Within a tight-binding formalism, we present a Bethe-lattice-type approximation which can be applied to the whole Hamiltonian or to a hybridization part only and which is expected to be valid in disordered systems like liquids. In the first case, it gives simple scalar equations for the calculation of the densities of states and has been applied successfully to some transition-metal alloys. In the second case, it can be used to study the sp-d hybridization. We predict a Fano effect on the sp density of states which can lead to the creation of a pseudogap at the top of the d band. We recover an expression for the sp self-energy which is the basis for an explanation of positive Hall coefficients in amorphous transition metals and also implies the well-known s-d resistivity proportional to the d density of states at the Fermi level.
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