We present a theoretical model of charge exchange between an ion and a solid surface which includes resonant transfer and Auger-coupling processes. The Auger processes are treated through an equation of motion approach which results in an Auger self-energy identical to that obtained through the second-order Keldysh-Green functions formalism. The model which we report involves a Lorentzian-shaped level width for the resonant processes and a wide band form for the Auger processes. It permits an exact solution of the problem in terms of well-known functions. The roles played by the characteristic parameters of the problem, which are related to the atom velocity, energy level positions, interaction potential and band structure are illustrated in some simple cases. (C) 2002 Elsevier Science Ltd. All rights reserved.1249317321