Doppler Broadening and Voigt Profiles

Lifetime broadening is ubiquitous, because all excited states decay. The observed absorption lineshape is seldom Lorentzian, however, since other mechanisms than lifetime broadening usually dominate the actual lineshape. 

As a result of the Doppler effect, a molecule traveling with velocity component along the propagation axis of an incident light beam will experience a light frequency that is shifted from that experienced by a stationary molecule by 

Here (Oq is the frequency experienced by the stationary molecule. In a thermal gas sample at temperature T, the one-dimensional Boltzmann velocity distribu- 

This is the Gaussian lineshape function, which arises from Doppler broadening. Like the Lorentzian function Pl( ) it maximizes at a = coq, and approaches zero as to - + oo. The fwhm of Pg o ) is 

Both lifetime and Doppler broadening are always present in gas samples. If these two are the only important broadening mechanisms, the resulting profile is given by the convolution 

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