Photoluminescence lifetimes of the $n=2$ level in a large quantum well show a clear nonmonotonic dependence on the density of optically generated carriers. Varying the power density over five orders of magnitude we prove directly the high efficiency of carrier-carrier interaction for intersubband scattering when longitudinal-optical phonon emission is suppressed. For low densities, the observed $n=2$ decay times get shorter (from 40 down to 5 ps) as the density is increased. At high densities Pauli blocking reduces significantly the intersubband scattering rates.