Validity of perturbation theory. I. The single band gap model

Abstract

A simple test of the validity of perturbation theory in the evaluation of energy differences between different crystal structures for sp- bonded metals is provided by a model in which the effect of only one band gap is considered. This model, which was previously discussed semi-quantitatively by Harrison and by Pick and Blandin, is here solved exactly for a local pseudopotential. Former ideas concerning the nature of 'Brillouin zone-Fermi surface interactions' are discussed in the light of perturbation theory and this more exact model.