Microscopically based energy density functionals for nuclei using the density matrix expansion. II. Full optimization and validation
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 gradientlike 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 groundstate properties that is suitable for largescale calculations of nuclear properties. Methods: Our energy functional comprises two main components. The first component is a nonlocal 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, finiterange components of the chiral potential onto Gaussian functions. Themore »
 Authors:

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 Ohio Univ., Athens, OH (United States). Institute of Nuclear and Particle Physics and Department of Physics and Astronomy
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Nuclear and Chemical Sciences Division
 The Ohio State Univ., Columbus, OH (United States). Department of Physics
 Michigan State Univ., East Lansing, MI (United States). National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy
 Publication Date:
 Report Number(s):
 LLNLJRNL745116
Journal ID: ISSN 24699985; PRVCAN; 900506
 Grant/Contract Number:
 AC5207NA27344; FG0293ER40756; SC0008533; RC107839OSU
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review C
 Additional Journal Information:
 Journal Volume: 97; Journal Issue: 5; Journal ID: ISSN 24699985
 Publisher:
 American Physical Society (APS)
 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) (SC21); USDOE Office of Science (SC), Nuclear Physics (NP) (SC26)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
 OSTI Identifier:
 1458672
 Alternate Identifier(s):
 OSTI ID: 1435680
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.,
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.. 2018.
"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.
@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 gradientlike 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 groundstate properties that is suitable for largescale calculations of nuclear properties. Methods: Our energy functional comprises two main components. The first component is a nonlocal 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, finiterange 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 nexttonexttoleading order with and without threebody forces and contributions from Δ excitations. These functionals are validated on the calculation of nuclear and neutron matter, nuclear mass tables, singleparticle shell structure in closedshell nuclei, and the fission barrier of 240Pu . Quantitatively, they perform noticeably better than the more phenomenological Skyrme functionals. Conclusions: The inclusion of higherorder 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 singlereference level of the energy density functional approach, where important collective correlations such as centerofmass correction, rotational correction, or zeropoint 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}
}