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 ${\ensuremath{\alpha}}^{2}(\ensuremath{\Omega})F(\ensuremath{\Omega})$. Results are obtained using the low-frequency approximate form ${\ensuremath{\alpha}}^{2}(\ensuremath{\Omega})F(\ensuremath{\Omega})=b{\ensuremath{\Omega}}^{2}$, with $b$ determined from electron tunneling measurements. For the strong-coupling superconductors Pb and Hg, the full tunneling form for ${\ensuremath{\alpha}}^{2}(\ensuremath{\Omega})F(\ensuremath{\Omega})$ is used. The phonon lifetimes are shown to depend on ${\ensuremath{\alpha}}^{2}(\ensuremath{\Omega})$. Results are compared with experiment.

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