The second Born approximation for the double ionization of N2 by electron impact

Abstract

In their (e,3e) and (e,3-1e) experiments of the double ionization (DI) of the outermost orbital of N2, Li et al (2012 J. Phys. B: At. Mol. Opt. Phys. 45 135201) recently showed that the process is largely dominated by a two-step-2 mechanism, which is a double interaction of the incident electron with the target. From a theoretical point of view, this should entail the use of the second Born approximation. In the past, very few theoretical calculations had been carried out this way because it requires a difficult numerical triple integration. We propose here to take into account the second Born approximation for the DI of N2 by using the closure approximation. The initial state is described by a single-center wave function derived from the usual multi-center wave function obtained in the self-consistent-field Hartree–Fock method using the linear combination of atomic orbitals-molecular orbital (LCAO-MO) approximation. The final state describes the interaction between each of the ejected electrons and the target by a Coulomb wave and the interaction between the two ejected electrons with the use of the Gamow factor. We calculate differential cross sections using the same kinematic conditions as Li et al (intermediate incident energy about 600 eV) for (e,3e) and (e,3-1e) DI of N2. The results show that the model does not allow a shift of the variation of the four-fold differential cross section near the momentum transfer to be obtained nor its opposite when we include the contribution given by the second Born approximation, as in (e,3-1e) experiments.