Hartree-Fock study of the Anderson model coupled to a boson field; mixed valence states

We generalize the Anderson model of magnetic impurities in metals, introducing a local coupling between the impurity orbital and a boson field. A systematic finite-temperature Hartree-Fock and random-phase-approximation investigation is presented; particular attention is paid to the problem of multiple solutions of the Hartree-Fock equation, and the various phase transitions in parameter space appearing in this approximation. Regions of slow interconfigurational valence fluctuations are identified, and applications to the problems of mixed-valence rare-earth materials and resonant two-electron states in amorphous materials are suggested.