Anharmonic corrections to the electrostatic energy of a Coulomb crystal

Model calculations of the electrostatic energy of body-centered-cubic and face-centered-cubic Coulomb crystals are presented. The electrostatic energy is calculated using a pair distribution function of ions in the harmonic approximation. This distribution function is shown to be in a good agreement with the function derived by the Monte Carlo method in the high-temperature classical limit (T⪢ℏωp, ωp being the ion plasma frequency). It is also in a good agreement with the distribution function obtained by the path integral Monte Carlo method in the low-temperature quantum limit (T⪡ℏωp). First- and second-order anharmonic corrections to the electrostatic energy are analyzed in a wide temperature range, from the high-temperature classical regime to the low-temperature quantum regime. For typical conditions in the envelopes of neutron stars and the cores of white dwarfs the anharmonic corrections to the electrostatic energy do not exceed a few percent of the electrostatic energy of harmonic lattice.