  We study the evolution of the absorption spectrum of a modulation doped
GaAs/AlGaAs semiconductor quantum well with decreasing the carrier density. We
find that there is a critical density which marks the transition from a Fermi
edge singularity to a hydrogen-like behavior. At this density both the
lineshape and the transitions energies of the excitons change. We study the
density dependence of the singularity exponent $\alpha $ and show that disorder
plays an important role in determining the energy scale over which it grows.
