Particle-number projected two-proton separation energy of the proton-rich even–even rare-earth nuclei using an isovector pairing approach

The two-proton separation energy (S_2P) has been studied by describing the pairing correlations using four various approaches: in the pairing between like-particles case with (SBCS) and without (BCS) inclusion of the particle-number projection, as well as in the isovector pairing case with (NP-PROJ) and without (NP) inclusion of the particle-number projection. It has been numerically evaluated for the even–even rare-earth proton-rich nuclei such as Δ_np ≠ 0. Among the four used methods, NP-PROJ is the one that provides the results that are closest to the experimental data when available. On the other hand, it has been shown that the S_2P values deduced from the four approaches join, for almost all the considered elements, for the highest values of (N - Z). The fact that the BCS and NP (respectively, SBCS and NP-PROJ) values join may be explained by the fact that Δ_np decreases with increasing values of (N - Z). It has also been shown that the BCS and SBCS (respectively, NP and NP-PROJ) values of S_2P are very close because the discrepancy between the projected and unprojected energy values is quasi-constant as a function of the deformation. Finally, the four used methods lead to the same prediction of the two-proton drip-line position except for the Dysprosium and the Tungsten. (author)