Towards full variation after projection solutions through restricted variational spaces

We have obtained very close approximations to the projection before the variation solutions with a restricted variation after projection method in a multilevel pairing Hamiltonian and particle number projection. The study of the projected potential energy surfaces defined along the direction of (ΔN)2 and (ΔN)4 allows the enlargement of the variational space in order to take into account more correlations within the projection after variation framework. The results show the equivalence of the full variational projected solution to a restricted one, the latter obtained with a more feasible method from a computational point of view than the former