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We study the application of various forms of the coupled cluster method tosystems with paired fermions. The novel element of the analysis is the study ofthe breaking and eventual restoration of particle number in the CCM variants.We specifically include Arponen's extended coupled cluster method, whichdescribes the normal Hartree-Fock-Bogoliubov mean field at lowest level oftruncation. We show that all methods converge to the exact results as weincrease the order of truncation, but that the breaking of particle number atan intermediate level means that this convergence occurs in a surprising way.We argue that the most straightforward form of the method seems to be the moststable approach to implement for realistic (large number of particles) pairingproblems

The extended coupled cluster method and the pairing problem