The dependences of the transport scattering time {tau}t, quantum lifetime {tau}q, and their ratio {tau}t/{tau}q on the density ne of the electron gas in modulation-doped single GaAs quantum wells with AlAs/GaAs short-period super-lattice barriers are investigated. The experimental dependences are explained in terms of electron scattering by remote ionized donors with an effective two-dimensional concentration n*R and background impurities with a three-dimensional concentration nB. An expression for n*R(ne) is obtained including the contribution of X-valley electrons localized in AlAs layers to the suppression of scattering by the random potential of remote donors. It is shown that the experimentally observed abrupt increase in {tau}t and {tau}q with an increase in ne above a certain critical value nec is related to a decrease in n*R. It is established that the drop in {tau}t/{tau}q observed for electron densities ne > nec occurs because scattering by the random potential of background impurities in this two-dimensional system with a decrease in n*R limits an increase in {tau}t more considerably than an increase in {tau}q.
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