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Hartree-Fock equations for plasma atoms are proposed and used in the superconfiguration method of photoabsorption calculation. They involve statistical sums, taking into account integer shell occupation numbers and finite temperature effects. These sums are evaluated using electron and hole counting. Their use is also shown to be relevant to the treatment of orbital relaxation in the final states of optical transitions. ͓S1063-651X͑97͒50805-1͔ PACS number͑s͒: 52.25. Ϫb, 31.15.Ϫp, 78.70.Dm In this communication we propose a new statistical Hartree-Fock approach to atoms in plasmas at finite temperature. It is based on the superconfiguration approximation successfully applied in the superconfiguration transition arrays method ͑STA͒ ͓1-5͔ to interpret transmission spectra of lowdensity plasmas measured in laboratories ͓1-16͔.The original STA method ͓1-5͔ is applied in conjunction with the use of parametric potentials calculated by the RELAC code ͓17͔ for free ions. In this sense the superconfigurations, as introduced in ͓1-5͔, are not fully selfconsistent.The finite temperature Hartree-Fock ͑HF͒ method presented here is derived in the framework of the superconfiguration approximation. The average shell populations and interaction matrices are given in terms of statistical sums that are averages of the corresponding quantities for configurations. This allows us to avoid problems stemming from noninteger occupation numbers in other thermal HF theories ͑see, for instance, discussion in Ref. ͓14͔͒. The statistical sums appear to be key quantities in all the calculations required by the superconfiguration method: energies, moments of the photoabsorption spectrum . . . . They are also needed in the relaxation effects described below. The mixed counting ͑electron or holes͒, proposed in this work, is applied to HF equations and to all statistical sums in our superconfiguration code.The superconfiguration contains configurations that are close in energy, i.e., the differences of configuration energies within a superconfiguration are less than kT. The interaction of superconfigurations is neglected. A superconfiguration ⌶ is specified by the set of supershell populations ͚ s q s (C) ϭQ , i.e. the sum of the populations in the shells belonging to ͓1͔. The superconfiguration of the bound electrons is neutralized by free electrons. The one-electron states are common within each superconfiguration. In thermal equilibrium, assuming that the superconfigurations do not interact, it is sufficient to require that the free energy of each superconfiguration be stationary with respect to its wave functions. The free energy of ⌶ is calculated using the configuration-averaged energies of bound electrons and includes a Thomas-Fermi ͑TF͒ contribution for the free electrons. In the Boltzmann factor, following ͓1͔, we use for the configuration energy (C b is the bound-electron configuration͒:only the first linear term depends explicitly on the boundshell populations q i (C b ) , the other terms being averaged over⌶) is the free energy of fr...

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