  We present here a new method based on a transfer of population by adiabatic
passage that allows to prepare cold atomic samples with a well defined ratio of
atomic density and atom number. This method is used to perform a measurement of
the cold collision frequency shift in a laser cooled cesium clock at the
percent level, which makes the evaluation of the cesium fountains accuracy at
the $10^{-16}$ level realistic. With an improved set-up, the adiabatic passage
would allow measurements of atom number-dependent phase shifts at the $10^{-3}$
level in high precision experiments.
