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: $2\propto E{\left(\ln E\right)}^{-2\mathrm{}}[1+Csin(\alpha \ln E+\mu \left)\right]$. 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 $C\cong {\alpha }^{-1\mathrm{}}$, and it also suggests that $\alpha$ is large. The same law also applies to positron-atom impact ionization.