Theory of Plasma Waves in Metals

The Hartree approximation is used to investigate the effect of the crystal lattice on plasma oscillations in metals. The plasma frequency is given by ^2=4e^2n₀〈1{{mₙ}^*}〉, where the average is over filled electron states. For free electrons this equation reduces to that given by Bohm and Gross: for insulators 〈1{{mₙ}^*}〉=0 and there are no oscillations. In metals with occupied d bands, such as Cu, Ni, and Ag, there is a strong coupling between the plasma wave and the d electrons which gives rise to frequency broadening. This explains why the plasma lines observed by Ruthemann and Lang are so much wider in these elements than in Be or Al. Further confirmation of this mechanism could be obtained by repeating their experiments on the transition metals Sc---Ni.