The cross-section for a selected wavenumber r nm e m nm
ð Þ and the absorption line
center r nm e m
0
nm
À Á
[cm
2 ] are
r nm e m nm
ð Þ ¼
Z m 2
m 1
r nm e m nm
ð Þde m Á L e m nm ; e m
0
nm ; De m nm
À
Á
ð4:3:21Þ
r nm e m
0
nm
À Á ¼
Z m 2
m 1
r nm e m nm
ð Þde m Á
2
p Á De m nm
ð4:3:22Þ
for a Lorentzian lineshape, and
r nm e m nm
ð Þ ¼
Z m 2
m 1
r nm e m nm
ð Þde m Á G e m nm ; e m
0
nm ; De m nm
À
Á
ð4:3:23Þ
r nm e m
0
nm
À Á ¼
Z m 2
m 1
r nm e m nm
ð Þde m Á
4ln2
p
1
2 Á
1
De m nm
ð4:3:24Þ
for a Gaussian lineshape.
Since cross-section integrated over the absorption line is [31], p. 351:
Z m 2
m 1
r nm e m nm À e m
0
nm
À
Á de m ¼ 4:166 Á 10
À19
Á e m nm Á l
nm
e
2
ð4:3:25Þ
for R
nm
e in Debye, the r nm e m
0
nm
À Á
is
r nm e m
0
nm
À Á ¼ 2:652 Á 10
À19
Á
e m nm
De m nm
Á l
nm
e
2
ð4:3:26Þ
for a Lorentzian lineshape, and
r nm e m
0
nm
À Á ¼ 3:914 Á 10
À19
Á
e m nm
De m nm
Á l
nm
e
2 :
ð4:3:27Þ
for a Gaussian lineshape. A Lorentzian lineshape is used when collision broadening
occurs. A Lorentzian FWHM is equal to [9], p. 30
De m L ¼
Z L
c Á p
;
ð4:3:28Þ
Z L = 3.54 Á 10
16
Á p M (Torr) is a collision number with species M at T = 273 K.
A Gaussian lineshape is used for the description of the Doppler contour, and
Doppler FWHM is
100
4 Photolysis of Free Molecules