A Hartree-Fock statistical approach to atoms in plasmas - Electron and hole countings in evaluation of statistical sums

We derive finite temperature self-consistent field (SCF) Hartree-Fock equations for atoms in plasmas based on the superconfiguration method proposed by :Bar-Shalom, Oreg and collaborators. The populations of shells and the shell interaction matrices in the HF equations are given in terms of statistical sums which are averages of corresponding expressions for configurations. In such a way the Pauli principle and the exchange interaction are taken into account exactly. This allows us to avoid problems stemming from non-integer occupation numbers in other approaches to thermal HF theories. The SCF calculations include free electrons in the Thomas-Fermi approximation. Our method uses the hole counting in the statistical sums for each supershell in which the number of holes is lower than the number of electrons. The use of both electron and hole counting ensures high numerical precision of the recurrent relations for the statistical sums. (C) 1997 Elsevier Science Ltd. All rights reserved.