Generating functions for canonical systems of fermions.

The method proposed by Pratt to derive recursion relations for systems of degenerate fermions [S. Pratt, Phys. Rev.

Jensen-Feynman approach to the statistics of interacting electrons.

Faussurier [Phys. Rev. E 65, 016403 (2001)] proposed to use a variational principle relying on Jensen-Feynman (or Gibbs-Bogoliubov) inequality in order to optimize the accounting for two-particle interactions in the calculation of canonical partition functions.

Impact of high-order moments on the statistical modeling of transition arrays.

The impact of high-order moments on the statistical modeling of transition arrays in complex spectra is studied. It is shown that a departure from the Gaussian, which is usually employed in such an approach, may be observed even in the shape of unresolved spectra due to the large value of the kurtosis coefficient. The use of a Gaussian shape may also overestimate the width of the spectra in some cases.

Further stable methods for the calculation of partition functions in the superconfiguration approach.

The extension to recursion over holes of the Gilleron and Pain method for calculating partition functions of a canonical ensemble of noninteracting bound electrons is presented as well as a generalization for the efficient computation of collisional line broadening.

Stable method for the calculation of partition functions in the superconfiguration approach.

A general method for the calculation of the partition function of a canonical ensemble of noninteracting bound electrons is presented. It consists in a doubly recursive procedure with respect to the number of electrons and the number of orbitals. Contrary to existing approaches, this recursion relation contains no alternate summation of positive and negative numbers, which was the main source of numerical uncertainties.