Impurity Problem in the Tight-Binding Approximation: Application to Transition-Metal Alloys

Abstract

The characteristics of a metal with one impurity atom are deduced with a view towards application to dilute transition-metal alloys. We assume that the band structure of the pure metal is described by a tight-binding approximation. The scattering problem is expressed in a new representation whose basis functions have the symmetry of the point group of the metal. For example, it is shown that the Friedel sum rule can be expressed with a finite number of phase shifts, each of them being related to one irreducible representation of the point group. Two simple examples are studied, and detailed studies of the effects of the degeneracy and of the potential extension are made.