  We present a theory of recoil effects in two zone Ramsey spectroscopy,
particularly adapted to microwave frequency standards using laser cooled atoms.
We describe the atoms by a statistical distribution of Gaussian wave packets
which enables us to derive and quantify effects that are related to the
coherence properties of the atomic source and that have not been considered
previously. We show that, depending on the experimental conditions, the
expected recoil frequency shift can be partially cancelled by these effects
which can be significant at microwave wavelengths whilst negligible at optical
ones. We derive analytical expressions for the observed interference signal in
the weak field approximation, and numerical results for realistic caesium
fountain parameters. In the near future Cs and Rb fountain clocks are expected
to reach uncertainties which are of the same order of magnitude (10^{-16}) as
first estimates of the recoil shift at microwave frequencies. We show, however,
that the partial cancellation predicted by the complete theory presented here
leads to frequency shifts which are up to an order of magnitude smaller.
Nonetheless observation of the microwave recoil shift should be possible under
particular experimental conditions (increased microwave power, variation of
atomic temperature and launching height etc.). We hope that the present paper
can provide some guidance for such experiments that would test the underlying
theory and its assumptions, which in turn is essential for the next generation
of microwave frequency standards.
