The T matrix and the K matrix in cluster scattering

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Abstract
The authors investigate the scattering properties of small clusters of atoms using the multiple scattering formalism developed by Lloyd (1967). The transition and reaction matrices for different ensembles of scatterers are evaluated and used to calculate the density of electron eigenstates and the angular scattering cross sections. The dependence of the convergence of the angular momentum expansions for these quantities on the orientation, geometry and size of the cluster is examined. The calculations have been made for clusters of carbon atoms arranged in the geometry of the diamond lattice. It is found that it is more expedient to determine the density of states from an expression derived by Lloyd than to employ the cluster scattering matrices. An initial insight is obtained into the scattering properties of the tetrahedrally bonded elemental semiconductors and correlation with the known existence of an absolute energy gap in the corresponding crystalline and amorphous solids is discussed. Definite evidence is given for the 'channelling' of electrons along the bonds at energies well above the muffin tin zero.