  We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) pairing to
a Bose-Einstein condensate (BEC) in a relativistic superfluid within a
boson-fermion model. The model includes, besides the fermions, separate bosonic
degrees of freedom, accounting for the bosonic nature of the Cooper pairs. The
crossover is realized by tuning the difference between the boson mass and boson
chemical potential as a free parameter. The model yields populations of
condensed and uncondensed bosons as well as gapped and ungapped fermions
throughout the crossover region for arbitrary temperatures. Moreover, we
observe the appearance of antiparticles for sufficiently large values of the
crossover parameter. As an application, we study pairing of fermions with
imbalanced populations. The model can potentially be applied to color
superconductivity in dense quark matter at strong couplings.
