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Superconducting pairing of electrons in nanoscale metallic particles withdiscrete energy levels and a fixed number of electrons is described by thereduced BCS model Hamiltonian. We show that this model is integrable by thealgebraic Bethe ansatz. The eigenstates, spectrum, conserved operators,integrals of motion, and norms of wave functions are obtained. Furthermore, thequantum inverse problem is solved, meaning that form factors and correlationfunctions can be explicitly evaluated. Closed form expressions are given forthe form factors that describe superconducting pairing.Comment: revised version, 5 pages, revtex, no figure

Superconducting correlations in metallic nanoparticles: Exact solution of the BCS model by the algebraic Bethe ansatz