Double ionization of helium-like ions by electron impact: from fully differential to total cross section

Using a wavefunction with the radial correlation only for the bound electrons and a correlated double-continuum wavefunction for the ejected electrons, an analytical expression is obtained in the Born approximation for the fully differential cross Section of double ionization of helium-like ions by electrons. The result is found within the framework of the shake-off model considering only the radial correlation of electrons in the target. An analytical expression is obtained for the fourfold differential cross section following integration of the fully differential cross section over the solid angles of the ejected electrons. For the first time the total cross sections (TCS) are calculated for direct double ionization of two-electron atomic systems from H-(Z = 1) to N5+(Z = 7). The calculations are carried out for energies extending up to a maximum 200 times the double-ionization threshold. The calculated values of TCS are found to be in fair agreement with the available experimental data for He and Li+ Disagreement between theory and experiment is discussed. TCS are found to be very sensitive to the inclusion of repulsion between the ejected electrons in the final state.