Longitudinal sound in impure jellium for small frequency and wavevector
The behaviour of long wavelength (q ≪kF) and low frequency (ω ≪ εf) longitudinal sound in jellium containing a small concentration of defects (τ−1≪εf) is discussed without making use of the unitary transformation to a frame moving with the ion velocity. The relevant contributions for the phonon Green's function are formulated in terms of diagrams within a laboratory-frame perturbation theory. As a special result Pippard's formula for sound-damping is rederived within this formalism.