and so-called dimensionless oscillator strength
f nm ¼ l
nm
e
2 Áe m nm
4p Á m e Á c
3 he 2
ð4:3:13Þ
(m e and e are the mass and charge of the electron) are also used to characterize
intensities of transitions.
The relations between quantities under discussion are as follows [9], p. 26, [10],
p. 418, [31], p. 350]:
f nm ¼ 4:20 Á 10
À8
Z
e m 2
e m 1
k e m
ð Þde m
ð4:3:14Þ
f nm ¼
m e Á h Á c
2
Á e m nm
p Á e 2
Á B mn
ð4:3:15Þ
f nm ¼ 4:703 Á 10
À7
Á e m nm Á l
nm
e
2
ð4:3:16Þ
for l
nm
e in Debye.
There are relations between cross-section for the absorption line center r nm e m
0
nm
À Á
[cm
2 ], selected wavenumber e m remote the absorption line center, r nm e m nm
ð Þ [cm
2 ]
and cross-section integrated over the absorption line
R m 2
m 1
r nm e m nm À e m
0
nm
À
Á de m [cm
2
Á
cm
−1 ] [31], p. 351. They are different for Lorentzian
L e m nm ; e m
0
nm ; De m nm
À
Á ¼
1
p
Á
De m nm =2
ð
Þ
De m nm =2
ð
Þ
2 þ e m nm À e m 0
nm
À
Á 2
ð4:3:17Þ
and Gaussian
G e m nm ; e m
0
nm ; De m nm
À
Á ¼
4ln2
p
1
2 Á
1
De m nm
Á exp À e m nm À e m
0
nm
À
Á 2 Á
4ln2
De m nm
ð
Þ
2
"
#
ð4:3:18Þ
lineshapes ðDe m nm is FWHM of the line). Both L e m nm ; e m
0
nm ; De m nm
À
Á
,
G e m nm ; e m
0
nm ; De m nm
À
Á
are normalized to 1:
Z m 2
m 1
L e m nm ; e m
0
nm ; De m nm
À
Á de m ¼ 1
ð4:3:19Þ
Z m 2
m 1
G e m nm ; e m
0
nm ; De m nm
À
Á de m ¼ 1:
ð4:3:20Þ
4.3 Absorption. Absorption Band Intensities …
99