  We re-examine the quantum tau_q and transport tau_t scattering lifetimes due
to background impurities in two-dimensional systems. We show that the
well-known logarithmic divergence in the quantum lifetime is due to the
non-physical assumption of an infinitely thick heterostructure, and demonstrate
that the existing non-divergent multiple scattering theory can lead to
unphysical quantum scattering lifetimes in high quality heterostructures. We
derive a non-divergent scattering lifetime for finite thickness structures,
which can be used both with lowest order perturbation theory and the multiple
scattering theory. We calculate the quantum and transport lifetimes for
electrons in generic GaAs-AlGaAs heterostructures, and find that the correct
`rule of thumb' to distinguish the dominant scattering mechanisms in GaAs
heterostructures should be tau_t/tau_q < 10 for background impurities and
tau_t/tau_q > 10 for remote impurities. Finally we present the first comparison
of theoretical results for tau_q and tau_t with experimental data from a GaAs
2DEG in which only background impurity scattering is present. We obtain
excellent agreement between the calculations and experimental data, and are
able to extract the background impurity density in both the GaAs and AlGaAs
regions.
