Scattering of cold atom coherences by hot atoms: Background gas collision shifts of primary fountain clocks

We theoretically analyze frequency shifts of cold-atom clocks due to background gas collisions. Because nearly all collisions with room-temperature background gases that transfer momentum eject cold atoms from a clock, the frequency shifts for cold atoms are significantly different than those of room-temperature clocks. From general arguments, measurements of the loss of Ramsey fringe amplitude can usefully bound this source of systematic error.