Abstract
Self-consistent methods for calculating the effects of anharmonicity on the vibrational properties of the Wigner electron lattice are described. First, the renormalized harmonic approximation (RHA) is derived from a variational principle for the free energy. The solution of a simplified set of equations resulting from the RHA is fully discussed; it shows large deviation from harmonic type behavior for r s < 50 and predicts an instability in the electron lattice at r s = 21.9. A treatment of higher order anharmonic effects is outlined and the results of a calculation based on the quartic and square of the cubic anharmonic interaction are presented. This calculation shows that deviation from harmonic type behavior already sets in at much larger r s values and predicts lattice instability for r s < 700. Reexamination of the empirical Lindemann melting criterion results in a similar prediction about the range of r s values for which the lattice state is stable.
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