Electron-impact double-ionization processes of light positive ions from He- to Ne-like isoelectronic sequences, as well as of the heavy ions Arq+ (q = 1–7) and Kr q+ (q = 1–4) are considered for incident-electron energies E < 50 Ith where Ith is the threshold energy for double-electron ionization. On the basis of reliable experimental data and quantum-mechanical calculations, simple semiempirical formulae with three fitting parameters, by taking into account the contribution of direct double ionization and of inner-shell ionization processes, are obtained which describe the experimental cross sections within an accuracy of 20–30%. With this accuracy, the formulae suggested can be used for prediction of the double-ionization cross sections of positive ions with the nuclear charge Z ⩽ 26 in the electron energy range of E < 50Ith. According to the model suggested, the direct ionization cross section σdir (simultaneous ionization of two outer electrons) is scaled as I−3th against scaled electron energy E/Ith and contains only one fitting parameter. Two additional fitting parameters are obtained using the least-squares method in conjunction with numerically calculated single-electron inner-shell ionization cross sections. All fitting parameters are found to be constant for ions within a given isoelectronic sequence. The present analysis also provides a method for indirect determination of K-shell ionization cross sections for ions from Be-like to Ne-like sequences. The fluorescence yields ωK for a single K-shell vacancy in ions from Li-like to Ne-like sequences with nuclear charges 3 ⩽ Z ⩽ 26 are calculated as well.

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Electron-impact double-ionization processes of multi-electron heavy ions from Ti up to Bi (nuclear charge from Z = 22 up to Z = 83) are investigated for incident electron energies E < 50 Ith where Ith is the threshold energy for double ionization. The following ions are considered: Tiq+ (q = 1–6), Feq+ (q = 1, 3–6), Niq+ (q = 1–6), Gaq+ (q = 1–6), Krq+ (q = 1–4), Moq+ (q = 1–6), Prq+ (q = 1–4), Smq+ (q = 1–6), Wq+ (q = 1–6), Pbq+ (q = 1–9) and Biq+ (q = 1–10, 12). On the basis of experimental data, mostly obtained at an electron–ion crossed-beams set-up in Giessen, and quantum-mechanical considerations, a simple semi-empirical formula with six fitting parameters is developed taking into account the contribution of direct double ionization of two outer-shell electrons of the ions and also of single inner-shell ionization processes followed by autoionization with additional ejection of an electron as was suggested in our previous paper (Shevelko et al 2005). The formula obtained there was found to describe well the available experimental double-ionization cross sections within an accuracy of 20–30%. However, for multi-electron, very heavy ions significant deviations of that formula from experiment are found in the low-energy region. These deviations are most likely caused by higher order processes, including inner-shell excitation and subsequent double autoionization (EDA). The tabulated parameters can be used for easy analytical representation of the double-ionization cross sections of heavy positive ions in the modelling of laboratory and astrophysical plasmas.

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