Abstract
A general treatment of the resolvent operator in Liouville space using the Goldberger-Watson approach is presented. Exact, formal expressions for the matrix elements of the resolvent, as well as approximate expressions based on an iteration procedure, are given. The formalism is then applied to the study of the line shape of atomic transitions in the presence of both weak collisions and an intense radiation field. The dependence of the line shape on the intensity and spectral composition of the field is discussed, and expressions for shifts and widths are derived.