Number-Conserving Approximation for the Theory of the Pairing Interaction in Nuclei

Abstract

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.