Novel theoretical approaches to small-angle electron scattering

Abstract

The difficulties of obtaining reliable measurements of the electron differential cross sections (DCSs) for atomic, ionic and molecular transitions at and near zero scattering angles are well documented. Hence, the need for reliable theoretical calculations. Recently, three theoretical approaches have been derived to investigate and guide measurements of small-angle, including zero, electron DCSs in atoms, ions and molecules. The first method, the momentum dispersion method (MDM), based on Regge Pole theory, uses the analytical continuation of the generalized oscillator strength (GOS) function to obtain the smaller angle, including zero, data from the more reliably measured larger angular data. The second method, the forward scattering function (FSF), represents a unique path of the GOS function to the OOS. It is therefore useful for normalizing the measured relative electron DCSs through the GOSs. Very recently, a singular behavior has been found in the electron–atom scattering DCS at small momentum transfer, K coming from second-order terms and a new generalized Lassettre expansion has been derived. At forward scattering, it is expected to yield the unique long sought after curve that normalizes the measured relative electron DCSs to the OOSs. The utility of the methodologies is demonstrated using atomic, ionic and molecular transitions.