Using indium as a test case, we investigate the accuracy of the electron-phonon coupling calculated with state-of-the-art ab initio and many-body theory methods. The ab initio calculations—where electrons are treated in the local-density approximation, and phonons and the electron-phonon interaction are treated within linear response—predict an electron-phonon spectral function ${\alpha }^{2}F\left(\omega \right)$ that translates into a relative tunneling conductance that agrees with experiment to within one part in ${10}^3.$ The many-body theory calculations— where ${\alpha }^{2}F\left(\omega \right)$ is extracted from tunneling data by means of the McMillan-Rowell tunneling inversion method —provide spectral functions that depend strongly on details of the inversion process. For the most important moment of ${\alpha }^{2}F\left(\omega \right),$ the mass-renormalization parameter $\lambda ,$ we report $0.9\pm 0.1,$ in contrast to the value 0.805 quoted for nearly three decades in the literature. The ab initio calculations also provide the transport electron-phonon spectral function ${\alpha }_{\mathrm{tr}}^{2}F\left(\omega \right)$ from which we calculate the resistivity as a function of temperature in good agreement with experiment.

• Received 3 June 1998

DOI:https://doi.org/10.1103/PhysRevB.58.14511