Shrinking of a condensed fermionic cloud in a trap approaching the Bose-Einstein condensation limit

We determine the zero-temperature density profile of a cloud of fermionic atoms in a trap subject to a mutual attractive interaction, as the strength of the interaction is progressively increased. We find a significant decrease of the size of the atomic cloud as it evolves from the weak-coupling regime of overlapping Cooper pairs to the strong-coupling ~Bose-Einstein! regime of nonoverlapping bound-fermion pairs. Most significantly, we find a pronounced increase of the value of the density at the center of the trap ~even by an order of magnitude! when evolving between the two regimes. Our results are based on a generalized Thomas-Fermi approximation for the superfluid state, which covers continuously all coupling regimes.