Intra- site 4f-5d electronic correlations in the quadrupolar model of the gamma-alpha phase transition in Ce

As a possible mechanism of the $\gamma -\alpha$ phase transition in pristine cerium a change of the electronic density from a disordered state with symmetry Fm-3m to an ordered state Pa-3 has been proposed. Here we include on-site and inter- site electron correlations involving one localized 4f-electron and one conduction 5d-electron per atom. The model is used to calculate the crystal field of $\gamma$-Ce and the temperature evolution of the mean-field of $\alpha$-Ce. The formalism can be applied to crystals where quadrupolar ordering involves several electrons on the same site.