Appearance and Effect of the Debye-Waller Factor in the Transport Coefficients of Simple Normal Metals

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Abstract
Analogous to the theory of the diffraction of x rays and neutrons by the lattice vibrations of crystals, the scattering of electrons in a metal by thermal vibrations gives rise to a temperature-dependent Debye-Waller factor in the matrix element. The factor is derived and its possible effects on electrical resistivity discussed for the case where Bloch functions are used for the electron wave function. A detailed numerical calculation for an umklapp process involving a particular phonon was performed, for cesium at room temperature, with the result that the new matrix element is about 0.7 times the 1937 Bardeen result, and consequently the contribution to the resistivity about 0.5 times the Bardeen value. It is even a possibility that, for some phonons, the matrix element may increase.