Phonon linewidths and electron-phonon interaction in Nb

We present first-principles calculations of the electron-phonon contribution to the phonon linewidth in Nb. The calculations employ a realistic band structure and the rigid-muffin-tin approximation for the electron-phonon matrix elements. The calculations predict strong electron-phonon coupling for longitudinal phonons propagating in the [110] direction, and for longitudinal phonons of momentum $q=0.7\left(\frac{2\pi }{a}\right)$ [100]. The origins of these peaks in the linewidth are discussed in terms of the joint Fermi-energy density of states and the symmetry properties of the electron-phonon matrix elements. Our results are in agreement with available experimental data concerning the mode and $q$ dependence of the phonon linewidth and with empirical values of the electron-phonon coupling constant $\lambda$.