Ultrasonic Attenuation in Normal Metals at Low Temperatures

Expressions for the attenuation ${\alpha }_d$ and ${\alpha }_t$ of plane dilatational and shear sound waves are obtained by solving the Boltzmann transport equation for the electron distribution function $f$ without assuming the existence of a relaxation time $\tau$ for the collision term in this equation. Instead the collision integral is considered to arise explicitly from the interaction of electrons with thermal phonons and impurities. Making the usual "ideal metal" assumptions, it is found that the attenuation in general depends on a set of effective relaxation times ${\tau }_{\mathrm{LM}}$ which are associated with the various terms in the expansion of $f$ in a series of spherical harmonics $Y_{\mathrm{LM}}(\theta , \varphi )$; the ${\tau }_{\mathrm{LM}}$ are independent of the subscript $M$, and hence the same set {${\tau }_L$} determines both ${\alpha }_d$ and ${\alpha }_t$. Explicit expressions for ${\tau }_L$ are derived.