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Polarizability and single particle spectra of two-dimensional s- and d-wave superconductors

We present analytic results for the polarizabilities, $χ({\bf Q},ω)$, in the charge, spin, and current channels for two-dimensional s- and d-wave superconductors for large momentum transfer. A collective mode in the charge channel is predicted to exist for extremum vectors of the Fermi-surface with energy below twice the maximum superconducting gap. Such modes are directly observable through inelastic x-ray or electron scattering. Scattering of single particle excitations by these collective modes leads to several unusual features in the single particle spectrum in the superconducting state which are seen in angle resolved photoemission experiments.