Quasiparticle and phonon lifetimes in superconductors

Low-energy quasiparticle scattering, recombination, and branch-mixing lifetimes and phonon pair-breaking and scattering lifetimes are calculated for superconductors. The quasiparticle calculations relate these lifetimes to the low-frequency behavior of ${\alpha }^2\left(\Omega \right)F\left(\Omega \right)$. Results are obtained using the low-frequency approximate form ${\alpha }^2\left(\Omega \right)F\left(\Omega \right)=b{\Omega }^2$, with $b$ determined from electron tunneling measurements. For the strong-coupling superconductors Pb and Hg, the full tunneling form for ${\alpha }^2\left(\Omega \right)F\left(\Omega \right)$ is used. The phonon lifetimes are shown to depend on ${\alpha }^2\left(\Omega \right)$. Results are compared with experiment.