Applying the Density Matrix Expansion with Coordinate-Space Chiral Interactions

Abstract

We apply the density matrix expansion (DME) at Hartree-Fock level with long-range chiral effective field theory interactions defined in coordinate space up to next-to-next-to-leading order. We consider chiral potentials both with and without explicit Delta isobars. The challenging algebra associated with applying the DME to three-nucleon forces is tamed using a new organization scheme, which will also facilitate generalizations. We include local regulators on the interactions to mitigate the effects of singular potentials on the DME couplings and simplify the optimization of generalized Skyrme-like functionals.

52 pages, 6 figures. Two equations corrected. Mathematica notebooks used in derivations are bundled in the submission. Corresponds to published version

References in corpus (22)

• Chiral effective field theory and nuclear forces
• Improved nuclear matter calculations from chiral low-momentum interactions
• Accurate nuclear radii and binding energies from a chiral interaction
• The In-Medium Similarity Renormalization Group: A Novel Ab Initio Method for Nuclei
• Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
• Local chiral effective field theory interactions and quantum Monte Carlo applications
• Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis (II) HFBTHO v2.00d: a new version of the program
• Minimally non-local nucleon-nucleon potentials with chiral two-pion exchange including $\Delta$'s
• In-Medium Similarity Renormalization Group for Open-Shell Nuclei
• Nuclear forces with Delta-excitations up to next-to-next-to-leading order I: peripheral nucleon-nucleon waves
• Ab Initio Multi-Reference In-Medium Similarity Renormalization Group Calculations of Even Calcium and Nickel Isotopes
• Uncertainty Quantification for Nuclear Density Functional Theory and Information Content of New Measurements
• Delta-excitations and the three-nucleon force
• Chiral EFT based nuclear forces: Achievements and challenges
• Microscopically-based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization
• Quantum Monte Carlo Calculations of Light Nuclei Using Chiral Potentials
• From the lightest nuclei to the equation of state of asymmetric nuclear matter with realistic nuclear interactions
• Regulator Artifacts in Uniform Matter for Chiral Interactions
• Elastic pion-nucleon scattering in chiral perturbation theory: A fresh look
• Error Analysis in Nuclear Density Functional Theory
• Density Matrix Expansion for Low-Momentum Interactions
• Uncertainty propagation within the UNEDF models

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• A Bayesian mixture model approach to quantifying the empirical nuclear saturation point
• Incorporating Brueckner-Hartree-Fock correlations in the Density Matrix Expansion approach
• Optimized nuclear energy density functionals including long-range pion contributions
• Towards a power counting in nuclear energy-density-functional theories through a perturbative analysis
• Approximate self-energy for Fermi systems with large s-wave scattering length: a step towards density functional theory
• Comparing different density-matrix expansions for long-range pion exchange
• Two-body weak currents in heavy nuclei
• Microscopically based energy density functionals for nuclei using the density matrix expansion