(V.B.4.a.3-2)
The second approach makes no attempt to identify and characterize individual lines, but rather seeks to predict, on a point-by-point basis, the spectra as a function of temperature. Because of the exponentials in the Gaussian lineshape and in the lower state energy term, the absorbance as a function of frequency can be recast as
(V.B.4.a.3-2)
with the Doppler width (HWHM) given by
(V.B.4.a.3-3)
where Na is Avogodro’s number, and M is the molecular mass.
The absorbance normalized by the nL/Q factor then becomes
, (V.B.4.a.3-4)
with
. (V.B.4.a.3-5)
According to equation (V.B.4.a.3-4) every frequency slice of the data (one for each temperature) can be represented by two parameters S̃ijµ 2 and Ê. On line center, when v = v0, Ê equals the lower state energy, while S̃ijµ 2 corresponds to the line strength. Off of line center, the meaning of S̃ijµ 2 and Ê are less physical, but equation (V.B.4.a.3-4) is still a valid fitting function for describing the spectral intensity for an unblended line.