Condensation of charged bosons hybridised with fermions

The boson self-energy and the Coulomb repulsion are taken into account to show that the Cooper pairing of fermions via transitions into virtual bosonic (preformed pair) states is impossible. The pairing of fermions is possible however if real bosons are condensed at a very low temperature T-c. The crucial role of the Coulomb screening in the Cooper pairing is elucidated which reduces both the boson self-energy and T-c. The relative value of the long-wave boson damping due to hybridisation of bosons with fermions remains finite. There is no condensation of bosons and consequently no Cooper pairing of fermions in the two dimensional boson-fermion model. For a realistic value of the Coulomb pseudopotential the normal-state fermion scattering rate is dominated by the boson density fluctuations rather than by hybridisation and has perfectly linear temperature dependence.