  Resonant optical pumping in dense atomic media is discussed, where the
absorption length is less than the smallest characteristic dimension of the
sample. It is shown that reabsorption and multiple scattering of spontaneous
photons (radiation trapping) can substantially slow down the rate of optical
pumping. A very slow relaxation out of the target state of the pump process is
then sufficient to make optical pumping impossible. As model systems an
inhomogeneously and a radiatively broadened 3-level system resonantly driven
with a strong broad-band pump field are considered.
