The two-proton separation energy (S2P) 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 Δnp ≠ 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 S2P 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 Δnp decreases with increasing values of (N - Z). It has also been shown that the BCS and SBCS (respectively, NP and NP-PROJ) values of S2P 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.
Rotational excitations in rare-earth nuclei: A comparative study within three cranking models with different mean fields and treatments of pairing correlations
