  We derived the energy gap of a breached pairing superfluidity phase of
fermionic atoms in an external magnetic field in Feshbach resonance experiments
which is determined by the magnetic - field detuning from the Feshbach
resonance. We show that a BCS superfluid state exists only for the magnetic -
field detuning smaller than one critical, and this critical magnetic - field
detuning is determined by the equality of the Zeeman energy splitting for the
magnetic - field detuning to the energy gap $ \Delta_0 $.
