Crossover from BCS superconductivity to BEC of pairs: The role of the lifetime of the pairs

The understanding of an electron gas with short coherence length pairs formed by an attractive interaction is believed to be one of the major keys to our theoretical knowledge of the high-T_c-superconductors. Mainly the deviations of the cuprates from usual metallic Fermi liquid behaviour already in the normal state like e.g. a linear resistivity or the observation of a pseudo gap can result from electron-electron correlations. We therefore investigate the negative U Hubbard model in two dimensions at low densities using the T-matrix approximation. In the non selfconsistent formulation of the theory the system always shows an instability towards Bose condensation of pairs into an infinite lifetime two-particle bound state. If the calculations are performed selfconsistently pair-pair scattering is included which causes the pairs to have finite lifetime. The physics of these finite lifetime pairs is discussed.