Disappearance of pairing correlations in a rotating nucleus and the role of particle-number projection discussed within a solvable model

The disappearance of pairing correlations in a rotating nucleus and the role of the particlenumber projection technique are discussed using a simple solvable two-level model. Exact solutions are compared to approximate ones obtained with the independent-quasiparticle method both with and without particle-number projection. Analytical formulas for particle-number projected quantities are obtained. It is shown that pairing correlations tend to disappear in a nucleus which rotates fast enough. It is also argued that the pairing parameter Δ which appears in the particle-number projected wave function does not provide an adequate measure of the pairing correlations in nuclei. The pair-transfer reaction cross section is shown to be related closely to the pairing correlation energy and it is suggested that it can be used as a criterion for the existence of the superfluidity in rotating nuclei.