
J þ 1
ð4:6:6Þ
For the R
+
, 0
þ
g and K 6 ¼ 0, X 6 ¼ 0 states, the e = +1 levels are labeled e and the
e = −1 levels, labeled f. This assignment is reversed for R
− states.
4.6 Intramolecular Perturbations …
109
ð Þ
JÀ1=2 is called e levels; and
levels with parity À À1
ð Þ
JÀ1=2 is called f levels:
ð4:6:2Þ
The e/f labels are independent of the coupling case; they depend on the total
angular momentum and the state parity.
If one uses e/f labels [31], p. 145, [40], perturbations are governed by the
DJ ¼ 0; e $ e; f $ f ; g $ g; u $ u
ð4:6:3Þ
selection rules. The g $ g, u $ u selection rules are valid for all types of perturbation except hyperfine and Stark perturbations.
Rovibronic wave functions of the isolated (free) diatomic molecules are
described in a Hund’s (a) case as follows [41]:
JMXeKv
j
i¼ 2
À
1
2 JMX
j
i
½
KR
j iþ e J; M; ÀX
j
iÀK; ÀR
j
iv j i:
ð4:6:4Þ
Here:
J denotes the total angular momentum with projection along space- and
molecule-fixed axes of M and X, respectively;
K; R
j
i denotes the electronic wave function with projections K and R, respectively, of the electronic orbital and spin angular momenta along the molecular axis;
v
j i denotes the vibrational wave function with quantum number v.
The symmetry index is e = ±1, and the total parity I of the molecular wave
function of the
2 R states is e(–1)
J−1/2−s where s = 0 and 1 for the R
+ and R
− states,
respectively, and zero otherwise. For P and R
+ states, the e = +1 levels are labeled
e, and the e = −1 levels are labeled f. This assignment is reversed for R
− states [41].
The assignment of quantum numbers, indices, labels, and parity to the P and R
molecular states in (4.6.2) are clarified in Table 4.3.
For the gerade (g) states
e ¼ À1
ð Þ
J
ð4:6:5Þ
For the ungerade (u) states
e ¼ À1
ð Þ
J þ 1
ð4:6:6Þ
For the R
+
, 0
þ
g and K 6 ¼ 0, X 6 ¼ 0 states, the e = +1 levels are labeled e and the
e = −1 levels, labeled f. This assignment is reversed for R
− states.
4.6 Intramolecular Perturbations …
109