The energy distribution cross section in threshold electron-atom impact ionization

The flatness of the energy differential cross section in impact ionization is derived analytically in the Wannier theory. However it is shown that the Wannier zone is confined to a region of the order E/5 is less than or equal to epsilon is less than or equal to 4E/5, where E is the available energy and epsilon is the energy of the electrons. By contrasting the known results of photoionization and photodetachment, one can cogently argue that in the complementary region where electrons share their energy very unequally the cross section rises to a value independent of E, and that this region determines the form of the threshold law.