Decay of single-particle excitations in weak-coupling superconductors

The superfluid perturbation theory is used to generalize Luttinger's theorem in the normal Fermi system for superconductors. It is shown that the imaginary part of the diagonal element of the self-energy matrix is not a smooth function of the energy but has sudden jumps characteristic of the different decay thresholds. The self-energy function can then be determined in perturbation theory employing a bootstrap method. It is pointed out that thie behaviour of the self-energy can be detected by the single particle tunneling experiment by extending the results beyond the existing data.