Eikonal Exchange Amplitude for the Excitation of Hydrogen-Like Ions by Electron Impact

Abstract

Validity of the Coulomb-eikonal approximation is examined in an excitation process of hydrogen-like ions. In particular, the Coulomb-eikonal exchange amplitude is formulated with a general expression which is reduced to a two-dimensional integral. The exchange amplitude evaluated for every excitation process from an arbitrary state (n, l, m) to any other state (n', l', m'). It is noted that the cross section calculated by this apporoximation with exchange never depends on any indefinite constant phase.