The eikonal approximation for the (e,2e) reaction

Abstract

The approximation of local translational invariance is necessary to produce a tractable effective interaction between two particles in a many-body system. This approximation is tested for the (e,2e) reaction by testing the shell-averaged eikonal approximation in which particles propagate in a constant average potential V, which is shown to depend on the recoil momentum. In this approximation the distorted-wave impulse approximation factorises into parts depending on the structure and the two-body interaction. Experiments are reported for neon in which the structure factor is kept constant in order to provide a test of the reaction theory. The incident energies are 800 eV and 1600 eV. The q-dependent eikonal approximation works well over a large kinematic range, but not for small values of the angle between the outgoing electrons, or for q near the maximum in the 2p cross section at the lower energy. Factorised calculations with fully evaluated optical-model distorted waves do not always work as well as the eikonal approximation.