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 write in a systematic way a set of refined equations for average ion models in which correlations between populations are taken into account, starting from a microscopic model for the evolution of the electronic configura- tion probabilities. Numerical simulations illustrating the improvements with respect to standard average ion models are presented at the end of the paper.