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Microscopic response theory for strongly-coupled superfluid fermionic systems

A consistent microscopic theory for the response of strongly-coupled superfluid fermionic systems is formulated. After defining the response as a two-point two-fermion correlation function in the basis of the Bogolyubov's quasiparticles, the equation of motion (EOM) method is applied using the most general fermionic Hamiltonian with a bare two-body interaction, also transformed to the quasiparticle space. As a superfluid extension of the case of the normal phase, the resulting EOM is of the Bethe-Salpeter-Dyson form with the static and dynamical interaction kernels, where the former determines the short-range correlations and the latter is responsible for the long-range ones. Both kernels as well as the entire EOM have the double dimension as compared to that of the normal phase. Non-perturbative approximations via the cluster decomposition of the dynamical kernel are discussed, with the major focus on a continuous derivation of the quasiparticle-phonon coupling variant of the latter kernel, where the phonons (vibrations) are composite correlated two-quasiparticle states unifying both the normal and pairing modes. The developed theory is adopted for nuclear structure applications, such as the nuclear response in various channels. In particular, the finite-amplitude method generalized beyond the quasiparticle random phase approximation, taking into account the quasiparticle-vibration coupling, is formulated for prospective calculations in non-spherical nuclei.