Electron-impact excitation at small scattering angles: The Lassettre limit and attendant normalization of measured relative differential cross sections

Abstract

The recent generalized Lassettre expansion (GLE) [Phys. Rev. Lett. 81, 961 (1998)] employing only a single Regge pole is used to demonstrate the applicability of the Lassettre limit theorem over the entire electron impact energy without the involvement of the nonphysical region of the apparent generalized oscillator strength (AGOS). At forward scattering the GLE yields the unique long-sought-after normalization curve to the optical oscillator strength of the measured relative electron differential cross sections (DCS's) through the AGOS. Optically allowed transitions in H, He, Xe, and ${\mathrm{N}}_{2}\mathrm{O}$ are used to illustrate the normalization procedure. We conclude that the GLE together with the momentum dispersion method of Haffad et al. [Phys. Rev. Lett 76, 2456 (1996)] now constitute a set of invaluable methods for use in guiding electron DCS measurements, including the identification of incorrectly normalized and/or spuriously behaved data in the difficult to measure small angular regime. It is hoped that this paper will inspire more measurements of DCS's at zero-angle scattering, since currently very few such measurements are available.