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

Abstract

Using a wavefunction with the radial correlation only for the boundelectrons and a correlated double-continuum wavefunction for the ejectedelectrons, an analytical expression is obtained in the Born approximationfor the fully differential cross section of double ionization of helium-likeions by electrons. The result is found within the framework of theshake-offmodel considering only the radial correlation of electrons in the target.An analytical expression is obtained for the fourfold differential crosssection following integration of the fully differential cross section overthe solid angles of the ejected electrons. For the first time the totalcross sections (TCS) are calculated for direct double ionization oftwo-electron atomic systems from H-(Z = 1)to N5+(Z = 7). Thecalculations are carried out for energies extending up to a maximum 200times the double-ionization threshold. The calculated values of TCS arefound to be in fair agreement with the available experimental data forHe and Li+. Disagreement between theory and experiment isdiscussed. TCS are found to be very sensitive to the inclusion of repulsionbetween the ejected electrons in the final state.