The formalism of particle number projection on a spatial domain for mean-field wave functions with pairing is revisited to account for the common situation where incomplete, finite-dimensional basis is used. The restriction to a spatial domain implies that the symmetry operators used in projection are always nonunitary and this property requires a specific treatment not considered in traditional approaches. Some deficiencies of previous implementations presented in the literature are highlighted and the correct implementation taking into account the nonunitary character of the symmetry operators in finite-dimensional spaces is presented. It is shown that the present formalism has the right limit in the well-known case of zero pairing, whereas some of the other implementations do not satisfy this basic requirement. By using a simple one-dimensional model, I illustrate the differences in the results obtained with both the correct methods and the incorrect one in the study of particle number distribution probability.

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• Nuclear many-body theory
• Nuclear structure & decays