Vertex-corrected tunneling inversion in electron-phonon mediated superconductors: Pb

The McMillan-Rowell tunneling inversion program, which extracts the electron-phonon spectral function alpha(2)F(Omega) and the Coulomb pseudopotential mu* from experimental tunneling data, is generalized to include the lowest-order vertex correction. We neglect the momentum dependence of the electron-phonon matrix elements, which is formally equivalent to using a local approximation. The perturbation theory is performed on the imaginary axis and then an exact analytic continuation is employed to produce the tunneling density of states on the real axis. Comparison is made with the experimental data for Pb. We find lambda is increased by approximately 1% due to the vertex corrections.