  We study the mass of a nucleon in a nucleus using a model recently introduced
for a nucleon current with a pion cloud component. The method of QCD sum rules
is used to determine the mass shifts for nucleons to first order in nuclear
density in oxygen-16 and calcium-40, with the pion propagator determined by an
optical potential for pion-nucleus scattering. Mass shifts due to the pionic
contributions range from negligible in oxygen to -100 MeV in calcium at central
nuclear density, with larger shifts in the nuclear surface. The consistency of
this model with chiral perturbation theory is demonstrated.
