Electronic response function of coupled chains of finite radius

Following Williams and Bloch, we consider the random-phase-approximation electronic response function of an array of parallel chains, treating the chains as cylindrical potentials of radius $r_0$. A careful discussion is given of the form-factored interchain Coulomb interaction, both in real space and in momentum space. We extend the calculations to include the Tomonaga-Luttinger model keeping only the small-momentum forward-scattering processes ($g_2$ and $g_4$). The finite chain radius is necessary in order to make the intrachain interaction well defined. The continuum approximation for the interchain interaction is examined in detail and compared to the analogous problem in type-II superconductors. We give the corrections to the plasmon frequency (for coupled chains) which depend on the ratio $r_0$/$d_{\perp }$, where $d_{\perp }$ is the distance between chains.