Implementation of a variational approach to approximate particle number projection with effective forces

Valor, A.; Egido, J.L.; Robledo, L. M.

doi:10.1016/s0375-9474(99)00841-6

Cited by 12 publications

(12 citation statements)

References 24 publications

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“…As pointed out in Refs. [18][19][20][21], the parabolic approximation, which corresponds to a sum up to the second order of the Lipkin or Kamlah [22] approximation, may fail at the limit of weak pairing. In this work we extend the Lipkin method beyond the second order used so far, so as to make the first tests of its convergence and accuracy.…”

Section: Introductionmentioning

confidence: 99%

Lipkin method of particle-number restoration to higher orders

et al. 2014

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Background: On the mean-field level, pairing correlations are incorporated through the Bogoliubov-Valatin transformation, whereby the particle degrees of freedom are replaced by quasiparticles. This approach leads to a spontaneous breaking of the particle-number symmetry and mixing of states with different particle numbers. In order to restore the particle number, various methods have been employed, which are based on projection approaches before or after variation. Approximate variation-after-projection (VAP) schemes, utilizing the Lipkin method, have mostly been used within the Lipkin-Nogami prescription. Purpose: Without employing the Lipkin-Nogami prescription, and using, instead, states rotated in the gauge space, we derive the Lipkin method of particle-number restoration up to sixth order and we test the convergence and accuracy of the obtained expansion. Methods: We perform self-consistent calculations using the higher-order Lipkin method to restore the particlenumber symmetry in the framework of superfluid nuclear energy-density functional theory. We also apply the Lipkin method to a schematic exactly solvable two-level pairing model. Results:Calculations performed in open-shell tin and lead isotopes show that the Lipkin method converges at fourth order and satisfactorily reproduces the VAP ground-state energies and energy kernels. Near closed shells, the higher-order Lipkin method cannot be applied because of a nonanalytic kink in the ground-state energies as a function of the particle number. Conclusions:In open-shell nuclei, the higher-order Lipkin method provides a good approximation to the exact VAP energies. The method is computationally inexpensive, making it particularly suitable, for example, for future optimizations of the nuclear energy density functionals and simultaneous restoration of different symmetries.

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Section: Introductionmentioning

confidence: 99%

Lipkin method of particle-number restoration to higher orders

et al. 2014

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“…Applications based on effective nuclear interactions have been particularly successful in the description of super-deformed rotational bands in several regions of the mass table [1][2][3][4][5]. In the cranking method, a rotational band is generated by the rotation of a deformed intrinsic state.…”

Section: Introductionmentioning

confidence: 99%

Configuration mixing of mean-field wave functions projected on angular momentum and particle number: Application to Mg

Valor¹,

Heenen²,

Bonche³

2000

Nuclear Physics A

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148

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We present in this paper the general framework of a method which permits to restore the rotational and particle number symmetries of wave functions obtained in Skyrme HF+BCS calculations. This restoration is nothing but a projection of mean-field intrinsic wave functions onto good particle number and good angular momentum. The method allows also to mix projected wave functions. Such a configuration mixing is discussed for sets of HF+BCS intrinsic states generated in constrained calculations with suitable collective variables. This procedure gives collective states which are eigenstates of the particle number and the angular momentum operators and between which transition probabilities are calculated. An application to 24 Mg is presented, with mean-field wave functions generated by axial quadrupole constraints. Theoretical spectra and transition probabilities are compared to the experiment.

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“…The second order in this expansion takes into account the particle number fluctuations and might cure some of the deficiencies of the first order approximation. However, full calculations up to second order are rather cumbersome [23,8,9] and most second order calculations have been done using the Lipkin-Nogami (LN) recipe proposed in Refs. [10][11][12].…”

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confidence: 99%

“…This behavior could be associated with a failure of the LN expansion at the phase transitions. As a matter of fact in reference [9] it has been shown that large changes in the h 2 parameter are associated with the breakdown of the second order expansion of the projected energy. On the left hand side of Fig.…”

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confidence: 99%

Mean-field based approaches to pairing correlations in atomic nuclei

2002

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The evolution of the pairing correlations from closed shell to midshell nuclei is analyzed in the Sn isotopes with the Finite Range Density Dependent Gogny force. As theoretical approaches we use the Hartree-Fock-Bogoliubov, the Lipkin-Nogami, their particle number projected counterparts and the full variation after particle number projection method. We find that whereas all approaches succeed rather well in the description of the total energy they differ significantly in the pairing correlation content of the wave functions. The description of the evolution from the weak to the strong pairing regime is also approach dependent, specially at shell closure.

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Implementation of a variational approach to approximate particle number projection with effective forces

Cited by 12 publications

References 24 publications

Lipkin method of particle-number restoration to higher orders

Lipkin method of particle-number restoration to higher orders

Configuration mixing of mean-field wave functions projected on angular momentum and particle number: Application to Mg

Mean-field based approaches to pairing correlations in atomic nuclei

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