Multiple scattering within finite and infinite systems of generalized muffin-tin potentials. Generalizations of the cluster equations, the Lloyd-formula and the KKR equations

Abstract

Clusters and (both disordered and periodic) ensembles of generalized muffin-tin potentials, nonzero only within arbitrary non-overlapping volumes, are considered, assuming the scattering states of each of these single muffin-tin potentials are known. Generalizations of the equations for the cluster scattering states, of the Lloyd-formula for the density of states and of the KKR equations for the band structure are obtained. The usual separation into potential and structure appears only if the muffin-tin potentials can be enveloped with non-overlapping spheres. Otherwise, near field properties must be taken into account.