  We develop a strong stretching approximation for a polymer brush made of
self-avoiding polymer chains. The density profile of the brush and the
distribution of the end monomer positions in stretching direction are computed
and compared with simulation data. We find that our approach leads to a clearly
better approximation as compared to previous approaches based upon Gaussian
elasticity at low grafting densities (moderate chain stretching), for which
corrections due to finite extensibility can be ignored.
