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    $\begingroup$ So, if I'm correct, what you're saying is that light of frequencies different from that of the transition frequency is doppler shifted to the transition frequency. However, the atom still must 'accept' a range of values, since there is a 0 probability that any frequency will be shifted to the exact transition frequency. $\endgroup$
    – Gerard
    Commented Mar 29, 2015 at 16:31
  • $\begingroup$ Actually the final acceptance is governed by the energy-time uncertainty m0nhawk mentioned in his answer. But normally (in 19th century physics) you do not observe single atoms. When you take $10^{23}$ atoms , their velocities are not the same but distributed (Maxwell&Boltzmann distribution). So you have a good chance that some of your atoms actually match the doppler shifted light frequency. Since they move in different directions with different velocities your observed spectral line is quite broad. $\endgroup$
    – bernd
    Commented Mar 29, 2015 at 16:38
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    $\begingroup$ This is only part of the answer. Even using spectroscopy that eliminates the Doppler shift, there is an innate Lorentzian line spread. $\endgroup$
    – zeldredge
    Commented Mar 29, 2015 at 16:42