Measurement and Cancellation of the Cold Collision Frequency Shift in an ${}^{87}\mathrm{Rb}$ Fountain Clock

We measure a cold collision frequency shift in an ${}^{87}\mathrm{Rb}$ fountain clock that is fractionally 30 times smaller than that for Cs. The shift is $-0.38\mathrm{}\left(8\right)\mathrm{mHz}$ for a density of $1.0\left(6\right)\times {10}^9{\mathrm{cm}}^{-3\mathrm{}}$. We study the cavity pulling of the atomic transition and use it to cancel the cold collision shift. We also measure the partial frequency shifts of each clock state finding $2({\lambda }_{10}-{\lambda }_{20})/({\lambda }_{10}+{\lambda }_{20})=0.1\mathrm{}\left(6\right)$.