Superconductivity in quasi one-dimensional metals and the optimal phonon frequency

The transition temperature, T_s to singlet superconductivity in quasi one-dimensional metals is studied as a function of the phonon frequency ω₀. When both electron-phonon and electron-electron couplings are present, T_s has a maximum at a finite ω₀. When the electron-phonon interaction dominates and ω₀ is too small, superconductivity is eliminated by charge density waves, while if the electron-electron interaction dominates and ω₀ is too large, superconductivity is eliminated by spin density waves.