2014/03/25 by Xiaobao Wang, X. B. Wang, J. Dobaczewski +3
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Ground state #Mathematics #Nuclear physics research studies #Pairing #Particle number #Physics #Projection (relational algebra) #Quantum mechanics #Quantum, superfluid, helium dynamics #Statistical physics #Wave function #nucl-th
paper · pdf · doi:10.1103/physrevc.90.014312
published as Phys. Rev. C 90, 014312 (2014) · 10 RevTeX pages, 11 figures
arxiv created 2014/03/25 · openalex publication_date 2014/07/17 · arxiv updated 2014/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 particle-number 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.