Particle number projecting method for the description of pairing effects in metal clusters

The particle number projecting method for the description of pairing effects in metal clusters is proposed. In contrast with-the Bardeen-Cooper-Schrieffer method (BCS) which does not conserve the particle number (thus not providing the necessary accuracy of calculations for small clusters) and has no solutions at sufficiently weak pairing, the projecting method can be applied to both small and large clusters with any pairing strength. As an example, the projection method is used to check the assertion on the pairing origin of the odd-even staggering (OES) in the ionization potentials (IP) of sodium clusters. Both effects of pairing and shape deformation are taken into account simultaneously. In general, the results obtained show that the existence of pairing in sodium clusters is doubtful.