High pressure limiting forms of the zero-temperature equations of state of Ta and Pu from relativistic Thomas-Fermi theory

There is considerable current interest in the equations of state (EOS) of the two heavy metals, tantalum and plutonium. For the former, Boettger [Phys. Rev. B 64, 035103 (2001)] has recently carried out calculations based on the Dirac relativistic wave equation. Our purpose here is different, namely, it is to work with the simplest form of relativistic density-functional theory which is the relativistic Thomas-Fermi (TF) method. The predictions of this approach should come into their own at sufficiently high pressures (we work throughout at T=0) and direct contact has been made, for Ta, with the (lower-pressure) predictions of Boettger's study. Similar results for the high-pressure limiting form of the T=0 EOS for Pu are presented. Because the relativistic TF method is purely "local density" in character, the results on Ta and Pu are preceded by a full study of the relativistic homogeneous electron gas, including the relativistic exchange contribution to its EOS. An important finding there is that in the high-density limit the relativistic exchange contribution to the pressure becomes proportional to the kinetic contribution, the proportionality constant being linear in the fine-structure constant.