Number-Projected Electric Quadrupole Moments of Even–even Proton-Rich Nuclei in the Isovector Pairing Case

Abstract

An expression of the number-projected electric quadrupole moment Q2 has been established in the isovector pairing case using the SBCS discrete projection before variation method. It has been verified that this expression reduces to the pairing between like-particles one at the limit when the np pairing gap parameter Δ np goes to zero. The convergence of the projection method has been numerically tested and a fast convergence has been observed. The electric quadrupole moment has been numerically calculated for some even–even proton-rich nuclei such as 16 ≤ Z ≤ 56 and 0 ≤ (N-Z) ≤ 4. The single-particle energies and eigen-states used are those of a Woods–Saxon mean-field. The np pairing effect on Q2 has been studied either before and after the projection; it seems that it is somewhat small since the relative discrepancies do not exceed 12%. Moreover, the np pairing effect is roughly the same in both situations. However, it has been shown that this effect diminishes with increasing values of (N-Z). The projection effect on Q2 has also been studied when including, or not, the np pairing correlations. It appears that this effect is slightly less important in the np pairing case than when only the pairing between like-particles is considered.

Particle-number projected electric quadrupole moment of even-even proton-rich nuclei in the isovector pairing case

“…The neutrons and the protons are assumed to occupy the same energy levels. The total Hamiltonian of the system is given, in the isovector case, by [7][8][9][10]: …”

“…It is thus projected using the method described in Refs. [7][8][9][10]. The corresponding wave-function is given by:…”

Quadrupole moment of 14B exotic nucleus

“…Douici et al [6] studied the effect of the particle-number projection on the electric quadrupole moment (Q2) of eveneven proton-rich nuclei in the isovector neutron-proton pairing case. As a first step, an expression of the electric quadrupole moment, which takes into account the isovector neutron-proton pairing effect and which conserves the particle number, is established within the Sharp-Bardeencooper-Schrietter (SBCS) method.…”

Particle-number conservation in charge-radii of odd-mass proton-rich nuclei in the isovector neutron-proton pairing case

“…[2]). The study of the isovector np pairing effect on the proton-system radius has already been performed for even-even proton-rich nuclei using the Sharp-BCS (SBCS) particle-number projection method [3]. The goal of the present work is to extend this study to odd-mass nuclei using a recently proposed expression of the projected ground-state of odd-mass nuclei [4].…”