S-model calculations for high-energy-electron-impact double ionization of helium

Abstract

In this paper the double ionization of helium by high-energy electron impact is studied. The corresponding four-body Schr ̈ dinger equation is transformed into a set of driven equations containing successive orders in o the projectile-target interaction. The transition amplitude obtained from the asymptotic limit of the first-order solution is shown to be equivalent to the familiar first Born approximation. The first-order driven equation is solved within a generalized Sturmian approach for an S-wave (e,3e) model process with high incident energy and small momentum transfer corresponding to published measurements. Two independent numerical implementations, one using spherical and the other hyperspherical coordinates, yield mutual agreement. From our ab initio solution, the transition amplitude is extracted, and single differential cross sections are calculated and could be taken as benchmark values to test other numerical methods in a previously unexplored energy domain.