Analytic Born completion in the calculation of electron-molecule differential cross sections

Abstract

In calculating the elastic differential cross section for electron scattering from linear nonpolar molecules, one must include elements of the transition matrix corresponding to a large number of partial waves in order to obtain convergence at small angles. We present an analytic correction to the widely used expression for the differential cross section in terms of body-frame T-matrix elements calculated in the fixed-nuclear-orientation approximation. This correction incorporates contributions from all high-order partial waves via the Born approximation. It efficiently produces accurate differential cross sections and shows rapid convergence even at small angles. We illustrate the importance and accuracy of this procedure for low-energy (less than 10 eV) collisions of electrons with ${\mathrm{H}}_{2}$ and ${\mathrm{N}}_{2}$. \textcopyright{} 1996 The American Physical Society.