Resistivity and Hall Effect in Liquid Metals

Abstract

We assume a liquid metal in which the unscreened electron-ion interaction is the sum of spherically symmetric potentials. Using an exact expression for the conductivity tensor in a magnetic field H, we obtain expressions for the Hall constant $R$ and for the zero-magnetic-field frequency-dependent conductivity tensor ${{\sigma }_{\mu \mu }}^0\left(\omega \right)$ in the form of power-series expansions in the potential. Effects due to the electron spin are ignored. Calculations are done for Zn, Li, and Na using the pseudopotentials calculated by Harrison. For Zn it is shown that the series for ${{\sigma }_{\mu \mu }}^0\left(\omega \right)$ converges slowly if it converges at all. It is concluded that the small-pseudopotential approximation is not convenient for, and possibly not valid for, dealing with electrical transport in liquid metals.