We report the measurement of collision rate coefficient for collisions between ultracold Cs atoms and low energy Cs+ ions. The experiments are performed in a hybrid trap consisting of a magneto-optical trap (MOT) for Cs atoms and a Paul trap for Cs+ ions. The ion-atom collisions impart kinetic energy to the ultracold Cs atoms resulting in their escape from the shallow MOT and, therefore, in a reduction in the number of Cs atoms in the MOT. By monitoring, using fluorescence measurements, the Cs atom number and the MOT loading dynamics and then fitting the data to a rate equation model, the ion-atom collision rate is derived. The Cs-Cs+ collision rate coefficient $9.3(pm0.4)(pm1.2)(pm3.5) times 10^{-14}$ m$^{3}$s$^{-1}$, measured for an ion distribution with most probable collision energy of 95 meV ($approx k_{B}.1100$ K), is in fair agreement with theoretical calculations. As an intermediate step, we also determine the photoionization cross section of Cs $6P_{3/2}$ atoms at 473 nm wavelength to be $2.28 (pm 0.33) times 10^{-21}$ m$^{2}$.
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