The role of vertex corrections, associated with electron-phonon interactions, for electron scattering in metals is studied quantitatively. It is found that the correction, proportional to (m/M${)}^{1/2}$, is multiplied by a large numerical factor, ∼30. As a consequence the residual resistivity of a metal is not left unchanged by electron-phonon interactions. The resistivity suffers an increase by a factor ∼(1+0.16λ), where λ is the mass renormalization caused by electron-phonon interactions. The coefficient of λ depends on the square root of the ratio v/$v_F$ of sound velocity to Fermi velocity, and the value 0.16 is obtained for the ratio (1/200.

• Received 18 January 1988

DOI:https://doi.org/10.1103/PhysRevB.37.8618