The parametrization of simple-metal Fermi surfaces by a set of band gaps leads to a model for umklapp electron-electron (Coulomb) scattering and its contribution to electrical resistivity. We discuss transport coefficients in general, but emphasize electrical resistivity, which would vanish without umklapp processes. We treat deviations from Matthiessen's rule resulting from the energy dependence of the deviation function, for the case in which both electron-electron and electron-impurity scattering are present. The resulting $T^2$ power law is too small to be seen in polyvalent metals. In potassium, the $T^2$ term is comparable to the phonon contribution at about 2 °K.

• Received 11 September 1972

DOI:https://doi.org/10.1103/PhysRevB.7.2317