Convergence Comparisons of the Third-Ordert-Matrix Method with an Exact Multiple-Scattering Method

Detailed comparisons are presented between the elastic low-energy-electron-diffraction (LEED) intensity spectra calculated by a third-order $t$-matrix method and those obtained from an exact multiple-scattering method. In the $t$-matrix method, multiple-scattering events are expanded in terms of individual ion-core $t$ matrices and the resulting scattering terms are summed for an infinite number of layers up to third order in the individual ion-core scattering matrices. The exact method, on the other hand, treats multiple-scattering events by inverting a complex matrix for scattering events in the plane and then inverts another complex matrix for scattering events among planes for a finite number of layers. Hence, the exact method includes intra- and interlayer multiple-scattering events for a finite number of layers to infinite order. Direct comparisons of elastic intensity-energy spectra are made for aluminum (001) and nickel (001). Comparisons are also made for rotation diagrams at different energies on aluminum (001). The results show that the third-order $t$-matrix method adequately describes LEED intensity-energy spectra and rotation diagrams. A simple parameterization scheme is introduced which improves qualitative agreements between third-order results and exact-method results. It is concluded that the $t$-matrix formalism provides a useful approach to the analysis of LEED spectra.