  Using the equation of motion technique for Green's functions we derive the
exact solution of the boson fermion model in the atomic limit. Both (fermion
and boson) subsystems are characterised by the effective three level excitation
spectra. We compute the spectral weights of these states and analyse them in
detail with respect to all possible parameters.
  Although in the atomic limit there is no true phase transition, we notice
that upon decreasing temperature some pairing correlations start to appear.
Their intensity is found to be proportional to the depleted amount of the
fermion nonbonding state. We notice that pairing correlations behave in a
fashion observed for the optimally doped and underdoped high $T_{c}$
superconductors. We try to identify which parameter of the boson fermion model
can possibly correspond to the actual doping level. This study c larifies the
origin of pairing correlations within the boson fermion model and may elucidate
how to apply it for interpretation of experimental data.
