METHODS IN ANGLE-RESOLVED PHOTOELECTRON DIFFRACTION - SLAB METHOD VERSUS SEPARABLE PROPAGATOR CLUSTER APPROACH

We have compared multiple-scattering results of angle-resolved photoel ectron diffraction spectra between the exact slab method and the separ able propagator perturbation cluster method. In the slab method, the s ource wave and multiple scattering within strongly scattering layers a re expanded in spherical waves while the scattering among different la yers is expressed in plane waves. The transformation between spherical waves and plane waves is done exactly. The plane waves are then match ed across the solid-vacuum interface to a single outgoing plane wave i n the detector's direction. The slab is infinitely extended parallel t o the surface. Normal to the surface, enough layers are included to en sure convergence of the calculated intensity. The separable propagator perturbation approach uses two approximations: (i) A separable repres entation of the Green's-function propagator and (ii) a perturbation ex pansion of multiple-scattering terms. The cluster size is finite, typi cally containing 50 atoms or less. Results of this study show that usi ng a cluster of 148 atoms, the largest cluster used to date, the clust er size is still too small for the cluster results on Ni(001) to conve rge with those of the slab method. Ideas to improve the perturbation e xpansion cluster method are discussed.