Pairing correlations in the rotating nucleus discussed within the generator coordinate method

The influence of nuclear rotation on pairing correlations is discussed using a simple solvable two-level model. Exact solutions are compared to approximate ones obtained with the generator coordinate method both with and without particle-number projection. The collective subspace associated with the generator coordinates used has a finite dimension and it can be exactly separated from the full Hilbert space of the generating functions. Analytical formulas for the norm matrix and Hamiltonian kernels are obtained. It is shown that the generator coordinate method improves considerably the calculations based on the random-phase-approximation approach, in particular near the critical frequency where the pairing gap collapses