  The exact renormalization group methods is applied to many fermion systems
with short-range attractive force. The strength of the attractive
fermion-fermion interaction is determined from the vacuum scattering length. A
set of approximate flow equations is derived including fermionic and bosonic
fluctuations. The numerical solutions show a phase transition to a gapped
phase. The inclusion of bosonic fluctuations is found to be significant only in
the small-gap regime.
