  With reference to the broad and narrow Fano-Feshbach resonances of 6Li at
about 822 G and 543 G, we show that for the broad resonance a molecular
coupled-channel calculation can be mapped with excellent accuracy onto an
effective single-channel problem with a contact interaction. This occurs for a
wide enough range of the magnetic field, that the full BCS-BEC crossover can be
realized with a typical trap. For the narrow resonance, the mapping onto a
single-channel problem and the realization of the BCS-BEC crossover are
restricted to too narrow a range of the magnetic field to obtain them in
practice. In this way, the BCS-BEC crossover for Fermi atoms with the broad
resonance is placed on the same footing as the corresponding crossover for
different physical systems.
