Validity of empirical expressions for the low-temperature electrical resistivity

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Abstract
An analysis is presented of the range of validity of the most commonly used empirical expression for the low-temperature phonon-limited electrical resistivity of the alkali metals. The analysis is based on the temperature dependence of the mean phonon frequency, calculated by weighting each frequency according to its contribution to the electrical resistivity at temperature T when carrying out the average over the phonon spectrum. For potassium, it is found that the important temperature range 1-2K definitely lies outside the domain of validity of the empirical expression. For those temperature ranges and situations for which the empirical expression is valid, the values of the parameters are derived. Previously results are discussed and related to the present analysis.