Comment on "Acoustic plasma modes"

In a recent treatment of the $T=0\mathrm{}$ acoustic plasma modes of a two-component Fermi liquid with Coulomb forces, Appel, and Overhauser conclude that there exist three generally damped longitudinal acoustic branches. We observe that this conclusion results from an inapplicable analytic continuation in their solution of the transport equations. There is only one longitudinal acoustic branch, and, in fact, when applied to the standard one-component Fermi-liquid model, the method of Appel and Overhauser also leads to the incorrect conclusion that there exist two longitudinal acoustic branches.