Nature of correlations in the atomic limit of the boson fermion model

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.