  Recent ARPES experiments show a narrow quasiparticle peak at the gap edge
along the antinodal [1,0]-direction for the overdoped cuprate superconductors.
We show that within weak coupling BCS theory for a d-wave superconductor the
s-wave single-impurity scattering cross section vanishes for energies of the
gap edge. This coherence effect occurs through multiple scattering off the
impurity. For small impurity concentrations the spectral function has a
pronounced increase of the (scattering) lifetime for antinodal quasiparticles
but shows a very broad peak in the nodal direction, in qualitative agreement
with experiment and in strong contrast to the behavior observed in underdoped
cuprates.
