The ratio of double to single ionization of helium: The relationship of photon and bare charged particle impact ionization

In this paper the author derives expressions for the ratio of double to single ionization of helium from its ground state, by both single photons, and charged particle impact. He shows that in the limit of large reduced incident energy T of a charged particle, that the ratio of the double to single ionization cross sections at some energy transfer ΔE is equal to the ratio of photoionization cross sections for a photon of energy hν = ΔE, independent of T. He then goes on to find a relationship for this ionization ratio which is not restricted to some specific energy transfer, and shows that the double to single ionization cross section ratio approaches an asymtotic limit for large enough T