Properties of a Fermi liquid at the superfluid transition in the crossover region between BCS superconductivity and Bose-Einstein condensation

The self-consistent equations, which have been derived recently as a microscopic model for the crossover between BCS superconductivity and Bose-Einstein condensation in a three-dimensional interacting Fermi system [R. Haussmann, Z. Phys. B 91, 291 (1993)], are solved numerically by repeated Fourier transformation. We find a superfluid transition temperature T_c which increases monotonically with increasing attractive coupling strength. Furthermore, we determine the chemical potential μ, the fermion distribution function n(k), and the complex effective mass 2m^* of the fermion pairs at T=T_c. The bound fermion pairs cause a power-law tail ~k^-4 in n(k) for large k and behave as short-living quasiparticles in the crossover region, which is indicated by a large imaginary part of 2m^*.