The cross section for the reaction Pr 141 (7,w)Pr 140 has been measured through 65 MeV. Yield curves of Pr 140 radioactivity were analyzed by least-structure analysis. Eleven distinct resonances are resolved below 25 MeV with a total integrated cross section to 30 MeV of 1790±100 MeV mb. The cross section falls to zero in the region of 30 MeV and rises slightly with no resolved structure above 35 MeV. The integrated cross section from 30 to 65 MeV is 440 MeV mb.The pairing interaction is studied by means of the equations of motion. An approximation is derived which adheres strictly to particle-number conservation, but is otherwise quite close to the formalism of the Bardeen-Cooper-Schrieffer (BCS) theory. It yields ground-state energies and single-particle properties considerably improved over those of the latter theory, as evidenced by calculations for (i) the model of Pawlikowski and Rybarska, (ii) the model of the Ni isotopes solved exactly by Kerman, Lawson, and Mac Farlane. Though it does not yet surpass in accuracy several alternative improvements of the BCS theory, it is capable of systematic further development, including the treatment of more realistic potentials.