Self-consistent phonon approximations for the solid phase of a one-component plasma

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Abstract
We applied the self-consistent harmonic (SCH) approximation to the solid phase of the one-component plasma (OCP) to study effects of anharmonicity on its melting transition and equation of state. We calculated both the zero-temperature (Wigner lattice) and high-temperature (classical OCP) limits and compared the high-temperature results with those of Monte Carlo simulations. Our principal findings are that the anharmonic effects are generally small, the dynamic instability in the SCH is unrelated to the melting transition, and except near the instability the SCH predicts anharmonic contributions to the internal energy opposite in sign from those found in the high-temperature Monte Carlo simulations. We also studied two simpler self-consistent phonon approximations, the self-consistent Einstein and Debye approximations, and report their zero- and high-temperature predictions.