A binary-encounter calculation with realistic velocity distribution of the target electron

The introduction of a realistic velocity distribution into the binary-encounter approximation (BEA), both for K shells and L subshells of target elements other than hydrogen, leads to the same scaling rules for the proton impact ionisation cross section as those obtained in the plane-wave Born (PWBA) and semiclassical approximations (SCA). K shell ionisation cross sections for the same element calculated with the BEA, PWBA and SCA differ by less than 20% in the region of proton energies currently employed.