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: Implementation and pre-optimization

Abstract

In a recent series of articles, Gebremariam, Bogner, and Duguet derived a microscopically based nuclear energy density functional by applying the density matrix expansion (DME) to the Hartree-Fock energy obtained from chiral effective field theory two- and three-nucleon interactions. Owing to the structure of the chiral interactions, each coupling in the DME functional is given as the sum of a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the finite-range pion exchanges. Because the contact contributions have essentially the same structure as those entering empirical Skyrme functionals, a microscopically guided Skyrme phenomenology has been suggested in which the contact terms in the DME functional are released for optimization to finite-density observables to capture short-range correlation energy contributions from beyond Hartree-Fock. The present article is the first attempt to assess the ability of the newly suggested DME functional, which has a much richer set of density dependencies than traditional Skyrme functionals, to generate sensible and stable results for nuclear applications. The results of the first proof-of-principle calculations are given, and numerous practical issues related to the implementation of the new functional in existing Skyrme codes are discussed. Using a restricted singular value decompositionmore » optimization procedure, it is found that the new DME functional gives numerically stable results and exhibits a small but systematic reduction of our test {chi}{sup 2} function compared to standard Skyrme functionals, thus justifying its suitability for future global optimizations and large-scale calculations.« less

Authors:
; ;  [1]; ;  [2];  [3];  [2];  [3];  [4];  [5]
  1. Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996 (United States) and Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States)
  2. National Superconducting Cyclotron Laboratory, 1 Cyclotron Laboratory, East Lansing, Michigan 48824 (United States)
  3. (United States)
  4. (France)
  5. Department of Physics, Ohio State University, Columbus, Ohio 43210 (United States)
Publication Date:
OSTI Identifier:
21499165
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 82; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevC.82.054307; (c) 2010 The American Physical Society
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; CAPTURE; CHIRALITY; COUPLING; COUPLING CONSTANTS; DENSITY; DENSITY FUNCTIONAL METHOD; DENSITY MATRIX; ELECTRON CORRELATION; ENERGY DENSITY; FIELD THEORIES; FUNCTIONALS; HARTREE-FOCK METHOD; INTERACTIONS; NUCLEAR ENERGY; NUCLEI; NUCLEONS; OPTIMIZATION; PIONS; SKYRME POTENTIAL; APPROXIMATIONS; BARYONS; BOSONS; CALCULATION METHODS; CORRELATIONS; ELEMENTARY PARTICLES; ENERGY; FERMIONS; FUNCTIONS; HADRONS; MATRICES; MESONS; NUCLEON-NUCLEON POTENTIAL; PARTICLE PROPERTIES; PHYSICAL PROPERTIES; POTENTIALS; PSEUDOSCALAR MESONS; VARIATIONAL METHODS

Citation Formats

Stoitsov, M., Kortelainen, M., Schunck, N., Bogner, S. K., Gebremariam, B., Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, Duguet, T., Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, CEA, Centre de Saclay, IRFU/Service de Physique Nucleaire, F-91191 Gif-sur-Yvette, and Furnstahl, R. J.. Microscopically based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization. United States: N. p., 2010. Web. doi:10.1103/PHYSREVC.82.054307.
Stoitsov, M., Kortelainen, M., Schunck, N., Bogner, S. K., Gebremariam, B., Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, Duguet, T., Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, CEA, Centre de Saclay, IRFU/Service de Physique Nucleaire, F-91191 Gif-sur-Yvette, & Furnstahl, R. J.. Microscopically based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization. United States. doi:10.1103/PHYSREVC.82.054307.
Stoitsov, M., Kortelainen, M., Schunck, N., Bogner, S. K., Gebremariam, B., Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, Duguet, T., Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, CEA, Centre de Saclay, IRFU/Service de Physique Nucleaire, F-91191 Gif-sur-Yvette, and Furnstahl, R. J.. 2010. "Microscopically based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization". United States. doi:10.1103/PHYSREVC.82.054307.
@article{osti_21499165,
title = {Microscopically based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization},
author = {Stoitsov, M. and Kortelainen, M. and Schunck, N. and Bogner, S. K. and Gebremariam, B. and Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824 and Duguet, T. and Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824 and CEA, Centre de Saclay, IRFU/Service de Physique Nucleaire, F-91191 Gif-sur-Yvette and Furnstahl, R. J.},
abstractNote = {In a recent series of articles, Gebremariam, Bogner, and Duguet derived a microscopically based nuclear energy density functional by applying the density matrix expansion (DME) to the Hartree-Fock energy obtained from chiral effective field theory two- and three-nucleon interactions. Owing to the structure of the chiral interactions, each coupling in the DME functional is given as the sum of a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the finite-range pion exchanges. Because the contact contributions have essentially the same structure as those entering empirical Skyrme functionals, a microscopically guided Skyrme phenomenology has been suggested in which the contact terms in the DME functional are released for optimization to finite-density observables to capture short-range correlation energy contributions from beyond Hartree-Fock. The present article is the first attempt to assess the ability of the newly suggested DME functional, which has a much richer set of density dependencies than traditional Skyrme functionals, to generate sensible and stable results for nuclear applications. The results of the first proof-of-principle calculations are given, and numerous practical issues related to the implementation of the new functional in existing Skyrme codes are discussed. Using a restricted singular value decomposition optimization procedure, it is found that the new DME functional gives numerically stable results and exhibits a small but systematic reduction of our test {chi}{sup 2} function compared to standard Skyrme functionals, thus justifying its suitability for future global optimizations and large-scale calculations.},
doi = {10.1103/PHYSREVC.82.054307},
journal = {Physical Review. C, Nuclear Physics},
number = 5,
volume = 82,
place = {United States},
year = 2010,
month =
}
  • In a recent series of papers, Gebremariam, Bogner, and Duguet derived a microscopically-based nuclear energy density functional by applying the Density Matrix Expansion (DME) to the Hartree-Fock energy obtained from chiral effective field theory (EFT) two- and three-nucleon interactions. Due to the structure of the chiral interactions, each coupling in the DME functional is given as the sum of a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the finite-range pion exchanges. Since the contact contributions have essentially the same structure as those entering empirical Skyrme functionals, a microscopically guided Skyrme phenomenologymore » has been suggested in which the contact terms in the DME functional are released for optimization to finite-density observables to capture short-range correlation energy contributions from beyond Hartree-Fock. The present paper is the first attempt to assess the ability of the newly suggested DME functional, which has a much richer set of density dependencies than traditional Skyrme functionals, to generate sensible and stable results for nuclear applications. The results of the first proof-of-principle calculations are given, and numerous practical issues related to the implementation of the new functional in existing Skyrme codes are discussed. Using a restricted singular value decomposition (SVD) optimization procedure, it is found that the new DME functional gives numerically stable results and exhibits a small but systematic reduction in {chi}^{2} compared to standard Skyrme functionals, thus justifying its suitability for future global optimizations and large-scale calculations.« less
  • A major goal of the SciDAC project 'Building a Universal Nuclear Energy Density Functional' is to develop next-generation nuclear energy density functionals that give controlled extrapolations away from stability with improved performance across the mass table. One strategy is to identify missing physics in phenomenological Skyrme functionals based on our understanding of the underlying internucleon interactions and microscopic many-body theory. In this contribution, I describe ongoing efforts to use the density matrix expansion of Negele and Vautherin to incorporate missing finite-range effects from the underlying two- and three-nucleon interactions into phenomenological Skyrme functionals.
  • Although nuclear energy-density functionals are determined primarily by fitting to ground-state properties, they are often applied in nuclear astrophysics to excited states, usually through the quasiparticle random-phase approximation (QRPA). Here we test the Skyrme functionals SkM* and SLy4 along with the self-consistent QRPA by calculating properties of low-lying vibrational states in a large number of well-deformed even-even rare-earth nuclei. We reproduce trends in energies and transition probabilities associated with {gamma}-vibrational states, but our results are not perfect and indicate the presence of multiparticle-hole correlations that are not included in the QRPA. The Skyrme functional SkM* performs noticeably better than SLy4.more » In a few nuclei, changes in the treatment of the pairing energy functional have a significant effect. The QRPA is less successful with ''{beta}-vibrational'' states than with the {gamma}-vibrational states.« less