Extremely small natural line width

The small natural width of 2E = 0.0065 mm s implies an extremely narrow relative line width of r/ y = 1.1 lO, which is about 30 times narrower than that for the 14.4 keV state of Fe. 

Using the dispersion profiles of Doppler-free molecular lines in polarization spectroscopy (Sect.7.4) it is possible to stabilize a laser to the line center without frequency modulation. An interesting proposal for stabilizing a dye laser on atomic or molecular transitions is based on Doppler-free two-photon transitions (Sect.7.5) [5.74]. This has the additional advantage that the lifetime of the upper state can be very long, and the natural line-width may become extremely small. An example of a promising candidate is the ls- 2s transition of atomic hydrogen, which should have a natural linewidth of less than 1 Hz. 

The problem of transit-time broadening was recognized many years ago in electric or magnetic resonance spectroscopy in molecular beams [1253]. In these Rabi experiments [1254], the natural linewidth of the radio frequency or microwave transitions is extremely small because the spontaneous transition probability is, according to Vol. 1, (2.22), proportional to co. The spectral widths of the microwave or RF lines are therefore determined mainly by the transit time AT = d/v of molecules with the mean velocity v through the interaction zone in the C field (Fig. 5.10a) with length d. 

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