Calculations of cross sections for electron-impact double ionization of ions with electron number N ≤10 using two-step approaches

This paper investigates the capability of the two-step (TS) approaches in calculating the cross section of the electron-impact double ionization (DI) of ions. The TS approach proposed by Gryzin<acute accent>ski [M. Gryzin<acute accent>ski, Phys. Rev. 138, A336 (1965)] considers electron-impact direct DI as two sequential electron-impact single ionizations. Furthermore, we introduce the energetic differential cross sections of primary single ionization as the energy distribution for intermediate electrons that participate in the subsequent single ionization process. Such differential cross sections can be calculated using the analytic Mott formula [Y.-K. Kim and M. E. Rudd, Phys. Rev. A 50 , 3954 (1994)]. The electron-impact indirect DI is considered as TS, in which a primary electron-impact single ionization of an inner-shell electron is followed by a single autoionization. The cross sections of the direct and indirect DI are calculated independently to result in the total DI cross section. Comparing with the available experimental data shows that the present TS approach can reproduce well the DI cross sections for ions with electron number N 10 such as Li+, C+, N+, N2+, O+, O2+, Neq+ (q = 1, 2, 3, and 5), and Arq+ (q = 8, 9, 10, and 11) ions. The contributions of the direct and indirect DI can be identified based on our calculations.