Electron-phonon interaction, ultrasonic attenuation, and Eliashberg function<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>F(ω) in impure metals

A relation between the ultrasonic attenuation coefficient and the Eliashburg function ${\ensuremath{\alpha}}^{2}$F is derived, which holds up to leading order in the impurity density. This shows that all electron-phonon interaction models which yield Pippard's result for the sound attenuation are equivalent with respect to calculation of electronic properties as well. The low-frequency behavior of ${\ensuremath{\alpha}}^{2}$F(\ensuremath{\omega}) is calculated for a jellium model, and several mutually contradicting results in the literature are discussed.

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