Pairing correlations and particle-number projection methods

A systematic study of the pairing correlations derived from various particle-number projection methods is performed in an exactly soluble cranked-deformed shell model Hamiltonian. It is shown that most of the approximate particle-number projection methods including the method of Lipkin and Nogami, which is used quite extensively in nuclear structure studies, break down in the weak pairing limit. The results obtained from the recently formulated number-projected Hartree-Fock-Bogoliubov (PHFB) equations, on the other hand, are in complete agreement with the exact solutions of the model Hamiltonian. The pairing energy calculated from the PHFB method is shown to be finite in all the studied limits.