  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 (BCS) regime
of overlapping Cooper pairs to the strong-coupling (Bose-Einstein) regime of
non-overlapping 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,
that covers continuously all coupling regimes.
