Double ionization of heavy positive ions by electron impact:: empirical formula and fitting parameters for ionization cross sections

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 I-th where I-th 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 multielectron, 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.