Electron-impact direct double ionization as a sequence of processes

It is shown that the electron-impact direct double ionization (DDI) process can be presented as a sequence of two- and three-step processes. Contribution from ionization-ionization, ionization-excitation-ionization, and excitation-ionization-ionization processes is taken into account. A good agreement with experimental measurements is obtained for double ionization cross sections of ${\text{O}}^{1+}$, ${\text{O}}^{2+}$, ${\text{O}}^{3+}$, ${\text{C}}^{1+}$, and ${\text{Ar}}^{2+}$ ions. We show that distribution of the energy of scattered and ejected electrons, which participate in the next step of ionization, strongly affects DDI cross sections.