A simple model is considered of an alloy consisting of a free-electron gas with a dilute concentration of impurities. Electron states at the Fermi energy have a spread in wave numbers which blurs the Fermi surface. Only up to second order in perturbation theory is the average wave number of an alloy state the same as that given by the rigid-band model. A renormalization of the alloy wave function occurs which decreases the weight of that part of the state that is associated with a given wave number. The effect of renormalization shows itself in positron-annihilation experiments in alloys as an apparent decrease in the number of electrons in the vicinity of the Fermi momentum.

• Received 25 August 1967

DOI:https://doi.org/10.1103/PhysRev.168.730