On the boson-fermion model of superconductivity

The existence of pair excitations in a Fermi gas interacting via a short-range attractive potential is investigated. Within the ladder approximation to the Bethe-Salpeter equation for the effective two-particle interaction, evidence of pair excitation is found at energies slightly larger than the chemical potential. The link between those excitations and a boson-fermion model of superconductivity (Phys. Lett. A, 196 (1995) 359) is discussed. In particular it is shown that the charge carrier density dependence of the pair excitation (boson) energy, assumed phenomenologically in the boson-fermion model, is consistent with the properties of the interacting Fermi gas studied. These results give support to the microscopic origin of the phenomenological boson-fermion model of superconductivity.