Velocity selection in a Doppler-broadened ensemble of atoms interacting with a monochromatic laser beam

There is extensive use of monochromatic lasers to select atoms with a narrow range of velocities in many atomic-physics experiments. For the commonplace situation of the inhomogeneous Doppler-broadened (Gaussian)linewidth exceeding the homogeneous (Lorentzian) natural linewidth by typically two orders of magnitude, a substantial narrowing of the velocity class of atoms interacting with the light can be achieved. However this is not always the case, and here we show that for a certain parameter regime there is essentially no selection---all of the atoms interact with the light in accordance with the velocity probability density. An explanation of this effect is provided, emphasizing the importance of the long tail of the constituent Lorentzian distribution in a Voigt profile.