Effects of the particle-number projection on the isovector pairing energy

Renewed interest in the study of the neutron-proton (NP) pairing correlations occurred recently due to the development of the radioactive beam facilities that made possible the experimental study of nuclei such as N ∼ Z. Most often, pairing is treated within the BCS approximation. However, the shortcomings of this approach are well known: the most important of them is the number symmetry breaking that may imply serious errors in the evaluation of several physical observables. In the present contribution, the usual isovector NP BCS wave function is simultaneously projected on both the good neutron and proton numbers using a discrete projection operator. The projected energy of the system is deduced as a limit of a rapidly convergent sequence. It is numerically studied for the N=Z nuclei of which the 'experimental' pairing gaps Δp, Δn and Δnp may be deduced from the experimental odd-even mass differences. The single-particle energies used are those of a Woods-Saxon deformed mean-field. The differences δE between the projected and BCS energies without (first row) and with (second row) inclusion of the NP pairing correlations are reported in the table below. It then appears that the particle-number fluctuations effect is even more important than in the usual case. (author)