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.

Partial ionization in dense plasmas: Comparisons among average-atom density functional models

“…This conclusion is consistent with MIS calculations reported in Ref. [77], wherein an approximate, but different, T -dependent exchange interaction was used.…”

“…Attention has been given to adding XC-interactions to the original finite-T TF scheme [55,77]. It is worthwhile to note subtleties that arise when one considers the MIS definitions for TF calculations (TFxc) that include these terms.…”

Structural and thermodynamic properties of spin-polarized fluid hydrogen

“…Moreover, it is highly unlikely that the simple TFW functional is adequate in the recombination zone, which may be more adequately described by ''average atom'' models. 25 As a consequence of these limitations, the free energy of the plasma phase calculated from the present DFT/HNC scheme turns out to be too low to lead to an intersection with the free energy curve of the atomic phase, which is expected to be more accurate. The predictions of linear response theory, which yields an upper bound to the free energy of the plasma phase, do intersect the free energy curve of the metastable atomic phase at a density which is necessarily too high, and should be considered as an upper bound for the density of the plasma-insulator transition.…”

Behavior of the coupling parameter under isochoric heating in a high-Zplasma

“…At high temperature and for high Z elements ionizations predicted by TF, TFD and TFDW are almost indistinguishable (see Fig. 2 in reference [23]). …”

“…This ionization is obtained for a temperature of about 300 eV leading to a plateau coupling parameter of Γ p = 22. One could prefer the TFDW model to get better estimations of the ionizations, particularly at low temperature, but it has been shown by Fromy et al [23] that the improvement is very weak at the expense of much heavier calculations. At high temperature and for high Z elements ionizations predicted by TF, TFD and TFDW are almost indistinguishable (see Fig.…”