Restoring broken symmetries for nuclei and reaction fragments

In typical microscopic approaches, particularly when pairing correlations are present, nuclei and nuclear fragments do not have well-defined quantum numbers and symmetries should be restored. I present here a formalism for the simultaneous projection of total particle numbers of a nucleus, particle numbers of reaction fragments, and of the reaction fragment intrinsic spins and of their correlation, and also for their symmetry-restored densities and total energies. These formulas for the symmetry restored quantities, are free of any singularities, unlike those in the previously introduced prescriptions.