Particle-Number Projected Two-Proton Separation Energy of the Proton-Rich Even–even Rare-Earth Nuclei Using an Isovector Pairing Approach

Abstract

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.

Number projected isovector neutron–proton pairing effect in odd-mass nuclei

“…However, the particle-number symmetry may be restored using a particlenumber projection method. In the present work, we use the sharp-BCS (SBCS) one [37][38][39][40].…”

“…In the isovector pairing case, the ground-state (9) is simultaneously projected on the good neutron and proton numbers, i.e. [38][39][40]:…”

“…Several methods have been already proposed in the np pairing case, as the quasiparticle random phase approximation (QRPA) [23][24][25][26][27][28][29][30][31], the LipkinNogami method [32], the generator coordinate method [33], and the PBCS-type projection methods [34], of FBCS-type [35] or the isospin and particle-number projection one [36]. In previous papers [37][38][39][40], we proposed and applied a generalization of the SBCS (sharp-BCS) projection method [41][42][43]. However, this generalization is valid only for even-even nuclei and has not been yet extended to odd-mass systems.…”

Effect of the Particle-Number Symmetry Restoration on Root Mean Square Radii of Even–even Neutron-Deficient Nuclei in the Isovector Pairing Case

“…As the state (13) is not an eigenstate of the particle-number operator, one performs a projection on both the good proton and neutron numbers, that is [33][34][35] :…”

Evaluation of theβ+-decay logftvalue with inclusion of the neutron-proton pairing and particle-number projection

“…This is done within the framework of the BCS approach. As the BCS theory does not conserve the particle number, a particle-number projection is performed using the Sharp-BCS (SBCS) exact projection method [8] a e-mail: kerrouchis@gmail.com which has been extended to the isovector pairing case [9][10][11][12].…”