skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Microscopically based energy density functionals for nuclei using the density matrix expansion. II. Full optimization and validation

Journal Article · · Physical Review C
 [1];  [2];  [3];  [3];  [4]
  1. Ohio Univ., Athens, OH (United States). Institute of Nuclear and Particle Physics and Department of Physics and Astronomy
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Nuclear and Chemical Sciences Division
  3. The Ohio State Univ., Columbus, OH (United States). Department of Physics
  4. Michigan State Univ., East Lansing, MI (United States). National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy

Background: Energy density functional methods provide a generic framework to compute properties of atomic nuclei starting from models of nuclear potentials and the rules of quantum mechanics. Until now, the overwhelming majority of functionals have been constructed either from empirical nuclear potentials such as the Skyrme or Gogny forces, or from systematic gradient-like expansions in the spirit of the density functional theory for atoms. Purpose: In this study, we seek to obtain a usable form of the nuclear energy density functional that is rooted in the modern theory of nuclear forces. We thus consider a functional obtained from the density matrix expansion of local nuclear potentials from chiral effective field theory. We propose a parametrization of this functional carefully calibrated and validated on selected ground-state properties that is suitable for large-scale calculations of nuclear properties. Methods: Our energy functional comprises two main components. The first component is a non-local functional of the density and corresponds to the direct part (Hartree term) of the expectation value of local chiral potentials on a Slater determinant. Contributions to the mean field and the energy of this term are computed by expanding the spatial, finite-range components of the chiral potential onto Gaussian functions. The second component is a local functional of the density and is obtained by applying the density matrix expansion to the exchange part (Fock term) of the expectation value of the local chiral potential. We apply the UNEDF2 optimization protocol to determine the coupling constants of this energy functional. Results: We obtain a set of microscopically constrained functionals for local chiral potentials from leading order up to next-to-next-to-leading order with and without three-body forces and contributions from Δ excitations. These functionals are validated on the calculation of nuclear and neutron matter, nuclear mass tables, single-particle shell structure in closed-shell nuclei, and the fission barrier of 240Pu . Quantitatively, they perform noticeably better than the more phenomenological Skyrme functionals. Conclusions: The inclusion of higher-order terms in the chiral perturbation expansion seems to produce a systematic improvement in predicting nuclear binding energies while the impact on other observables is not really significant. In conclusion, this result is especially promising since all the fits have been performed at the single-reference level of the energy density functional approach, where important collective correlations such as center-of-mass correction, rotational correction, or zero-point vibrational energies have not been taken into account yet.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Nuclear Physics (NP)
Grant/Contract Number:
AC52-07NA27344; FG02-93ER40756; SC0008533; RC107839-OSU
OSTI ID:
1458672
Alternate ID(s):
OSTI ID: 1435680
Report Number(s):
LLNL-JRNL-745116; PRVCAN; 900506; TRN: US1901500
Journal Information:
Physical Review C, Vol. 97, Issue 5; ISSN 2469-9985
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 28 works
Citation information provided by
Web of Science

References (99)

On the Gaussian overlap approximation for the collective excitations of odd nuclei journal January 2015
The Negele–Vautherin density-matrix expansion applied to the Gogny force journal May 2010
Barcelona-Catania-Paris-Madrid functional with a realistic effective mass journal January 2017
Ab initio no core shell model journal March 2013
Microscopically based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization journal November 2010
Lipkin method of particle-number restoration to higher orders journal July 2014
Isovector properties of the Gogny interaction journal November 2014
Nuclear energy density optimization: Shell structure journal May 2014
Gaussian matrix elements in a cylindrical harmonic oscillator basis journal July 2009
Surface symmetry energy of nuclear energy density functionals journal March 2011
Renormalization of chiral two-pion exchange NN interactions with Δ excitations: Central phases and the deuteron journal April 2009
Particle-number restoration within the energy density functional formalism: Nonviability of terms depending on noninteger powers of the density matrices journal April 2009
Odd nuclei and single-particle spectra in the relativistic mean-field model journal May 1998
Optimized Chiral Nucleon-Nucleon Interaction at Next-to-Next-to-Leading Order journal May 2013
Nonlocal energy density functionals for low-energy nuclear structure journal March 2014
Pion–nucleon scattering inside the Mandelstam triangle journal March 2000
The AME2016 atomic mass evaluation (II). Tables, graphs and references journal March 2017
The AME2016 atomic mass evaluation (I). Evaluation of input data; and adjustment procedures journal March 2017
Local nuclear energy density functional at next-to-next-to-next-to-leading order journal October 2008
Gaussian overlap approximation for the quadrupole collective states journal July 2012
Solution of the Skyrme–Hartree–Fock–Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. journal November 2009
Renormalization of the NN interaction with a chiral two-pion-exchange potential: Central phases and the deuteron journal November 2006
Nuclear Fission: from more phenomenology and adjusted parameters to more fundamental theory and increased predictive power journal January 2017
Precision Nucleon-Nucleon Potential at Fifth Order in the Chiral Expansion journal September 2015
Continuity equation and local gauge invariance for the N 3 LO nuclear energy density functionals journal December 2011
Variations on a theme by Skyrme: A systematic study of adjustments of model parameters journal March 2009
Axially deformed solution of the Skyrme–Hartree–Fock–Bogolyubov equations using the transformed harmonic oscillator basis (III) hfbtho (v3.00): A new version of the program journal November 2017
Microscopic justification of the equal filling approximation journal July 2008
Polarization corrections to single-particle energies studied within the energy-density-functional and quasiparticle random-phase approximation approaches journal January 2014
A note on the validity of the density matrix expansion journal November 1975
Variation after particle-number projection for the Hartree-Fock-Bogoliubov method with the Skyrme energy density functional journal July 2007
Local chiral potentials with Δ -intermediate states and the structure of light nuclei journal November 2016
Microscopically-constrained Fock energy density functionals from chiral effective field theory. I. Two-nucleon interactions journal February 2011
Accurate charge-dependent nucleon-nucleon potential at fourth order of chiral perturbation theory journal October 2003
Structure of even-even nuclei using a mapped collective Hamiltonian and the D1S Gogny interaction journal January 2010
Minimal nuclear energy density functional journal April 2018
Coupled-cluster computations of atomic nuclei journal September 2014
Solution of Hartree-Fock-Bogoliubov equations and fitting procedure using the N2LO Skyrme pseudopotential in spherical symmetry journal October 2017
Table of experimental nuclear ground state charge radii: An update journal January 2013
Global study of quadrupole correlation effects journal March 2006
Kohn–Sham density functional inspired approach to nuclear binding journal June 2008
Nuclear matter properties from local chiral interactions with Δ isobar intermediate states journal December 2016
Particle-number restoration within the energy density functional formalism journal April 2009
Configuration mixing within the energy density functional formalism: Removing spurious contributions from nondiagonal energy kernels journal April 2009
Pairing correlations. I. Description of odd nuclei in mean-field theories journal December 2001
Pairing correlations. II. Microscopic analysis of odd-even mass staggering in nuclei journal December 2001
Effect of particle-vibration coupling on single-particle states: A consistent study within the Skyrme framework journal December 2010
Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange including Δ resonances journal February 2015
Nuclear energy density optimization: Large deformations journal February 2012
Chiral Two-Pion Exchange and Proton-Proton Partial-Wave Analysis journal June 1999
Chiral EFT based nuclear forces: achievements and challenges journal July 2016
Hartree-Fock-Bogoliubov nuclear mass model with 0.50 MeV accuracy based on standard forms of Skyrme and pairing functionals journal December 2013
Renormalization of chiral two-pion exchange NN interactions with Δ excitations: Correlations in the partial-wave expansion journal April 2011
Non-empirical pairing energy functional in nuclear matter and finite nuclei journal October 2009
Determination of the chiral coupling constants c 3 and c 4 in new pp and np partial-wave analyses journal April 2003
Pairing gap and polarisation effects journal November 1999
Solution of self-consistent equations for the N3LO nuclear energy density functional in spherical symmetry. The program hosphe (v1.02) journal September 2010
Axially deformed solution of the Skyrme-Hartree–Fock–Bogoliubov equations using the transformed harmonic oscillator basis (II) hfbtho v2.00d: A new version of the program journal June 2013
Density-Matrix Expansion for an Effective Nuclear Hamiltonian journal May 1972
Applying the density matrix expansion with coordinate-space chiral interactions journal May 2017
Isospin effects in NZ nuclei in extended density functional theory journal January 2016
Nuclear energy density optimization journal August 2010
Density-matrix expansion for an effective nuclear Hamiltonian. II journal March 1975
The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei journal March 2016
Self-consistent mean-field models for nuclear structure journal January 2003
One-quasiparticle states in the nuclear energy density functional theory journal February 2010
Heavy-particle formalism with Foldy-Wouthuysen representation journal April 2011
New Kohn-Sham density functional based on microscopic nuclear and neutron matter equations of state journal June 2013
Chiral Dynamics of Few- and Many-Nucleon Systems journal November 2012
Improved density matrix expansion for spin-unsaturated nuclei journal July 2010
Accurate nuclear radii and binding energies from a chiral interaction journal May 2015
Uncertainty Analysis and Order-by-Order Optimization of Chiral Nuclear Interactions journal February 2016
Quantum Monte Carlo calculations of neutron matter with chiral three-body forces journal February 2016
Quantum Monte Carlo methods for nuclear physics journal September 2015
Coarse-grained NN potential with chiral two-pion exchange journal February 2014
The Skyrme interaction in finite nuclei and nuclear matter journal April 2007
Nuclear forces with Δ excitations up to next-to-next-to-leading order, part I: Peripheral nucleon-nucleon waves journal May 2007
Pairing gap and polarisation effects text January 1999
Local nuclear energy density functional at next-to-next-to-next-to-leading order text January 2008
Non-empirical pairing energy functional in nuclear matter and finite nuclei text January 2009
One-quasiparticle States in the Nuclear Energy Density Functional Theory text January 2009
Structure of even-even nuclei using a mapped collective Hamiltonian and the D1S Gogny interaction text January 2009
Microscopically-based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization text January 2010
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 text January 2012
Coupled-cluster computations of atomic nuclei text January 2013
Lipkin method of particle-number restoration to higher orders text January 2014
Isovector properties of the Gogny interaction text January 2014
Precision nucleon-nucleon potential at fifth order in the chiral expansion text January 2014
Isospin effects in N~Z nuclei in extended Density Functional Theory text January 2015
The In-Medium Similarity Renormalization Group: A Novel Ab Initio Method for Nuclei text January 2015
The Barcelona-Catania-Paris-Madrid functional with a realistic effective mass text January 2016
Nuclear matter properties from local chiral interactions with $Δ$ isobar intermediate states text January 2016
Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis (III) hfbtho (v3.00): a new version of the program text January 2017
A Minimal Nuclear Energy Density Functional text January 2017
Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory text January 2003
Renormalization of NN Interaction with Chiral Two Pion Exchange Potential. Central Phases and the Deuteron text January 2005
Global study of quadrupole correlation effects text January 2005
The Skyrme Interaction in finite nuclei and nuclear matter text January 2006
Nuclear forces with Delta-excitations up to next-to-next-to-leading order I: peripheral nucleon-nucleon waves text January 2007

Cited By (4)


Similar Records

The Negele-Vautherin Density Matrix Expansion Applied to the Gogny Force
Journal Article · Fri Jan 01 00:00:00 EST 2010 · Journal of Physics G: Nuclear and Particle Physics · OSTI ID:1458672

Nuclear energy density optimization: Shell structure
Journal Article · Thu May 15 00:00:00 EDT 2014 · Physical Review. C. Nuclear Physics · OSTI ID:1458672

Isospin-invariant Skyrme energy-density-functional approach with axial symmetry
Journal Article · Mon May 19 00:00:00 EDT 2014 · Physical Review. C. Nuclear Physics · OSTI ID:1458672