  We present a theoretical study of the BEC-BCS crossover in the
Bose-Einstein-Condensate regime (BEC), in the case of an unequal number of
fermions of two species. We take full account of the composite nature of the
dimers made of fermions. In the limit of low densities, we calculate the ground
state energy of the system, or equivalentely the chemical potentials of each
species as well as the one-particle gap and the energy of an "impurity"
immersed in a Fermi sea. For the chemical potentials we go up to order
(density)^{4/3}.The results found involve the exact atom-dimer a_{AD} and
dimer-dimer a_{DD} scattering lengths and therefore include the 3 and 4-body
problems in the manybody problem. We briefly comment on the importance of the
different mean-field corrections for recent experiments.
