An improved density matrix expansion for spin-unsaturated nuclei

Abstract

A current objective of low-energy nuclear theory is to build non-empirical nuclear energy density functionals (EDFs) from underlying inter-nucleon interactions and many-body perturbation theory (MBPT). The density matrix expansion (DME) of Negele and Vautherin is a convenient method to map highly non-local Hartree-Fock expressions into the form of a quasi-local Skyrme functional with density-dependent couplings. In this work, we assess the accuracy of the DME at reproducing the non-local exchange (Fock) contribution to the energy. In contrast to the scalar part of the density matrix for which the original formulation of Negele and Vautherin is reasonably accurate, we demonstrate the necessity to reformulate the DME for the vector part of the density matrix, which is needed for an accurate description of spin-unsaturated nuclei. Phase-space averaging techniques are shown to yield a significant improvement for the vector part of the density matrix compared to the original formulation of Negele and Vautherin. The key to the improved accuracy is to take into account the anisotropy that characterizes the local-momentum distribution in the surface region of finite Fermi systems. Optimizing separately the DME for the central, tensor and spin-orbit contributions to the Fock energy, one reaches a few-percent accuracy over a representative set of semi-magic nuclei. With such an accuracy at hand, one can envision using the corresponding Skyrme-like energy functional as a microscopically-constrained starting point around which future phenomenological parameterizations can be built and refined.

24 pages, 11 figures, updated typos and plots.

References in corpus (7)

• Relativistic Nuclear Energy Density Functionals: adjusting parameters to binding energies
• Isovector splitting of nucleon effective masses, ab-initio benchmarks and extended stability criteria for Skyrme energy functionals
• Tensor part of the Skyrme energy density functional. II: Deformation properties of magic and semi-magic nuclei
• Effective pairing interactions with isospin density dependence
• Effects of the Tensor Force on the Multipole Response in Finite Nuclei
• Density Matrix Expansion for Low-Momentum Interactions
• Global nuclear structure aspects of tensor interaction

Cited by in corpus (42)

• Improved nuclear matter calculations from chiral low-momentum interactions
• Nuclear energy density optimization: Shell structure
• Future of Nuclear Fission Theory
• Ab-initio self-consistent Gorkov-Green's function calculations of semi-magic nuclei - I. Formalism at second order with a two-nucleon interaction
• Accurate nuclear masses from a three parameter Kohn-Sham DFT approach (BCPM)
• Nuclear chiral dynamics and thermodynamics
• Properties of the nuclear medium
• Quark-Meson-Coupling (QMC) model for finite nuclei, nuclear matter and beyond
• Microscopically-based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization
• Effective pseudopotential for energy density functionals with higher order derivatives
• A Minimal Nuclear Energy Density Functional
• Computational Nuclear Quantum Many-Body Problem: The UNEDF Project
• Convergence of density-matrix expansions for nuclear interactions
• Testing the density matrix expansion against ab initio calculations of trapped neutron drops
• Microscopically-based energy density functionals for nuclei using the density matrix expansion: Full optimization and validation
• A global microscopic description of nucleon-nucleus scattering with quantified uncertainties
• Effective density functionals beyond mean field
• Proton elastic scattering on calcium isotopes from chiral nuclear optical potentials
• Nuclear energy density functional from chiral two- and three-nucleon interactions
• Role of three-nucleon forces and many-body processes in nuclear pairing
• Microscopically-constrained Fock energy density functionals from chiral effective field theory. I. Two-nucleon interactions
• First applications of Fayans functional to deformed nuclei
• Sloppy nuclear energy density functionals: effective model reduction
• Isovector part of nuclear energy density functional from chiral two- and three-nucleon forces
• From bare interactions, low--energy constants and unitary gas to nuclear density functionals without free parameters: application to neutron matter
• The nuclear energy density functional formalism
• Current Developments in Nuclear Density Functional Methods
• Continuity equation and local gauge invariance for the N3LO nuclear Energy Density Functionals
• Instabilities in the Nuclear Energy Density Functional
• Neutron elastic scattering on calcium isotopes from chiral nuclear optical potentials
• Applying the Density Matrix Expansion with Coordinate-Space Chiral Interactions
• Nuclear Energy Density Functionals: What do we really know?
• Incorporating Brueckner-Hartree-Fock correlations in the Density Matrix Expansion approach
• Exact-exchange density functional theory for neutron drops
• Optimized nuclear energy density functionals including long-range pion contributions
• Symbolic integration of a product of two spherical bessel functions with an additional exponential and polynomial factor
• Approximate self-energy for Fermi systems with large s-wave scattering length: a step towards density functional theory
• Symbolic computation of the Hartree-Fock energy from a chiral EFT three-nucleon interaction at N${}^2$LO
• Comparing different density-matrix expansions for long-range pion exchange
• Chiral nuclear dynamics with three-body forces
• Two-body weak currents in heavy nuclei
• Examining the justification for the introduction of a fermion localization function