The Threshold Law for Single Ionization of Atoms or Ions by Electrons

When an electron hits an atom or ion, it may knock off an electron. This process is fundamental in almost all types of gas discharge. The reaction is endothermic; hence there is a threshold value in the electron energy below which it does not occur. In this paper, the dependence of the yield on the energy just above this threshold is derived. The derivation is not rigorous because it circumvents some of the difficulties of the three-body problem by applying ergodicity, albeit in a weakened form. The result is that, for atoms, the yield rises as the 1.127th power of the energy excess. For ions the exponent lies between this number and unity.