Perturbation Theory

Abstract

We show that the interaction between a fast continuum electron with the nucleus can be described in perturbation theory. For processes on the Bethe ridge the plane wave can be the lowest-order approximation. For processes outside the Bethe ridge, the lowest-order approximation should include one interaction between the electron and the nucleus. We demonstrate that the interaction between the fast electron and the electrons bound in the atom (final-state interactions, abbreviated as FSI) can be presented as power series of the Sommerfeld parameter $\xi _{ee}$. The lowest-order FSI corrections to the cross sections are of order $\xi _{ee}^2$. In order to find them, one should calculate the FSI amplitude up to the second order in $\xi _{ee}$. The infrared divergent terms emerging in the intermediate steps cancel automatically in the expressions for the cross sections.