Abstract
The role of the particle-particle $p$-wave spin interaction in Fermi liquids with an $s$-wave pairing is studied. Depending on the sign of the interaction, there arises either a new exciton collective mode below the pair-breaking threshold or a diffusive excitation mode above the threshold. The Landau parameters that control the interaction strength are evaluated for various systems: dilute fermion gases, a 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. How these effects influence the neutrino emissivity in neutron Cooper-pair recombinations in neutron stars is shown.
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