  Although usually considered as a technique for predicting electron states in
dense plasmas, atom-in-jellium calculations can be used to predict the mean
displacement of the ion from its equilibrium position in colder matter, as a
function of compression and temperature. The Lindemann criterion of a critical
displacement for melting can then be employed to predict the melt locus,
normalizing for instance to the observed melt temperature or to more direct
simulations such as molecular dynamics (MD). This approach reproduces the high
pressure melting behavior of Al as calculated using the Lindemann model and
thermal vibrations in the solid. Applied to Fe, we find that it reproduces the
limited-range melt locus of a multiphase equation of state (EOS) and the
results of ab initio MD simulations, and agrees less well with a Lindemann
construction using an older EOS. The resulting melt locus lies significantly
above the older melt locus for pressures above 1.5\,TPa, but is closer to
recent ab initio MD results and extrapolations of an analytic fit to them. This
study confirms the importance of core freezing in massive exoplanets,
predicting that a slightly smaller range of exoplanets than previously assessed
would be likely to exhibit dynamo generation of magnetic fields by convection
in the liquid portion of the core.
