Quasiparticle disintegration in fermionic superfluids

We study the fermionic quasiparticle spectrum in a zero-temperature superfluid Fermi gas, and in particular how it is modified by different disintegration processes. On top of the disintegration by emission of a collective boson (1 -> 2, subject of a previous study, PRL 124, 073404), we consider here disintegration events where three quasiparticles are emitted (1 -> 3). We show that both disintegration processes are described by a t -matrix self-energy (as well as some highly off-resonant vacuum processes), and we characterize the associated disintegration continua. At strong coupling, we show that the quasiparticle spectrum is heavily distorted near the 1 -> 3 disintegration threshold. Near the dispersion minimum, where the quasiparticles remain well-defined, the main effect of the off-shell disintegration processes is to shift the location of the minimum by a value that corresponds to the Hartree shift in the BCS limit. With our approximation of the self-energy, the correction to the energy gap with respect to the mean-field result however remains small, in contrast with experimental measurements.