Microscopically based energy density functionals for nuclei using the density matrix expansion: Implementation and preoptimization
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 HartreeFock energy obtained from chiral effective field theory two and threenucleon 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 zerorange contact interactions and a coupling function of the density arising from the finiterange 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 finitedensity observables to capture shortrange correlation energy contributions from beyond HartreeFock. 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 proofofprinciple 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 »
 Authors:
 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)
 National Superconducting Cyclotron Laboratory, 1 Cyclotron Laboratory, East Lansing, Michigan 48824 (United States)
 (United States)
 (France)
 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; HARTREEFOCK METHOD; INTERACTIONS; NUCLEAR ENERGY; NUCLEI; NUCLEONS; OPTIMIZATION; PIONS; SKYRME POTENTIAL; APPROXIMATIONS; BARYONS; BOSONS; CALCULATION METHODS; CORRELATIONS; ELEMENTARY PARTICLES; ENERGY; FERMIONS; FUNCTIONS; HADRONS; MATRICES; MESONS; NUCLEONNUCLEON 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, F91191 GifsurYvette, and Furnstahl, R. J.. Microscopically based energy density functionals for nuclei using the density matrix expansion: Implementation and preoptimization. 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, F91191 GifsurYvette, & Furnstahl, R. J.. Microscopically based energy density functionals for nuclei using the density matrix expansion: Implementation and preoptimization. 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, F91191 GifsurYvette, and Furnstahl, R. J.. 2010.
"Microscopically based energy density functionals for nuclei using the density matrix expansion: Implementation and preoptimization". 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 preoptimization},
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, F91191 GifsurYvette 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 HartreeFock energy obtained from chiral effective field theory two and threenucleon 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 zerorange contact interactions and a coupling function of the density arising from the finiterange 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 finitedensity observables to capture shortrange correlation energy contributions from beyond HartreeFock. 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 proofofprinciple 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 largescale 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 microscopicallybased nuclear energy density functional by applying the Density Matrix Expansion (DME) to the HartreeFock energy obtained from chiral effective field theory (EFT) two and threenucleon 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 zerorange contact interactions and a coupling function of the density arising from the finiterange pion exchanges. Since the contact contributions have essentially the same structure as those entering empirical Skyrme functionals, a microscopically guided Skyrme phenomenologymore »

Microscopically Based Nuclear Energy Functionals
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Testing Skyrme energydensity functionals with the quasiparticle randomphase approximation in lowlying vibrational states of rareearth nuclei
Although nuclear energydensity functionals are determined primarily by fitting to groundstate properties, they are often applied in nuclear astrophysics to excited states, usually through the quasiparticle randomphase approximation (QRPA). Here we test the Skyrme functionals SkM* and SLy4 along with the selfconsistent QRPA by calculating properties of lowlying vibrational states in a large number of welldeformed eveneven rareearth 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 multiparticlehole correlations that are not included in the QRPA. The Skyrme functional SkM* performs noticeably better than SLy4.more »