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Time Dependence of the Atomic Density in a Magneto-optical Trap

We have studied the evolution of the atomic density in magneto-optical traps. We have observed that the density increases according to (1-e-t/ τn ), where the characteristic time τn may differ only slightly from the trap lifetime. We discuss the implications this has on the constant density approximation and solve the rate equation for trapped atom number in the case of a time-dependent density.