Abstract
The accuracy of the variation before (VBP) and after (VAP) particle-number projection methods, the Lipkin-Nogami (LN) prescription, and the projected Lipkin-Nogami (PLN) method have been studied using two exactly solvable models. It is shown that the VBP and the LN methods are rather dubious not only in a weak pairing regime, but also in strong pairing for the evaluation of quantities other than the ground state energy. The PLN method provides good results for the ground and the excited state energies, but it must be used with caution for the occupation probabilities and the observables that strongly depend on it. It seems that the VAP is the only suitable method for a global description of the nuclear properties.
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