Electron-impact direct double ionization (DDI) process is studied as a sequence of two and three step processes. Contribution from ionization-ionization, ionization-excitationionization, and excitation-ionization-ionization processes is taken into account. The present results help to resolve the long-standing discrepancies; in particular, a good agreement with experimental measurements is obtained for double ionization cross-sections of O 1+ , O 2+ , O 3+ , C 1+ , and 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.
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