Abstract
The pairing correlations in odd-A nuclei are analyzed in the mean field approximation and beyond. In particular the role of symmetry conservation is investigated. We find that particle number projection after the variation (PN-PAV) has little effect on the pairing correlations specially in the weak pairing regime. This is in contrast to the variation after particle number projection (PN-VAP) approach where a strong effect is found. The situation is specially critical in odd nuclei because the pairing correlations vanish due to the blocking effect and the Hartree-Fock-Bogoliubov wave function collapses to the Hartree-Fock one. The PN-VAP, however, handles perfectly the exact blocking providing highly correlated wave functions. The role of the angular momentum projection is studied only in the PAV approach. We find small changes of the pairing correlation, at least at small angular momentum. In the calculations we use the Gogny interaction well suited to this kind of studies.
Highlights
Pairing correlations play a predominant role in the description of nuclear phenomena [1]
BCS and HFB theories, have some drawbacks like the pairing collapse in the weak pairing regime and the non-conservation of the particle number (PN) and angular momentum (AM) symmetries. To overcome these problems and at the same time to benefit from the simplicity of product wave functions the symmetry conserving mean field (SCMF) approach has been developed [2,3,4]. In this theory use is made of the projectors technique to obtain eigenstates of the particle number operator and the angular momentum from symmetry breaking HFB wave functions [5]
Concerning the density dependence of the force we adopt the projected density prescription for the PNP and the mixed one for the AMP, for further details see for example Refs. [8, 11, 25]
Summary
Pairing correlations play a predominant role in the description of nuclear phenomena [1]. In this theory use is made of the projectors technique to obtain eigenstates of the particle number operator and the angular momentum from symmetry breaking HFB wave functions [5].
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