  We investigate the Bose-Einstein condensation of Fermionic pairs in a uniform
two-component Fermi gas obtaining an explicit formula for the condensate
density as a function of the chemical potential and the energy gap. We analyze
the condensate fraction in the crossover from the Bardeen-Cooper-Schrieffer
(BCS) state of weakly-interacting Cooper pairs to the Bose-Einstein Condensate
(BEC) of molecular dimers. By using the local density approximation we study
confined Fermi vapors of alkali-metal atoms for which there is experimental
evidence of condensation also on the BCS side of the Feshbach resonance. Our
theoretical results are in agreement with these experimental data and give the
behavior of the condensate on both sides of the Feshbach resonance at zero
temperature.
