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The zero-temperature response of an interacting electron liquid to a time-dependent vector potential of wave vector q and frequency, such that qq₅, qv₅E₅/ (where q₅, v₅, and E₅ are the Fermi wave vector, velocity, and energy, respectively), is equivalent to that of a continuous elastic medium with nonvanishing shear modulus, bulk modulus K, and viscosity coefficients and. We establish the relationship between the viscoelastic coefficients and the long-wavelength limit of the ``dynamical local-field factors'' G₋ (ₓ) (q, ), which are widely used to describe exchange-correlation effects in electron liquids. We present several exact results for, including its expression in terms of Landau parameters, and practical approximate formulas for, , and as functions of density. These are used to discuss the possibility of a transverse collective mode in the electron liquid at sufficiently low density. Finally, we consider impurity scattering and/or quasiparticle collisions at nonzero temperature. Treating these effects in the relaxation-time () approximation, explicit expressions are derived for and as functions of frequency. These formulas exhibit a crossover from the collisional regime (1), where 0 and nE₅, to the collisionless regime (1), where nE₅ and 0.
Conti et al. (Wed,) studied this question.