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We show that it is possible to restore the symmetry associated with theGoldstone mode within the Self Consistent Random Phase Approximation (SCRPA)applied to the three-level Lipkin model. We determine one and two-bodydensities as very convergent expansions in terms of the generators of the RPAbasis. We show that SCRPA excitations correspond to the heads of somerotational bands in the exact spectrum. It turns out that the SCRPA eigenmodesfor N=2 coincide with exact solutions, given by the diagonalisation procedure

Self-consistent random phase approximation and the restoration of symmetries within the three-level Lipkin model