On the Accuracy of the Thomas-Fermi Atom for Opacities

Carson, Mayers, and Stibbs have suggested using the hot Thomas-Fermi model of the atom for Rosseland mean-opacity calculations. They found that opacities based on the Thomas-Fermi model were larger than the Cox opacities by factors of up to three. The present work was undertaken to study the accuracy of the Thomas-Fermi model. Several atomic parameters for bound states of neon, including dipole matrix elements, line wavelengths, and pressure ionization, were computed for typical stellar-interior conditions, and were compared to the Hartree-Fock model with statistical exchange. Calculations of the opacity of a pure neon plasma and of a pure silicon plasma indicate that opacities based on the Thomas-Fermi model are probably not reliable because of inaccuracies in the pressure ionization. The resulting errors in the positions of the bound-free absorption edges are able to account for at least a part of the differences between the Thomas-Fermi and Cox opacities. The Thomas-Fermi bound--state occupation numbers are larger than those computed from the Saha equation, which also can account for part of the differences. Inconsistencies in the free- electron pressure and the number of electrons in each ion sphere are also noted. (auth)