BEHAVIOR OF IONIZATION CROSS SECTION IN COLLISIONS OF HIGH-ENERGY ELECTRONS WITH HYDROGENIC ATOMS

The ionization cross section per unit range of the energy ε of the ejected electrons for collision of an incident charged particle of high energy E with an atomic system is given by dQdε=E-1[A(ε)lnE+B(ε)], where A and B are functions of ε, and the total cross section is given by Q=E-1[AτlnE+Bτ]. The coefficients A(ε) and B(ε) for the particular case of the atomic hydrogen are derived analytically as an expansion with respect to k=ε. The expansion converges for all values of k. By integrating A(ε) and B(ε) with respect to ε, Aτ and Bτ are obtained and compared with the values given by Bethe using a different method. The coefficients of the first two leading terms of the expansion of dQdε with respect to ε or 1ε when ε is small or large are found. A relationship for the average energy of the ejected electrons is given. Different features of the high-energy impact ionization and a certain connection between the ionization and the discrete level excitation are discussed. © 1969 The American Physical Society.