Investigation of Surface Properties by the Inclusion of Nonspherical Potential Components for Surface Atoms

Abstract

Publisher Summary In this chapter, it is assumed that the non-spherical contributions are most important for surface atoms. Hence, using the muffin-tin picture, the influence of non-spherical potential components of surface atoms on the scattering properties of these atoms is investigated. For this purpose, the chapter considers the solutions of the Schrodinger equation for a non-spherical potential V(r), using an angular momentum expansion and lattice harmonics are used as the basis. For such arrangement with the symmetry C 3v , there are three irreducible representations Γ = A1,A2,E with dimensions 1, 1, 2, respectively. The potential is an A1 representation. Its behavior is of interest inside the muffin-tin sphere. Nonspherical contributions for a Ni atom are presented in the chapter. They do not have a singularity at the origin (center of the sphere), and they increase with increasing distance from the center. The eigenvectors and the generalized phase shifts have been calculated for different energies for the non-spherical muffin-tin potential of a Ni atom. Even for relatively high energies of 4 Ryd the deviations from the spherical case are remarkable. The scattering amplitude for 4 Ryd in the complex plane is shown. The scattering angle is indicated as a parameter, and the scattering amplitude for the spherical case is presented for comparison.