Abstract
We combine the exact particle-number projection method with the method of Peierls-Yoccoz in order to build the simultaneous eigen-functions of the particle number and the angular momentum operators. In the axial symmetry case, the general expression of the system energy resulting from this double projection is derived. In order to overcome the complexity of the method, the calculations are performed within the Gaussian overlap approximation. It turns out that, on the one hand, the double projection introduces a non–negligible correction of the energy of the system, and on the other hand, this correction is sensitive to the deformation. Future calculations have to therefore include an evaluation of the equilibrium deformation.
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