Theory of Ultrasonic Attenuation in Metals

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Abstract
A quantum mechanical theory of the attenuation of the longitudinal ultrasonic wave in metals due to the conduction electrons is developed according to the general theory of linear response given by Kubo. When the mean free path of electrons is longer than the wavelength of the ultrasonic wave, the result is reduced to that given by the ordinary perturbational treatment and is not equivalent to the semiclassical one obtained by Pippard. The discrepancy between these two treatments appears mainly in the effect of the interaction between conduction electrons and moving impurities. It arises because in Pippard's theory the interaction is averaged out from the outset and appears as a fictitious field driving electrons, not as a random force. The treatment of scattering in Pippard's theory seems to be incorrect when the mean free path is longer than the wavelength. Though the correction is small in the absence of a static magnetic field, it seems to be important when a static magnetic field is applied in perpendicular to the wave propagation.

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