  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 $10^7$g/cm$^3$ and $10^{-4}$ to $10^{6}$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, suggesting that, contrary to recent studies of the
crystallization of WDs, the amount of gravitational energy that could be
released by separation of oxygen and carbon is small. A generalized Lindemann
criterion based on the amplitude of the ion-thermal oscillations calculated
using atom-in-jellium theory, 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.
