  We study the dispersion interaction of the van der Waals and Casimir-Polder
(vdW-CP) type between a neutral atom and the surface of a metal by allowing for
nonlocal electrodynamics, i.e. electron diffusion. We consider two models: (i)
bulk diffusion, and (ii) diffusion in a surface charge layer. In both cases the
transition to a semiconductor is continuous as a function of the conductivity,
unlike the case of a local model. The relevant parameter is the electric
screening length and depends on the carrier diffusion constant. We find that
for distances comparable to the screening length, vdW-CP data can distinguish
between bulk and surface diffusion, hence it can be a sensitive probe for
surface states.
