Eliashberg treatment of the microwave conductivity of niobium

High-precision microwave measurements have recently been carried out on superconducting Nb samples. A BCS-like coherence peak has been observed below ${\mathit{T}}_{\mathit{c}}$. We find that a strong-coupling calculation of the microwave conductivity, using electron-phonon spectral functions obtained from tunneling measurements, is unable to account for the height of the peak. We also explain how, for microwave measurements at lower frequency, the height of the coherence peak can be used to provide information about the low-frequency part of the electron-phonon spectral function and the associated inelastic scattering rate.