Methods in angle-resolved photoelectron diffraction: Slab method versus separable propagator cluster approach

Abstract

We have compared multiple-scattering results of angle-resolved photoelectron diffraction spectra between the exact slab method and the separable propagator perturbation cluster method. In the slab method, the source wave and multiple scattering within strongly scattering layers are expanded in spherical waves while the scattering among different layers is expressed in plane waves. The transformation between spherical waves and plane waves is done exactly. The plane waves are then matched across the solid-vacuum interface to a single outgoing plane wave in the detector's direction. The slab is infinitely extended parallel to the surface. Normal to the surface, enough layers are included to ensure convergence of the calculated intensity. The separable propagator perturbation approach uses two approximations; (i) A separable representation of the Green's-function propagator and (ii) a perturbation expansion of multiple-scattering terms. The cluster size is finite, typically containing 50 atoms or less. Results of this study show that using a cluster of 148 atoms, the largest cluster used to date, the cluster size is still too small for the cluster results on Ni(001) to converge with those of the slab method. Ideas to improve the perturbation expansion cluster method are discussed.