Phase transitions in highly-correlated f-electron systems with fluctuating valence

A formalism is presented for treating electrons in highly-correlated spin-orbit coupled multiplet levels in f-shells, which are also hybridized with valence or conduction states. This is achieved by introducing operators which cause transitions between the configurations, but project out all other configurations. The Zwanzig-Mori projection operator technique is exploited to derive results for the electron Green's functions, which are then solved self-consistently. The lowest order self-consistent solutions bear a certain resemblance to unrestricted Hartree-Fock theory. Higher order terms exhibit Kondo-like singularities under certain conditions. It is shown that several phases, both configurational and magnetic, are possible depending on the relative values of the conduction electron bandwidth, the hybridization energy and the values of the Coulomb and exchange integrals