  Using the standard Hamiltonian of the BCS theory, we show that in an ensemble
of interacting fermions with the spin 1/2 there exist coherent states $|NC>$,
which nullify the Hamiltonian of the interparticle interaction (scattering).
These states have an analogy with the well-known in quantum optics the coherent
population trapping (CPT) effect. The structure of these CPT-like states
corresponds to Cooper pairs with the total spin $S$=1. The found states have a
huge degree of degeneracy and carry a macroscopic magnetic moment, that allows
us to construct a new model of the magnetism connected with the delocalized
electrons in metals (conductors). A principal possibility to apply the obtained
results to the superfluid $^3$He is also demonstrated.
