Toward ab initio density functional theory for nuclei

Abstract

We survey approaches to nonrelativistic density functional theory (DFT) for nuclei using progress toward ab initio DFT for Coulomb systems as a guide. Ab initio DFT starts with a microscopic Hamiltonian and is naturally formulated using orbital-based functionals, which generalize the conventional local-density-plus-gradients form. The orbitals satisfy single-particle equations with multiplicative (local) potentials. The DFT functionals can be developed starting from internucleon forces using wave-function based methods or by Legendre transform via effective actions. We describe known and unresolved issues for applying these formulations to the nuclear many-body problem and discuss how ab initio approaches can help improve empirical energy density functionals.

69 pages, 16 figures, many revisions based on feedback. To appear in Progress in Particle and Nuclear Physics

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• Relativistic Nuclear Energy Density Functionals: Mean-Field and Beyond
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• Microscopic Theory of Nuclear Fission: A Review
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• Global performance of covariant energy density functionals: ground state observables of even-even nuclei and the estimate of theoretical uncertainties
• Nuclear Equation of State from ground and collective excited state properties of nuclei
• Relativistic mean field interaction with density dependent meson-nucleon vertices based on microscopical calculations
• Ab-initio self-consistent Gorkov-Green's function calculations of semi-magic nuclei - I. Formalism at second order with a two-nucleon interaction
• Symmetry-guided large-scale shell-model theory
• Resonantly Interacting Fermions In a Box
• Nuclear chiral dynamics and thermodynamics
• Effects of symmetry breaking in finite quantum systems
• Spin and spin-isospin instabilities in asymmetric nuclear matter at zero and finite temperatures using Skyrme functionals
• New applications of renormalization group methods in nuclear physics
• Effective contact pairing forces from realistic calculations in infinite homogeneous nuclear matter
• Microscopically-based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization
• Subtraction method and stability condition in the extended RPA theories
• Nuclear shape coexistence: A study of the even-even Hg isotopes using the interacting boson model with configuration mixing
• Self-interaction errors in nuclear energy density functionals
• Non-observable nature of the nuclear shell structure. Meaning, illustrations and consequences
• Parametric correlations in energy density functionals
• Computational Nuclear Quantum Many-Body Problem: The UNEDF Project
• An improved density matrix expansion for spin-unsaturated nuclei
• Shape coexistence in the microscopically guided interacting boson model
• Effects of density dependence of the effective pairing interaction on the first $2^{+}$ excitations and quadrupole moments of odd nuclei
• Convergence of density-matrix expansions for nuclear interactions
• Symmetry energy in nuclear density functional theory
• Testing the density matrix expansion against ab initio calculations of trapped neutron drops
• Shape coexistence in even-even nuclei: A theoretical overview
• Skyrme functional with tensor terms from \textit{ab initio} calculations of neutron-proton drops
• Effects of tensor forces in nuclear spin-orbit splittings from ab initio calculations
• Effective density functionals beyond mean field
• Nuclear energy density functional from chiral two- and three-nucleon interactions
• Role of three-nucleon forces and many-body processes in nuclear pairing
• Ab Initio Derivation of Model Energy Density Functionals
• Microscopically-constrained Fock energy density functionals from chiral effective field theory. I. Two-nucleon interactions
• Turning the nuclear energy density functional method into a proper effective field theory: reflections
• Functional Renormalization Group and Kohn-Sham scheme in Density Functional Theory
• Challenges in Nuclear Structure Theory
• Partial-wave contributions to pairing in nuclei
• Uncertainty Quantification and Propagation in Nuclear Density Functional Theory
• Towards a Renormalization Group Approach to Density Functional Theory - General Formalism and Case Studies -
• Sloppy nuclear energy density functionals: effective model reduction
• Validating Simple Dynamical Simulations of the Unitary Fermi Gas
• Formation of Selfbound States in a One-Dimensional Nuclear Model -- A Renormalization Group based Density Functional Study
• Towards Quantum Turbulence in Cold Atomic Fermionic Superfluids
• Nuclear energy density functional from chiral pion-nucleon dynamics revisited
• Properties of exotic nuclei and their linkage to the nucleonic interaction
• Functional renormalization-group calculation of the equation of state of one-dimensional nuclear matter inspired by the Hohenberg--Kohn theorem
• Continuity equation and local gauge invariance for the N3LO nuclear Energy Density Functionals
• Toward ab initio charge symmetry breaking in nuclear energy density functionals
• Model nuclear energy density functionals derived from ab initio calculations
• Improvement of functionals in density functional theory by the inverse Kohn--Sham method and density functional perturbation theory
• Ab-initio description of excited states of a one-dimensional nuclear matter with the Hohenberg-Kohn-theorem-inspired functional-renormalization-group method
• Application of Coulomb energy density functional for atomic nuclei: Case studies of local density approximation and generalized gradient approximation
• Applying the Density Matrix Expansion with Coordinate-Space Chiral Interactions
• Hot and dense matter beyond relativistic mean field theory
• Neutron Shell Closure at N=32 and N=40 in Ar and Ca Isotopes
• Incorporating Brueckner-Hartree-Fock correlations in the Density Matrix Expansion approach
• A first step in the nuclear inverse Kohn-Sham problem: from densities to potentials
• Microscopic derivation of density functional theory for superfluid systems based on effective action formalism
• Optimized nuclear energy density functionals including long-range pion contributions
• Exact-exchange density functional theory for neutron drops
• Density Functional Theory with Spatial-Symmetry Breaking and Configuration Mixing
• Finite-range effects in dilute Fermi gases at unitarity
• Anchor-based optimization of energy density functionals
• Relativistic self-energy decomposition of nuclear symmetry energy and equation of state of neutron matter within QCD sum rules
• Towards a power counting in nuclear energy-density-functional theories through a perturbative analysis
• Comparing different density-matrix expansions for long-range pion exchange
• Nucleon localization function in rotating nuclei
• Sampling General N-Body Interactions with Auxiliary Fields
• Nuclear energy density functional from chiral pion-nucleon dynamics: Isovector terms
• Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• KIDS density functional for deformed nuclei: Examples of the even-even Nd isotopes
• The Similarity Renormalization Group for Three-Body Interactions in One Dimension
• Spin-orbit coupling rule in bound fermions systems
• Applications of the Similarity Renormalization Group to the Nuclear Interaction
• Shell Evolution in Neutron-rich Ge, Se, Kr and Sr Nuclei within RHB Approach
• The MC-QTAIM: A framework for extending the atoms in molecules analysis beyond purely electronic systems
• Many-body interactions and nuclear structure
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• Relativistic correction of the Coulomb interaction in the local density approximation for energies and radii in doubly-magic nuclei
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