  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 $1K$ 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 normal metal with strongly damped bosonic excitations.
The latter play the role of normal impurities.
