Semiempirical formulae for electron-impact double-ionization cross sections of light positive ions

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