Electron scattering states for low-energy spectroscopies

Abstract

In contrast to bound-state calculations for the valence band regime, the continuous states of half-space systems have not attained a level where a broad variety of methods ensures large applicability and sufficient accuracy for the needs of highly resolved spectroscopy. The multiple-scattering procedure works well in the high-energy range, but lacks either accuracy or convenience when applied to lower energies, where the anisotropic parts of the potential are strongly effective. The concept of Bloch-wave procedures in its original form is less well adapted to scattering boundary conditions, but requires additional theoretical adjustment, such as matching conditions, which often leads to an ill-posed boundary problem of the elliptic equation. The solution then suffers from instabilities preventing the development of stand-alone algorithms. The current state of the subject together with some promising solutions will be presented. Consideration will be given to the multiple scattering approach with anisotropic potentials and to the Bloch-wave development relying on pseudopotential, as well as on singular-potential formulations. The importance and quality of procedures is estimated through a comparison with very low energy electron diffraction (VLEED), low-energy electron diffraction (LEED) and total current spectroscopy (TCS) experiments.