Effective pseudopotential for energy density functionals with higher order derivatives

Abstract

We derive a zero-range pseudopotential that includes all possible terms up to sixth order in derivatives. Within the Hartree-Fock approximation, it gives the average energy that corresponds to a quasi-local nuclear Energy Density Functional (EDF) built of derivatives of the one-body density matrix up to sixth order. The direct reference of the EDF to the pseudopotential acts as a constraint that divides the number of independent coupling constants of the EDF by two. This allows, e.g., for expressing the isovector part of the functional in terms of the isoscalar part, or vice versa. We also derive the analogous set of constraints for the coupling constants of the EDF that is restricted by spherical, space-inversion, and time-reversal symmetries.

18 LaTeX pages, 2 EPS Figures, 27 Tables, and 18 files of the supplemental material (LaTeX, Mathematica, and Fortran), introduction rewritten, table XXVII and figure 2 corrected, in press in Physical Review C

References in corpus (15)

• Nuclear Energy Density Optimization
• From low-momentum interactions to nuclear structure
• Local nuclear energy density functional at next-to-next-to-next-to-leading order
• Microscopically-based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization
• Self-interaction errors in nuclear energy density functionals
• Microscopic calculations of isospin-breaking corrections to superallowed beta-decay
• An improved density matrix expansion for spin-unsaturated nuclei
• 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
• Breaking and restoring symmetries within the nuclear energy density functional method
• Exploration of a modified density dependence in the Skyrme functional
• The Negele-Vautherin density matrix expansion applied to the Gogny force
• Instabilities in the Nuclear Energy Density Functional
• Nuclear energy functional with a surface-peaked effective mass: Global properties
• Surface-peaked effective mass in the nuclear energy density functional and its influence on single-particle spectra

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• Transport Model Comparison Studies of Intermediate-Energy Heavy-Ion Collisions