Green-function method for a mixed-valence Hamiltonian

A Green-function diagrammatic method is utilized to calculate the occupation number of a narrow ($f$) band in a mixed-valence system. The method is a generalization of the Hubbard-I approximation for a two-band Hamiltonian. The results at $T=0\mathrm{}$ K indicate the existence of an intermediate-valence state for finite hybridization between the bands, and abrupt transitions for values of $G$ comparable to the half bandwidth of the conduction band. A metal-insulator transition is also obtained.