Quantum phase slips (QPS) in narrow superfluid channels generate momentum by
unwinding the supercurrent. In a uniform Bose gas, this momentum needs to be
absorbed by quasiparticles (phonons). We show that this requirement results in
an additional exponential suppression of the QPS rate (compared to the rate of
QPS induced by a sharply localized perturbation). In BCS-paired fluids,
momentum can be transferred to fermionic quasiparticles, and we find an
interesting interplay between quasiparticle scattering on QPS and on disorder.Comment: 4 pages, revtex, no figures; to be published in Phys. Rev. Letter