Effective density functionals beyond mean field

Abstract

I present a review on non relativistic effective energy--density functionals (EDFs). An introductory part is dedicated to traditional phenomenological functionals employed for mean--field--type applications and to several extensions and implementations that have been suggested over the years to generalize such functionals, up to the most recent ideas. The heart of this review is then focused on density functionals designed for beyond--mean--field models. Examples of these studies are discussed. Starting from these investigations, some illustrations of {\it{ab--initio}}--based or {\it{ab--initio}}--inspired functionals are provided. Constructing functionals by building bridges with {\it{ab--initio}} models represents an extremely challenging and timely objective. This will eventually reduce/eliminate the empirical character of EDFs and link them with the underlying theory of QCD. Conclusions are presented in the last part of the review.

To be published in Progress in Particle and Nuclear Physics

References in corpus (68)

• Many-Body Physics with Ultracold Gases
• Shapiro delay measurement of a two solar mass neutron star
• A Massive Pulsar in a Compact Relativistic Binary
• Theory of ultracold Fermi gases
• Improved nuclear matter calculations from chiral low-momentum interactions
• Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XII: Stiffness and stability of neutron-star matter
• Nuclear symmetry energy probed by neutron skin thickness of nuclei
• Accurate nuclear radii and binding energies from a chiral interaction
• Neutron matter at next-to-next-to-next-to-leading order in chiral effective field theory
• Recent developments in no-core shell-model calculations
• Spin-orbit splitting and the tensor component of the Skyrme interaction
• Minimally non-local nucleon-nucleon potentials with chiral two-pion exchange including $\Delta$'s
• Ultra-cold Polarized Fermi Gases
• Nucleon Effective Masses in Neutron-Rich Matter
• Neutron skin thickness in droplet model with surface width dependence: indications of softness of the nuclear symmetry energy
• Particle-Number Projection and the Density Functional Theory
• Neutron matter from chiral two- and three-nucleon calculations up to N${}^3$LO
• Local Density Functional Theory for Superfluid Fermionic Systems: The Unitary Gas
• Nuclear Structure in the Framework of the Unitary Correlation Operator Method
• Tensor interaction contributions to single-particle energies
• Spin-orbit and tensor mean-field effects on spin-orbit splitting including self-consistent core polarizations
• Evolution of nuclear shells with the Skyrme density dependent interaction
• Cold neutrons trapped in external fields
• Resonantly Interacting Fermions In a Box
• Superfluid Bose-Fermi mixture from weak-coupling to unitarity
• Equation of state of superfluid neutron matter and the calculation of ${}^1{S}_0$ pairing gap
• Khon-Sham Density Functional Inspired Approach to Nuclear Binding
• Exploring the extended density-dependent Skyrme effective forces for normal and isospin-rich nuclei to neutron stars
• Chiral EFT based nuclear forces: Achievements and challenges
• Microscopically-based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization
• Intrinsic-Density Functionals
• Effective pseudopotential for energy density functionals with higher order derivatives
• Second RPA and correlated realistic interactions
• Effective-Range Dependence of Resonantly Interacting Fermions
• Linear response of homogeneous nuclear matter with energy density functionals
• Density-functional theory for fermions in the unitary regime
• Self-consistent calculations of the strength function and radiative neutron capture cross section for stable and unstable tin isotopes
• Convergence of density-matrix expansions for nuclear interactions
• Large-scale exact diagonalizations reveal low-momentum scales of nuclei
• Realistic shell-model calculations for p-shell nuclei including contributions of a chiral three-body force
• Density Functional Theory for a Confined Fermi System with Short-Range Interaction
• The Three-Nucleon System at Next-To-Next-To-Leading Order
• Variational multiparticle-multihole configuration mixing method applied to pairing correlations in nuclei
• Microscopic optical potentials derived from ab initio translationally invariant nonlocal one-body densities
• Beyond-mean-field theories with zero-range effective interactions. A way to handle the ultraviolet divergence
• Solution of Hartree-Fock-Bogoliubov equations and fitting procedure using N2LO Skyrme pseudo-potential in spherical symmetry
• Three-cluster dynamics within the ab initio no-core shell model with continuum: How many-body correlations and $\alpha$-clustering shape ${}^6$He
• Electric dipole strength and dipole polarizability in ${}^{48}$Ca within a fully self-consistent second random-phase approximation
• Ab Initio study of neutron drops with chiral Hamiltonians
• Exploration of a modified density dependence in the Skyrme functional
• Density functional theory for fermions close to the unitary regime
• Effective Field Theory for Dilute Fermions with Pairing
• Second random-phase approximation, Thouless' theorem and the stability condition reexamined and clarified
• Energy-density functionals inspired by effective-field theories: Applications to neutron drops
• Angular-momentum projection of cranked symmetry-unrestricted Slater determinants
• From resonantly interacting fermions with effective range to neutron matter
• Simple regularization scheme for multi-reference density functional theories
• Spectra of Open-Shell Nuclei with Padé-Resummed Degenerate Perturbation Theory
• Microscopic derivation of the Bohr-Mottelson collective Hamiltonian and its application to quadrupole shape dynamics
• Scalar Nature of the Nuclear Density Functional
• Infinite matter properties and zero-range limit of nonrelativistic finite-range interactions
• Tools for incorporating a D-wave contribution in Skyrme energy density functionals
• On the formulation of functional theory for pairing with particle number restoration
• Static response, collective frequencies and ground state thermodynamical properties of spin saturated two-component cold atoms and neutron matter
• Effective 3-Body Interaction for Mean-Field and Density-Functional Theory
• A systematic study of giant quadrupole resonances with the subtracted second random--phase approximation: beyond--mean--field centroids and fragmentation
• Regularization of zero-range effective interactions in finite nuclei
• Semi-contact 3-body interaction for nuclear density functional theory

Cited by in corpus (25)

• Dense Nuclear Matter Equation of State from Heavy-Ion Collisions
• Turning the nuclear energy density functional method into a proper effective field theory: reflections
• Nuclear energy density functionals grounded in ab initio calculations
• Properties of exotic nuclei and their linkage to the nucleonic interaction
• Constraints on the neutron drip-line with the newly observed 39Na
• Embedding short-range correlations in relativistic density functionals through quasi-deuterons
• Linear Response Theory with finite-range interactions
• Neutron Shell Closure at N=32 and N=40 in Ar and Ca Isotopes
• Application of an ab-initio-inspired energy density functional to nuclei: impact of the effective mass and the slope of the symmetry energy on bulk and surface properties
• Bayesian inferences on covariant density functionals from multimessenger astrophysical data: Nucleonic models
• Lee-Yang-inspired energy-density functional including contributions from $p$-wave scattering
• Neutron star matter equation of state including $d^{\ast }$-hexaquark degrees of freedom
• Towards a power counting in nuclear energy-density-functional theories through a perturbative analysis
• Optimized nuclear energy density functionals including long-range pion contributions
• Approximate self-energy for Fermi systems with large s-wave scattering length: a step towards density functional theory
• Ladder resummation of spin 1/2 fermion many-body systems with arbitrary partial-wave content
• Initialization effects of nucleon profile on the $\pi$ yields in heavy-ion collisions at medium energies
• Topology change and nuclear symmetry energy in compact-star matter
• Nuclear matter from the ladder resummation in terms of the experimental nucleon-nucleon scattering amplitudes
• Bayesian inference of neutron star crust properties using an ab initio-benchmarked meta-model
• Finite-temperature infinite matter with effective-field-theory-inspired energy-density functionals
• Calculations for nuclear matter and finite nuclei within and beyond energy--density--functional theories through interactions guided by effective field theory
• Spurious dipole mode in random-phase approximation and in the RPA-based models
• Many-body perturbation theory for strongly correlated effective Hamiltonians using effective field theory methods
• Local energy density functional for superfluid Fermi gases from effective field theory