Multiple ionization processes involving fast charged particles

This review is devoted to certain aspects of the theory of multiple ionization of a quantum target by a fast charged particle. Atoms and molecules, and their ions as well, are considered as targets, while electrons and protons are considered as projectiles. Special attention is paid to the effective charge approximation while constructing continuum wave functions for several charged fragments in the exit channel of the reaction. Theoretical calculations of differential and total cross sections of various multiple ionization processes are presented and, where possible, comparison of the results of these calculations with experimental data is carried out.