[en] The modified free Hamiltonian for the Coulomb interaction is used to derive an equation for the S-matrix and renormalized asymptotic states. We obtain an effective potential and the corresponding finite perturbation expansion for the S-matrix. The Born approximation is shown to contain a term (α/vertical strokepvertical stroke)delta₃(p-p') the (divergent) phase correction which makes the second-order term finite is also explicitly derived. (orig.)