Evaluation of the second-order Doppler shift in the Mg frequency standard

We report in this paper the first evaluation of the second-order Doppler shift in the Mg frequency standard. Three methods are considered: direct theoretical computation, Fourier analysis of the experimental Ramsey curve, and Fourier analysis of the discrimination curve. The results obtained are compared in a practical experimental case and turn out in satisfactory agreement, allowing a good confidence on the determination of the shift at the accuracy level of /spl plusmn/3/spl times/10/sup -13/. The considerations reported in this paper may be of general interest for frequency standards based on atomic or molecular beams with transverse dimensions much larger than the transition wavelength.<
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