Ionization of hydrogenic targets by electron impact. Scaling laws

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