Boson-fermion model beyond the mean-field approximation

A model of hybridized bosons and fermions is studied beyond the mean-field approximation. The divergent boson self-energy at zero temperature makes the Cooper pairing of fermions impossible. The frequency and momentum dependence of the self-energy and the condensation temperature T-c of initially localized bosons are calculated analytically. The value of the boson condensation temperature T-c is below 1 K and the long-wave spectrum is strongly damped which rules out the boson-fermion model with the initially localized bosons as a phenomenological explanation of high-temperature superconductivity. The intra-cell density-density fermion-boson interaction dominates in the fermion self-energy. The model represents a dirty normal metal, in which localized bosons play the role of impurities.