ANHARMONIC CONTRIBUTIONS TO VIBRATIONAL PROPERTIES OF WIGNER ELECTRON LATTICE

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 rs < 50 and predicts an instability in the electron lattice at rs = 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 rs values and predicts lattice instability for rs < 700. Reexamination of the empirical Lindemann melting criterion results in a similar prediction about the range of rs values for which the lattice state is stable. © 1969.