A Coherent derivation of an average ion model including the evolution of correlations between different shells

We propose in this short note a method enabling to writein a systematic way a set of refined equations for average ion models inwhich correlations between populations are taken into account, startingfrom a microscopic model for the evolution of the electronic configura-tion probabilities. Numerical simulations illustrating the improvementswith respect to standard average ion models are presented at the end ofthe paper.