Novel theoretical approaches to small-angle electron scattering

The difficulties of obtaining reliable measurements of the electron differe ntial cross sections (DCSs) for atomic, ionic and molecular transitions at and near zero scattering angles are well documented. Hence, the need for re liable theoretical calculations. Recently, three theoretical approaches hav e been derived to investigate and guide measurements of small-angle, includ ing zero, electron DCSs in atoms, ions and molecules. The first method, the momentum dispersion method (MDM), based on Regge Pole theory, uses the ana lytical continuation of the generalized oscillator strength (GOS) function to obtain the smaller angle, including zero, data from the more reliably me asured larger angular data. The second method, the forward scattering funct ion (FSF), represents a unique path of the GOS function to the OOS. It is t herefore useful for normalizing the measured relative electron DCSs through the GOSs. Very recently, a singular behavior has been found in the electro n-atom scattering DCS at small momentum transfer, K coming from second-orde r terms and a new generalized Lassettre expansion has been derived. At forw ard scattering, it is expected to yield the unique long sought after curve that normalizes the measured relative electron DCSs to the OOSs. The utilit y of the methodologies is demonstrated using atomic, ionic and molecular tr ansitions. (C) 1999 Elsevier Science B.V. All rights reserved.