Finite-difference method for the calculation of low-energy positron diffraction

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Abstract
A scheme of calculation avoiding the muffin-tin approximation is presented for low-energy positron diffraction. The finite-difference method is used to solve the Schrödinger equation. All the steps of the calculation are described. The first one is the elaboration of a grid of points in the various areas, where the wave function must be known. The potential is then calculated including the electronic reorganization, due to interatomic bondings or dangling bonds. The wave function is obtained by solving a large system of linear equations. The tensor approach to compare experimental and theoretical spectra is also described. The main improvement with respect to conventional calculation resides in the possibility of evaluating the charge exchanges, orbital per orbital, inside atoms, and between atoms. An application to the GaAs(110) surface leads to a good agreement between experiment and theory with geometrical parameters close to those found in standard studies. An oscillatory behavior of the total atomic charge in the topmost layers is revealed. A cartography in three dimensions of the electronic density in the first atomic layers is provided. © 1996 The American Physical Society.