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The electron-phonon interactions in valence fluctuation systems have been reconsidered and a new procedure has been developed to transform the author's model Hamiltonian, which is a periodic Anderson model with indirect hybridisation, by a unitary transformation of the displacement operator type. Then, a variational ground state of the phonons subsystem has been constructed; thus the electron and the phonon subsystems could be separated approximately and an effective Hamiltonian for the electron subsystem could be obtained. Finally, a functional integration approach has been used to investigate the ground-state properties of the effective Hamiltonian, and the ground-state phase diagrams have been given. By requiring that the total ground-state energy of the model system should be a minimum, he has found that the ground state of the phonon subsystem must be a two-phonon coherent state which is different from any eigenstate of phonon number operators. Also, the author has shown that through the electron-phonon interaction the f-f Hubbard U-term could contribute to the d-f hybridisation and he considers that this contribution might be used to explain why most of valence fluctuation systems have a strongly correlated f band but are not in any magnetic state.
Hang Zheng (Sat,) studied this question.