Computational Methods for Electron-Atom Collisions

In recent years, much progress has been achieved in calculating reliable cross-section data for electron scattering from atoms and ions, in particular quasi-one and quasi-two electron systems such as H, He, the alkalis, and the alkaline-earth metals. Until recently, however, accurate calculations of electron collisions with more complex targets, such as the heavy noble gases Ne$-$Xe, have remained a significant challenge to theory. We will give an overview of the computational methods presently used for {\it ab initio} electron-atom collision calculations, with particular emphasis on their strengths and weaknesses, range of applicability, and expected accuracy. In particular, we will illustrate with a few examples how the $B$-spline $R$-matrix (BSR) method with non-orthogonal orbitals~[1-3] has been able to dramatically improve the quality of theoretical datasets for oscillator strengths~[4] and in particular for electron collisions with the heavy noble gases~[5]. \\[4pt] [1] O. Zatsarinny and K. Bartschat, J.~Phys. B~{\bf 37} (2004), 2173 and 4693.\\[0pt] [2] O. Zatsarinny, Comp. Phys. Commun. {\bf 174} (2006) 273.\\[0pt] [3] O. Zatsarinny and K. Bartschat, Phys. Rev. A {\bf 77} (2008) 062701.\\[0pt] [4] O. Zatsarinny and K. Bartschat, Phys. Scr. Rev. {\bf T134} (2009) 014020.\\[0pt] [5] K. Bartschat and O. Zatsarinny, Plasma Sources Sci. Technol. {\bf 20} (2011) 024012.