The collisional ionization of atomic systems by structureless charged particles of arbitrary mass and charge is considered. For the theoretical study, the classical impulse approximation is used. In this case, analytical expressions Q for the ionization cross-sections are given by Garcia et al. (1968). From these expressions, a reduced cross-section QR is obtained as a function of a scaled energy X. It is found that, for a particle of mass M, charge Z, and energy E, incident on a target having ξ equivalent electrons with a binding energy I, QR is given by:

where

IH is the hydrogen ionization potential and me is the electron mass.