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

Abstract

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. Themore » 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.« less

Authors:
 [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
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
OSTI Identifier:
1458672
Alternate Identifier(s):
OSTI ID: 1435680
Report Number(s):
LLNL-JRNL-745116
Journal ID: ISSN 2469-9985; PRVCAN; 900506; TRN: US1901500
Grant/Contract Number:  
AC52-07NA27344; FG02-93ER40756; SC0008533; RC107839-OSU
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review C
Additional Journal Information:
Journal Volume: 97; Journal Issue: 5; Journal ID: ISSN 2469-9985
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats

Navarro Perez, R., Schunck, N., Dyhdalo, A., Furnstahl, R. J., and Bogner, S. K. Microscopically based energy density functionals for nuclei using the density matrix expansion. II. Full optimization and validation. United States: N. p., 2018. Web. doi:10.1103/PhysRevC.97.054304.
Navarro Perez, R., Schunck, N., Dyhdalo, A., Furnstahl, R. J., & Bogner, S. K. Microscopically based energy density functionals for nuclei using the density matrix expansion. II. Full optimization and validation. United States. doi:10.1103/PhysRevC.97.054304.
Navarro Perez, R., Schunck, N., Dyhdalo, A., Furnstahl, R. J., and Bogner, S. K. Wed . "Microscopically based energy density functionals for nuclei using the density matrix expansion. II. Full optimization and validation". United States. doi:10.1103/PhysRevC.97.054304. https://www.osti.gov/servlets/purl/1458672.
@article{osti_1458672,
title = {Microscopically based energy density functionals for nuclei using the density matrix expansion. II. Full optimization and validation},
author = {Navarro Perez, R. and Schunck, N. and Dyhdalo, A. and Furnstahl, R. J. and Bogner, S. K.},
abstractNote = {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.},
doi = {10.1103/PhysRevC.97.054304},
journal = {Physical Review C},
number = 5,
volume = 97,
place = {United States},
year = {2018},
month = {5}
}

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