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 ͑PHFB͒ 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.

The numerical solution of the recently formulated number-projected Hartree-Fock-Bogoliubov equations is studied in an exactly soluble crankeddeformed shell model Hamiltonian. It is found that the solution of these number-projected equations involve similar numerical effort as that of bare HFB. We consider that this is a significant progress in the mean-field studies of the quantum many-body systems. The results of the projected calculations are shown to be in almost complete agreement with the exact solutions of the model Hamiltonian. The phase transition obtained in the HFB theory as a function of the rotational frequency is shown to be smeared out with the projection.