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Collisions in a ballistically expanding cloud of cold atoms in an atomic fountain

We have employed an intuitive model and 3D Monte Carlo simulations to study the effect of ballistic expansion of the atomic cloud on the collision energies and the resulting frequency shift in a fountain clock. In particular, we show that the energies relevant for collisions contributing to the clock shift correspond to temperatures which may be significantly smaller than the temperature of the cloud at launch. Both the assumptions and predictions of our model are related to realistic parameters of operating caesium fountain clocks.