Threshold law for electron-atom impact ionization

The threshold law for electron-atom ionization is derived on the basis of the Coulomb-dipole theory. The result is a modulated quasilinear law for the yield: QproportionalE(lnE)-2[1+C sin(αlnE+μ)]. The derivation depends on a more accurate description of the dipole moment seen by the outer electron as the distance of the inner electron from the nucleus. The derivation also implies Capprox. =α-1, and it also suggests that α is large. The same law also applies to positron-atom impact ionization