Electron-impact double ionization of He by applying the Jacobi matrix approach to the Faddeev-Merkuriev equations

Abstract

We apply the Jacobi matrix method to the Faddeev-Merkuriev differential equations in order to calculate the three-body wave function that describes the double continuum of an atomic two-electron system. This function is used to evaluate within the first-order Born approximation, the fully differential cross sections for $(e,3e)$ processes in helium. The calculations are performed in the case of a coplanar geometry in which the incident electron is fast and both ejected electrons are slow. Quite unexpectedly, the results obtained by reducing our double-continuum wave function to its asymptotic expression are in satisfactory agreement with all the experimental data of Lahmam-Bennani et al. [A. Lahaman-Bennani et al., Phys. Rev. A 59, 3548 (1999); A. Kheifets et al., J. Phys. B 32, 5047 (1999).] without any need for renormalizing the data. When the full double-continuum wave function is used, the agreement of the results with the experimental data improves significantly. However, a detailed analysis of the calculations shows that full convergence in terms of the basis size is not reached. This point is discussed in detail.