Quasiparticle disintegration in fermionic superfluids

We study the fermionic quasiparticle spectrum in a zero-temperature superfluid Fermi gas, and particular how it is modified by different disintegration processes. On top of emission collective boson ($1\to2$, subject previous study, PRL 124, 073404), we consider here events where three quasiparticles are emitted ($1\to3$). show that both processes described $t$-matrix self-energy (as well as some highly off-resonant vacuum processes), characterize associated continua. At strong coupling, heavily distorted near $1\to3$ threshold. Near dispersion minimum, remain well-defined, main effect off-shell to shift location minimum value corresponds Hartree BCS limit. With our approximation self-energy, correction energy gap with respect mean-field result however remains small, contrast experimental measurements.