Damping of long-wavelength collective excitations in quasi-onedimensional Fermi liquids

The imaginary part of the exchange-correlation kernel in the longitudinal current-current response function of a quasi-one-dimensional Fermi liquid is evaluated by an approximate decoupling in the equation of motion for the current density, which accounts for processes of excitation of two particle-hole pairs. The two-pair spectrum determines the intrinsic damping rate of long-wavelength collective density fluctuations, which is calculated and contrasted with a result previously obtained for a clean Luttinger liquid.