Lattice dynamics of sodium

The method of orthogonalized plane waves has been shown to lead to the concept of an effective potential for the interaction of the conduction electrons with the periodic potential of the lattice. It has been further demonstrated by Sham that the effective potential may be regarded as moving rigidly with the ions in the course of the lattice vibrations. The experimental results of Woods, Brockhouse, March, Stew art & Bowers (1962) on the phonon dispersion relation in sodium have been analyzed from this point of view. It is found that the results are consistent with the concept of an effective potential, which is deduced empirically and found to have qualitatively the form expected. Certain features of the matrix element for electron-phonon interaction can also be deduced from the experimental data. The force constants derived by Woods et al. can be interpreted quantitatively in terms of the effective potential and electron screening effects. Other features of the results are discussed.