Asymptotic behaviour of the total cross section for double ionization of helium-like ions by electrons

The total cross sections (TCS) for double ionization of helium-like ions by electrons are obtained at high incident energy. For the first time, the leading term and the following term of the asymptotic expression of the TCS are calculated for two-electron atomic systems from He (Z = 2) to N5+ (Z = 7). The obtained values of TCS are in perfect agreement with the numerically calculated ones in the asymptotic region. For helium the discrepancy between the theory and some of existing experimental data is revealed at high energies.