Publisher Summary This chapter presents an analytic independent particle model for atoms and focuses on the development of the GOS formalism for ionization. The GOS formalism for ionization has many features in common with the GOS formalism for excitation. A comparison in the region of the ionization threshold between the p to s partial wave contribution to the ionization GOS and the appropriately energy-normalized p to s excitation GOS is presented. In addition, the chapter presents the calculational results and shows that as one goes to higher Z atoms the differences between this model and simple hydrogenic results become very substantial. The Bethe continuum surface is shown as series of cuts at constant ejected electron energy and constant momentum transfer. The cross-section differential in both incident electron energy and ejected electron energy, S (E, T), is compared with recent experiments. A cross section can be obtained by integrating out the angular dependence of the GOS. The chapter assesses the current status of work and describes possible future directions. The use of an analytic independent particle model (IPM) potential for obtaining atomic wave functions provides a tractable means of exploring the trends of electron impact ionization cross sections. Furthermore, the analytic potential lends the calculation an adaptability that is not present in calculations using a fixed numerical potential such as the HFS potential.