Theory of Kohn Anomalies in the Phonon Spectra of Metals

An expression is derived for the change in frequency of the lattice vibrations in a metal caused by the interaction of the phonons with the conduction electrons. The various factors affecting the magnitude of these Kohn anomalies are considered, and a connection is made with the value of the electrical resistivity of the pure metal. The valence of the metal is found to be the most important factor determining whether such anomalies should be observable. The results of the calculations are applied to Pb, and give good agreement with experiment.