  We study the zero-temperature grand potential of a three-dimensional
superfluid made of ultracold fermionic alkali-metal atoms in the BCS-BEC
crossover. In particular, we analyze the zero-point energy of both fermionic
single-particle excitations and bosonic collective excitations. The bosonic
elementary excitations, which are crucial to obtain a reliable equation of
state in the BEC regime, are obtained with a low-momentum expansion up to the
forth order of the quadratic (Gaussian) action of the fluctuating pairing
field. By performing a cutoff regularization and renormalization of Gaussian
fluctuations, we find that the scattering length $a_B$ of composite bosons,
bound states of fermionic pairs, is given by $a_B = (2/3) a_F$, where $a_F$ is
the scattering length of fermions.
