Correlation energy of the pairing Hamiltonian

We study the correlation energy associated with the pair fluctuations in BC S theory. We use a schematic two-level pairing model and discuss the behavi or of the correlation energy across shell closures, including the even-odd differences. It is shown that the random phase approximation (RPA) to the g round state energy reproduces the exact solutions quite well both in the no rmal fluid and in the superfluid phases. In marked contrast, other methods to improve the BCS energies, such as Lipkin-Nogami method, only work when t he strength of a pairing interaction is large. We thus conclude that the RP A approach is better for a systematic theory of nuclear binding energies. ( C) 2000 Elsevier Science B.V. All rights reserved.