The interactions between simple charged particles and atoms will be examined within the framework of a perturbation series approach. A first and fundamental question concerns the rate of convergence of perturbation series and whether it is in practice possible to calculate accurate theoretical cross sections. The second aspect of the work will involve the application of these techniques to specific problems of current interest, including electron excitation of sodium, elastic positron scattering, electron impact ionization, and simultaneous electron-photon excitation. Second order amplitudes are evaluated with the method of Dalgarno and Lewis; the question is whether a particular choice for the distorted Green's function can be found which will optimize the rate of convergence of perturbation series.
