In the present work has been tried to do a generalized formalism of semi-classical method used in ion-atom impact. One of the current method to calculation of the differential and total cross section for ion-atom impact at high energy range is the first Born approximation because of the simplicity of its calculations, but not necessarily sufficiently accurate. In particular this approximation in the excitation channel take into account orthogonality of the initial and the final state wave functions of the bound subsystem and then disappears inter-nuclear effect in the calculations and offers the poor picture for viewing impact process. Also in this approximation the most important coupling has been considered between the initial and the final state. However the close-coupling method because of some restrictions in high impact energies is unusable. Therefore the aim of this work is correction the first Born approximation by implemented the multi-channel eikonal formalism. At last it will be shown that by simplifying this generalized theory it can be achieved a number of current formalism in terms of ion-atom impact.