  We investigate the BCS-BEC crossover taking into account an additional
three-body interaction, which is essentially the scattering between the Cooper
pairs and the newly formed bosons. We show that if the two-body interaction is
attractive, the presence of this additional three-body term makes the crossover
process a nonreversible one. Starting from a stable Bose-Einstein condensate
(BEC) state, crossover to BCS can be achieved; but if the BCS state is the
starting point, instead of a stable BEC region, what the system crosses over to
is a metastable condensed state.
