Ionization of hydrogenic targets by electron impact. Scaling laws

Abstract

A simple scaling law is obtained for ionization of hydrogenic targets by impact of fast electrons. This law is shown to be exact for the first-order Born approximation when MT>>1 (with MT the target mass) independently of the kinematical conditions considered. For high enough target nuclear charges, the scaling is proven to be valid in a Coulomb-Born approximation (CBA) in which correct boundary conditions are included in the initial wavefunction. The scaling formula is also studied for an extension with correct initial boundary conditions of the model introduced by Brauner, Briggs and Klar (BBK) in which an approximation to the exact final wavefunction is made, taking into account properly the asymptotic Coulombic character of the interactions between the aggregates of the collision system. In this case, the validity of the scaling is shown for a coplanar asymmetric geometry. At high enough impact energies, the scaling law works well for smaller target nuclear charges when the CBA and the BBK theoretical descriptions are used.