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

Until now, the Sharp-Bardeen-Cooper-Schrieffer (SBCS) particle-number projection method, in the isovector neutron-proton pairing case, has been developed in the particle representation. However, this formalism is sometimes complicated and cumbersome. In this work, the formalism is developed in the quasiparticle representation. An expression of the projected ground state wave function is proposed. Expressions of the energy as well as the expectation values of the total particle-number operator and its square are deduced. It is shown that these expressions are formally similar to their homologues in the pairing between like-particles case. They are easier to handle than the ones obtained using the particle representation and are more adapted to numerical calculations.The method is then numerically tested within the schematic one-level model, which allows comparisons with exact results, as well as in the case of even-even nuclei within the Woods-Saxon model. In each case, it is shown that the particle-number fluctuations that are inherent to the BCS method are completely eliminated by the projection. In the framework of the one-level model, the values of the projected energy are clearly closer to the exact values than the BCS ones. In realistic cases, the relative discrepancies between projected and unprojected values of the energy are small. However, the absolute deviations may reach several MeV.

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“…54 Let us note that this expression of |ψ mm is formally similar to its homologue in the pairing between like-particles case (see Eq. (A.9)).…”

Section: Wave Functionmentioning

confidence: 73%

Particle-number conservation in quasiparticle representation in the isovector neutron–proton pairing case

Fellah

Allal

Hammache

et al. 2015

Int. J. Mod. Phys. E

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“…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] :…”

Section: Projected Wave Functionmentioning

confidence: 99%

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

Douici

Allal

Fellah

et al. 2012

Int. J. Mod. Phys. E

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The effect of the particle-number symmetry restoration on the root mean square (rms) proton and neutron radii of neutron-deficient nuclei is studied in the isovector pairing case. As a first step, an expression of the nuclear radii which includes the neutron-proton pairing effects and which strictly conserves the particle-number has been established using the SBCS (Sharp BCS) method. It is shown that this expression generalizes the one obtained in the pairing between like-particles case. As a second step, the proton and neutron rms radii are numerically evaluated for even-even nuclei such as 16 Z 56 and 0 (N − Z) 4 using the single-particle energies of a Woods-Saxon mean-field. The results are compared with experimental data when available and with the results obtained when one considers only the pairing between like-particles.Finally, the projection effect, when including or not the isovector pairing effect, has been studied by evaluating the relative discrepancies: δr n-proj and δr n-proj-np . This effect is roughly the same in both cases since the average values of these latter are respectively 0.70% and 0.74%. These values are also very close to that of the proton system.However, one notices that, in the neutron case, the np pairing effect seems to be more important than that of the projection. The particle-fluctuation effects in the BCS states being, by definition, nonphysical it is difficult to explain why Figs. 1 and 2 show very different trends.

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“…In addition, in all the previously cited works dealing with the moment of inertia of N Z nuclei, the particle-number fluctuations, which are inherent to the BCS approach, are not taken into account although their importance was stressed in the like-particles pairing case. The aim of the present work is thus to study the moment of inertia of even-even systems by including the isovector pairing correlations and performing a particle-number projection using the Sharp-BCS (SBCS) method [21] which has been generalized to the np pairing case [22] and has been recently reformulated in quasiparticle representation [23].…”

Section: Introductionmentioning

confidence: 99%

Number-projected nuclear moment of inertia in the isovector pairing case within the Richardson model

Hammache¹,

Allal²,

Fellah³

et al. 2017

AIP Conference Proceedings

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

Cited by 22 publications

References 37 publications

Particle-number conservation in quasiparticle representation in the isovector neutron–proton pairing case

Particle-number conservation in quasiparticle representation in the isovector neutron–proton pairing case

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

Number-projected nuclear moment of inertia in the isovector pairing case within the Richardson model

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