  Renormalization of non-magnetic impurity potential by strong electron
correlation is investigated in detail. We adopt the t-t'-t"-J model and
consider mainly a delta-function impurity potential. The variational Monte
Carlo method shows that impurity potential scattering matrix elements between
Gutzwiller-projected quasi-particle excited states are as strongly renormalized
as the hopping terms. Such renormalization is also seen by the Bogoliubov-de
Gennes equation with an impurity, where the strong correlation is treated by a
Gutzwiller mean-field theory with local Gutzwiller factors and local chemical
potentials. Namely, the delta-function potential is effectively weakened and
broadened. We emphasize the importance of including the local chemical
potential, which is paid little attention to in the literature, by physical
consideration of the doping dependence of a local hole density. We also
investigate effect of smooth impurity potential variation; the strong
correlation yields anticorrelation between the gap energy and the coherence
peak height simultaneously with large gap distribution, which is consistent
with the experiments.
