Abstract: When quasiparticles in a BCS (Bardeen-Cooper-Schrieffer) superconductor recombine into Cooper pairs, phonons are emitted within a narrow band of energies above the pairing energy at 2 delta. We show that a phonon band gap restricting the escape of recombination phonons from a superconductor can increase the quasiparticle recombination lifetime by more than an order of magnitude. A phonon band gap can be realized and matched to the recombination energy with a phononic crystal, a periodically p…