Many recent ion-surface scattering experiments, e.g., He+ --> Pb, show
dramatic oscillations of the neutralization probability as a function
of the inverse ion velocity. These oscillations are qualitatively sim
ilar to the Stueckelberg oscillations that occur during quasiresonant
charge exchange in atom-atom collisions. We present here a general man
y-body approach for the description of such charge-exchange processes
near surfaces. We show that for the proper understanding of the oscill
atory behavior it is crucial to include intra-atomic correlation effec
ts. The interference between different tunneling channels influences b
oth the amplitude and the frequency of these oscillations.