Scattering theory and cluster calculations

Abstract

It is shown that a formula due to Lloyd (1967) for the density of states of a cluster of muffin-tin potentials can be derived very easily from a theorem in formal scattering theory that was proved by Krein (1953). Some questions in the usual interpretation of the formulae are discussed in the light of Krein's theorem and also the time-delay operator. Generalised Jost functions are introduced and used to furnish a picture of the limiting process in various kinds of cluster calculations.