Skyrme pseudopotentials at next-to-next-to-leading order Construction of local densities and first symmetry-breaking calculations

Abstract

There is an ongoing quest to improve on the spectroscopic quality of nuclear energy density functionals (EDFs) of the Skyrme type through extensions of its traditional form. One direction for such activities is the inclusion of terms of higher order in gradients in the EDF. We report on exploratory symmetry-breaking calculations performed for an extension of the Skyrme EDF that includes central terms with four gradients at next-to-next-to-leading order (N2LO) and for which the high-quality parametrization SN2LO1 has been constructed recently [P. Becker et al, Phys. Rev. C 96, 044330 (2017)]. Up to now, the investigation of such functionals with higher-order terms was limited to infinite matter and spherically symmetric configurations of singly- and doubly-magic nuclei. We address here nuclei and phenomena that require us to consider axial and non-axial deformation, both for reflection-symmetric and also reflection-asymmetric shapes, as well as the breaking of time-reversal invariance. Achieving these calculations demanded a number of formal developments. These all resulted from the formulation of the N2LO EDF requiring the introduction of new local densities with additional gradients that are not present in the EDF at NLO. Their choice is not unique, but can differ in the way the gradients are coupled. While designing a numerical implementation of N2LO EDFs in Cartesian 3d coordinate-space representation, we have developed a novel definition and a new unifying notation for normal and pair densities that contain gradients at arbitrary order. The resulting scheme resolves several issues with some of the choices that have been made for local densities in the past, in particular when breaking time-reversal symmetry. Guided by general practical considerations, we propose an alternative form of the N2LO contribution to the Skyrme EDF that is built from a different set of densities.

arXiv comment41 pages, 6 figures; second version fixes some typos

References in corpus (52)

• Mean-field description of ground-state properties of drip-line nuclei: Pairing and continuum effects
• Nuclear Energy Density Optimization
• Nuclear energy density optimization: Large deformations
• The tensor part of the Skyrme energy density functional. I. Spherical nuclei
• Spin-orbit splitting and the tensor component of the Skyrme interaction
• Local Density Approximation for proton-neutron pairing correlations. I. Formalism
• Nuclear energy density optimization: Shell structure
• Global study of quadrupole correlation effects
• Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XI: Stabilizing neutron stars against a ferromagnetic collapse
• Time-odd components in the mean field of rotating superdeformed nuclei
• Isovector splitting of nucleon effective masses, ab-initio benchmarks and extended stability criteria for Skyrme energy functionals
• Multidimensionally-constrained relativistic mean field models and potential energy surfaces of actinide nuclei
• One-quasiparticle States in the Nuclear Energy Density Functional Theory
• Particle-Number Restoration within the Energy Density Functional Formalism
• Superdeformed rotational bands in the Mercury region; A Cranked Skyrme-Hartree-Fock-Bogoliubov study
• Tensor part of the Skyrme energy density functional. II: Deformation properties of magic and semi-magic nuclei
• Particle-Number Restoration within the Energy Density Functional formalism: Nonviability of terms depending on noninteger powers of the density matrices
• Shape coexistence in neutron-deficient Kr isotopes: Constraints on the single-particle spectrum of self-consistent mean-field models from collective excitations
• Spin-orbit and tensor mean-field effects on spin-orbit splitting including self-consistent core polarizations
• Local nuclear energy density functional at next-to-next-to-next-to-leading order
• Effective pseudopotential for energy density functionals with higher order derivatives
• Properties of nuclei in the nobelium region studied within the covariant, Skyrme, and Gogny energy density functionals
• Structure of Krypton isotopes calculated with symmetry conserving configuration mixing methods
• Solution of the Skyrme HF+BCS equation on a 3D mesh. II. A new version of the Ev8 code
• The tensor part of the Skyrme energy density functional. III. Time-odd terms at high spin
• Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states
• Spurious finite-size instabilities in nuclear energy density functionals
• The unrestricted Skyrme-tensor time-dependent Hartree-Fock and its application to the nuclear response from spherical to triaxial nuclei
• Global microscopic calculations of ground-state spin and parity for odd-mass nuclei
• Remarks on the use of projected densities in the density dependent part of Skyrme or Gogny functionals
• Skyrme functional from a three-body pseudo-potential of second-order in gradients. Formalism for central terms
• Point symmetries in the Hartree-Fock approach: Densities, shapes and currents
• Solution of self-consistent equations for the N3LO nuclear energy density functional in spherical symmetry. The program HOSPHE (v1.00)
• Convergence of density-matrix expansions for nuclear interactions
• Skyrme pseudo-potential-based EDF parametrisation for spuriousity-free MR-EDF calculations
• Constraining the surface properties of effective Skyrme interactions
• Numerical accuracy of mean-field calculations in coordinate space
• Solution of Hartree-Fock-Bogoliubov equations and fitting procedure using N2LO Skyrme pseudo-potential in spherical symmetry
• Point symmetries in the Hartree-Fock approach: Symmetry-breaking schemes
• Fitting Skyrme functionals using linear response theory
• The impact of the surface energy coefficient on the deformation properties of atomic nuclei as predicted by Skyrme energy density functionals
• Exploration of a modified density dependence in the Skyrme functional
• Self-consistent symmetries in the proton-neutron Hartree-Fock-Bogoliubov approach
• Fitting N${}^3$LO pseudopotentials through central plus tensor Landau parameters
• Shape coexistence revealed in the $N=Z$ isotope ${}^{72}$Kr through inelastic scattering
• Extended Skyrme pseudo-potential deduced from infinite matter properties
• Iterative approaches to the self-consistent nuclear energy density functional problem. Heavy ball dynamics and potential preconditioning
• Continuity equation and local gauge invariance for the N3LO nuclear Energy Density Functionals
• Infinite matter properties and zero-range limit of nonrelativistic finite-range interactions
• Tools for incorporating a D-wave contribution in Skyrme energy density functionals
• The Tensor Part of the Skyrme Energy Density Functional
• Time-odd components in the rotating mean field and identical bands