Atom-in-jellium equations of state and melt curves in the white dwarf regime

Atom-in-jellium calculations of the electron states, and perturbative calculations of the Einstein frequency, were used to construct equations of state (EOS) from around 10⁻⁵ to 10⁷ g/cm³ and 10⁻⁴ to 10⁶ eV for elements relevant to white dwarf (WD) stars. This is the widest range reported for self-consistent electronic shell structure calculations. Elements of the same ratio of atomic weight to atomic number were predicted to asymptote to the same T = 0 isotherm. A generalized Lindemann criterion based on the amplitude of the jellium oscillations, previously used to extrapolate melt curves for metals, was found to reproduce previous thermodynamic studies of the melt curve of the one component plasma with a choice of vibration amplitude consistent with low pressure results. For elements for which low pressure melting satisfies the same amplitude criterion, such as Al, this melt model thus gives a likely estimate of the melt curve over the full range of normal electronic matter; for the other elements, it provides a useful constraint on the melt locus.