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