Study of Approximations in the Nuclear Pairing-Force Problem

Bishari, M.; Unna, I.; Mann, A.

doi:10.1103/physrevc.3.1715

Cited by 13 publications

(11 citation statements)

References 10 publications

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“…As already noted some times ago [17] and recently rediscussed [16,18], the two-body part V can be treated perturbatively to provide an accurate description of the pairing problem in the weak pairing interaction regime. Starting from the ground state |Φ 0 of H 0 , that corresponds to the Slater determinant obtained by occupying the lowest single-particle states while other excited states |Φ n of H 0 can be obtained by considering particle-hole (p-h), 2p-2h, ... excitations built on top of the |Φ 0 .…”

Section: Standard Perturbation Theorymentioning

confidence: 99%

“…[18] using a different approach based on the Richardson-Gaudin equation. It is known [16,17] that standard perturbation theory provides an appropriate description in the weak coupling regime. In figure 1, an example of standard perturbation theory (SPT) is presented for the N = 8 particles and constant coupling case, i.e.…”

Section: Standard Perturbation Theorymentioning

confidence: 99%

“…It is important to recall that here no diagonalization is required since the mixing coefficients are directly given by the quasiparticle perturbation theory, Eq. (17). These features make the approach rather simple to implement on existing HFB/BCS codes to provide a much better approximation than the PAV that is often currently used.…”

Section: Effect Of the Restoration Of Particle Numbermentioning

confidence: 99%

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Projected quasiparticle perturbation theory

Lacroix

Gambacurta

2012

Phys. Rev. C

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The BCS and/or HFB theories are extended by treating the effect of four quasi-particle states perturbatively. The approach is tested on the pairing hamiltonian, showing that it combines the advantage of standard perturbation theory valid at low pairing strength and of non-perturbative approaches breaking particle number valid at higher pairing strength. Including the restoration of particle number, further improves the description of pairing correlation. In the presented test, the agreement between the exact solution and the combined perturbative + projection is almost perfect. The proposed method scales friendly when the number of particles increases and provides a simple alternative to other more complicated approaches.

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Section: Standard Perturbation Theorymentioning

confidence: 99%

Section: Standard Perturbation Theorymentioning

confidence: 99%

Section: Effect Of the Restoration Of Particle Numbermentioning

confidence: 99%

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Projected quasiparticle perturbation theory

Lacroix

Gambacurta

2012

Phys. Rev. C

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“…The results of the BCS approximation, the LN prescription and the DMC and Metropolis projection methods (MCP) using v j and u j either from BCS (MCP BCS ) or LN (MCP LN M ) calculations are compared against exact results in Table I for Ω = 10 and N = 4, 10 for several values of the interaction strength, G. It is shown that Metropolis Projection methods give very good agreement with the exact results (the same quality of agreement as the DMC method). Recall that for N = Ω the BCS ansatz always have a nontrivial minimum 19 . For N = Ω, a nontrivial solution is found only for G greater than 1/(N − 1).…”

Section: A the Symmetric Two-level Modelmentioning

confidence: 99%

Stochastic number projection method in the pairing-force problem

Capote

Gonzalez

1999

Phys. Rev. C

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A new stochastic number projection method is proposed. The component of the BCS wave function corresponding to the right number of particles is obtained by means of a Metropolis algorithm in which the weight functions are constructed from the single-particle occupation probability. Either standard BCS or Lipkin-Nogami probability distributions can be used, thus the method is applicable for any pairing strength. The accuracy of the method is tested in the computation of pairing energies of model and real systems.Comment: LaTeX, 4 page

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“…[1][2][3]. While the Bardeen-Cooper-Schrieffer (BCS) and the more refined Hartree-Fock-Bogolyubov (HFB) approximations provide a simple and clear demonstration of the role of pairing correlations in nuclei [2,4,5], tremendous efforts have been made in finding accurate solutions to the problem [6][7][8][9][10][11] to overcome serious drawbacks in the BCS and the HFB, such as spurious states, nonorthogonal solutions, etc., resulting from particle number-nonconservation effects in these approximations [9,[11][12][13]. It is known that either spherical or deformed mean-field plus the standard pairing interaction can be solved exactly by using the Gaudin-Richardson method [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

An exactly solvable spherical mean-field plus extended monopole pairing model

et al. 2016

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An extended pairing Hamiltonian that describes pairing interactions among monopole nucleon pairs up to an infinite order in a spherical mean field, such as the spherical shell model, is proposed based on the localẼ2 algebraic structure, which includes the extended pairing interaction within a deformed mean-field theory [F. Pan, V. G. Gueorguiev, and J. P. Draayer, Phys. Rev. Lett. 92, 112503 (2004)] as a special case. The advantage of the model lies in the fact that numerical solutions of the model can be obtained more easily and with less computational time than the solutions to the standard pairing model. Thus, open-shell large-scale calculations within the model become feasible. As an example of the application, pairing contribution to the binding energy of 12−28 O is estimated in the present model with neutron pairs allowed to occupy a no-core shell model space of 11 j-orbits up to the fifth major harmonic oscillator shell including excitations up to 14hω for 12 O and up to 40hω for 28 O. The results for 12 O are also compared and found to be in agreement with those of ab initio calculations. It is shown that the pairing energy per particle in 12−28 O ranges from 0.4-1.8 MeV/A with the strongest one observed for a small number of pairs.

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Study of Approximations in the Nuclear Pairing-Force Problem

Cited by 13 publications

References 10 publications

Projected quasiparticle perturbation theory

Projected quasiparticle perturbation theory

Stochastic number projection method in the pairing-force problem

An exactly solvable spherical mean-field plus extended monopole pairing model

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