Thomas–Fermi-like and average atom models for dense and hot matter

Abstract

All the Thomas–Fermi approaches to the thermodynamics and atomic physics properties of dense and ionized matter consisting of a single element are systematically derived and compared within a density-functional theoretical framework. The corresponding results are contrasted to those of the average atom model by using similar approximations for exchange, correlation, and gradient corrections. Emphasis is led on equations of state, ionization, level shifts, and radial moments. The same numerical algorithms are used to unravel similar trends or identify specific ones, in terms of density and temperature variations. The most sophisticated Thomas–Fermi–Dirac–Weizäcker method yields the closest results to the hybrid average atom model using quantized bound states. Parameters ranges of potential interest for inertially confined thermonuclear fusion stress out density in the 0.1–10 times the solid, and temperature up to 10 keV.