Lipkin-Nogami pairing scheme in self-consistent nuclear structure calculations

We describe a new version of the Ev8 code that solves the nuclear Skyrme-Hartree-Fock+BCS problem using a 3-dimensional cartesian mesh. Several new features have been implemented with respect to the earlier version published in 2005. In particular, the numerical accuracy has been improved for a given mesh size by (i) implementing a new solver to determine the Coulomb potential for protons (ii) implementing a more precise method to calculate the derivatives on a mesh that had already been implemented earlier in our beyond-mean-field codes. The code has been made very flexible to enable the use of a large variety of Skyrme energy density functionals that have been introduced in the last years. Finally, the treatment of the constraints that can be introduced in the mean-field equations has been improved. The code Ev8 is today the tool of choice to study the variation of the energy of a nucleus from its ground state to very elongated or triaxial deformations with a well-controlled accuracy.Keywords: Self-consistent mean field; Hartree-Fock; Hartree-Fock+BCS; Skyrme interaction; Quadrupole deformation. The program expands the single-particle wave-functions on a 3D Cartesian mesh. The nonlinear mean-field equations are solved by the imaginary time step method. A quadratic constraint is used to obtain states corresponding to given values of the monopole and quadrupole operators. Summary of revisions: PROGRAM SUMMARY/NEW VERSION PROGRAM SUMMARY1. Skyrme energy functionals with tensor terms 2. Improved accuracy for calculating derivatives 3. Improved accuracy for solving Coulomb problem 4. Improvement of the numerics of constraints Restrictions:Ev8 assumes time-reversal invariance and nuclear shapes exhibiting three plane-reflection symmetries. Pairing correlations are treated at the BCS level of approximation. Running time: A few minutes for the examples provided, which concern rather heavy nuclei in modest boxes with an initial guess of Nilsson wavefunctions.

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“…One-body operators can be corrected in a simpler manner by calculating effective LN occupation numbers [78,79] …”

Section: Bcs+ln Schemementioning

confidence: 99%

Solution of the Skyrme–HF+BCS equation on a 3D mesh, II: A new version of the Ev8 code

Ryssens

Hellemans

Bender

et al. 2015

Computer Physics Communications

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“…A widely used method to stabilize pairing against breakdown is to employ the Lipkin-Nogami recipe, see e.g. [38]. This, however, is not always effective enough in the breakdown regime.…”

Section: A Shf Approach and Pairingmentioning

confidence: 99%

Fission properties forr-process nuclei

et al. 2012

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We present a systematics of fission barriers and fission lifetimes for the whole landscape of superheavy elements (SHE), i.e. nuclei with Z ≥ 100. The fission lifetimes are also compared with the α-decay half-lives. The survey is based on a self-consistent description in terms of the SkyrmeHartree-Fock (SHF) approach. Results for various different SHF parameterizations are compared to explore the robustness of the predictions. The fission path is computed by quadrupole constrained SHF. The computation of fission lifetimes takes care of the crucial ingredients of the large-amplitude collective dynamics along the fission path, as self-consistent collective mass and proper quantum corrections. We discuss the different topologies of fission landscapes which occur in the realm of SHE (symmetric versus asymmetric fission, regions of triaxial fission, bi-modal fission, and the impact of asymmetric ground states). The explored region is extended deep into the regime of very neutron-rich isotopes as they are expected to be produced in the astrophysical r process.

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“…The term ∝N 2 ν accounts for the approximate particle-number projection and its parameter ǫ 2,ν is given according to the LN recipe taking properly into account the feedback from the mean field to the variances [45]. The LN scheme performs also an approximate variation after projection.…”

Section: The Deformed Mean Fieldmentioning

confidence: 99%

“…As a synonym for its content we denote it by |Φ ≡ {ϕ n , v n }. In practice, we go somewhat beyond the BCS scheme by using the Lipkin-Nogami (LN) approximation for particle number projection [45]. The mean-field equations can be summarized as…”

Section: The Deformed Mean Fieldmentioning

confidence: 99%

Skyrme energy functional and low lying2+states in Sn, Cd, and Te isotopes

et al. 2004

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We study the predictive power of Skyrme forces with respect to low lying quadrupole spectra along the chains of Sn, Cd, and Te isotopes. Excitation energies and B(E2) values for the lowest quadrupole states are computed from a collective Schrödinger equation which as deduced through collective path generated by constraint Skyrme-Hartree-Fock (SHF) plus self-consistent cranking for the dynamical response. We compare the results from four different Skyrme forces, all treated with two different pairing forces (volume versus density-dependent pairing). The region around the neutron shell closure N = 82 is very sensitive to changes in the Skyrme while the mid-shell isotopes in the region N < 82 depend mainly on the adjustment of pairing. The neutron rich isotopes are most sensitive and depend on both aspects.

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Lipkin-Nogami pairing scheme in self-consistent nuclear structure calculations

Cited by 35 publications

References 46 publications

Solution of the Skyrme–HF+BCS equation on a 3D mesh, II: A new version of the Ev8 code

Solution of the Skyrme–HF+BCS equation on a 3D mesh, II: A new version of the Ev8 code

Fission properties forr-process nuclei

Skyrme energy functional and low lying2+states in Sn, Cd, and Te isotopes

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