  A role of a particle-particle p-wave spin interaction in Fermi liquids with
s-wave pairing is studied. Depending on the sign of the interaction there
arises either the new exciton collective mode below the pair-breaking threshold
or the diffusive excitation mode above the threshold. The Landau parameters
which control the interaction strength are evaluated for various systems: the
dilute fermion gases, degenerate electron liquid, metals, atomic nuclei and
neutron matter. The interaction removes also the square-root singularity in the
phase space of pair breaking processes. It is shown how these effects influence
the neutrino emissivity in the neutron Cooper-pair recombinations in neutron
stars.
