Statistical fluctuations in the yield of ionization due to protons or α particles

An analytic method is presented for the calculation of various indices that characterize statistical fluctuations in ionization yields, specifically for the incidence of an ion such as a proton or {α} particle at a high speed. A general expression for the Fano factor for ion incidence is derived, and the relation to the Fano factor for electron incidence is clarified. For an illustration, the theory is applied to protons incident on argon. The resulting Fano factor for protons of energies between 0.1 and 2 MeV is nearly the same as that for electrons at the same speeds, and it is considerably lower than the values measured with {α} particles.