Validity of the Born Approximation as Applied to Electron-Electron Scattering in Metals: Implications for Thermal Conductivity

Abstract

The frequently quoted result that the Born approximation overestimates electron-electron scattering in metals by a factor of 5 is found to be incorrect. We find for the screened Coulomb interaction $V=\frac{e^{-k_{s}r}}{r}$ that (i) the Born approximation overestimates the scattering cross section and the electron-electron contribution to the thermal resistivity by about a factor of 2; (ii) the cross section and the thermal resistivity are sensitive functions of the screening wave vector $k_s$; and (iii) neither the Thomas-Fermi nor the Bohm-Pines screening wave vector yields a thermal resistivity that agrees with recent experiments on the alkali metals. We conclude that knowledge of the appropriate interelectronic potential is considerably more important for calculating transport coefficients than the use of the Born approximation instead of the exact partial wave method.