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Title: Nuclear kinetic density from ab initio theory

Abstract

The nuclear kinetic density is one of many fundamental, nonobservable quantities in density functional theory (DFT) dependent on the nonlocal nuclear density. Often, approximations may be made when computing the density that may result in spurious contributions in other DFT quantities. With the ability to compute the nonlocal nuclear density from ab initio wave functions, it is now possible to estimate effects of such spurious contributions. Herein, we derive the kinetic density using ab initio nonlocal scalar one-body nuclear densities computed within the no-core shell model (NCSM) approach, utilizing two- and three-nucleon chiral interactions as the sole input. The ability to compute translationally invariant nonlocal densities allows us to gauge the impact of the spurious center-of-mass (c.m.) contributions in DFT quantities, such as the kinetic density, and provide ab initio insight into refining energy density functionals. The nonlocal nuclear densities are derived from the NCSM one-body densities calculated in second quantization. We present a review of c.m. contaminated and translationally invariant nuclear densities. We then derive an analytic expression for the kinetic density using these nonlocal densities, producing an ab initio kinetic density. The ground-state nonlocal densities of He 4 , 6 , 8 , C 12 , and O 16 are used to compute the kinetic densities of the aforementioned nuclei. The impact of c.m. removal techniques in the density are discussed and compared to a procedure applied in DFT. The results of this work can be extended to other fundamental quantities in DFT. The use of a general nonlocal density allows for the calculation of fundamental quantities taken as input in theories such as DFT. This allows benchmarking c.m. removal procedures and provides a bridge for comparison between ab initio and DFT many-body techniques.

Authors:
 [1];  [2]
  1. Univ. of Waterloo, ON (Canada)
  2. TRIUMF, Vancouver, BC (Canada)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); Natural Sciences and Engineering Research Council of Canada (NSERC)
OSTI Identifier:
1565772
Report Number(s):
arXiv:1808.10537v2
Journal ID: ISSN 2469-9985; PRVCAN
Grant/Contract Number:  
SAPIN-2016-00033
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review C
Additional Journal Information:
Journal Volume: 99; Journal Issue: 2; 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

Gennari, Michael, and Navrátil, Petr. Nuclear kinetic density from ab initio theory. United States: N. p., 2019. Web. doi:10.1103/physrevc.99.024305.
Gennari, Michael, & Navrátil, Petr. Nuclear kinetic density from ab initio theory. United States. doi:10.1103/physrevc.99.024305.
Gennari, Michael, and Navrátil, Petr. Thu . "Nuclear kinetic density from ab initio theory". United States. doi:10.1103/physrevc.99.024305. https://www.osti.gov/servlets/purl/1565772.
@article{osti_1565772,
title = {Nuclear kinetic density from ab initio theory},
author = {Gennari, Michael and Navrátil, Petr},
abstractNote = {The nuclear kinetic density is one of many fundamental, nonobservable quantities in density functional theory (DFT) dependent on the nonlocal nuclear density. Often, approximations may be made when computing the density that may result in spurious contributions in other DFT quantities. With the ability to compute the nonlocal nuclear density from ab initio wave functions, it is now possible to estimate effects of such spurious contributions. Herein, we derive the kinetic density using ab initio nonlocal scalar one-body nuclear densities computed within the no-core shell model (NCSM) approach, utilizing two- and three-nucleon chiral interactions as the sole input. The ability to compute translationally invariant nonlocal densities allows us to gauge the impact of the spurious center-of-mass (c.m.) contributions in DFT quantities, such as the kinetic density, and provide ab initio insight into refining energy density functionals. The nonlocal nuclear densities are derived from the NCSM one-body densities calculated in second quantization. We present a review of c.m. contaminated and translationally invariant nuclear densities. We then derive an analytic expression for the kinetic density using these nonlocal densities, producing an ab initio kinetic density. The ground-state nonlocal densities of He4,6,8,C12, and O16 are used to compute the kinetic densities of the aforementioned nuclei. The impact of c.m. removal techniques in the density are discussed and compared to a procedure applied in DFT. The results of this work can be extended to other fundamental quantities in DFT. The use of a general nonlocal density allows for the calculation of fundamental quantities taken as input in theories such as DFT. This allows benchmarking c.m. removal procedures and provides a bridge for comparison between ab initio and DFT many-body techniques.},
doi = {10.1103/physrevc.99.024305},
journal = {Physical Review C},
issn = {2469-9985},
number = 2,
volume = 99,
place = {United States},
year = {2019},
month = {2}
}

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Works referenced in this record:

Hartree-Fock calculations in the density matrix expansion approach
journal, May 1998


Ab Initio Study of Ca 40 with an Importance-Truncated No-Core Shell Model
journal, August 2007


Density functionals in the laboratory frame
journal, January 2008


Ab initio no core shell model
journal, March 2013

  • Barrett, Bruce R.; Navrátil, Petr; Vary, James P.
  • Progress in Particle and Nuclear Physics, Vol. 69
  • DOI: 10.1016/j.ppnp.2012.10.003

Few-nucleon systems in a translationally invariant harmonic oscillator basis
journal, March 2000


The limits of the nuclear landscape
journal, June 2012

  • Erler, Jochen; Birge, Noah; Kortelainen, Markus
  • Nature, Vol. 486, Issue 7404
  • DOI: 10.1038/nature11188

Nuclear energy density optimization: Shell structure
journal, May 2014


Similarity renormalization group for nucleon-nucleon interactions
journal, June 2007


Hartree-Fock calculations with Skyrme's interaction
journal, June 1970


Simple Formula for the General Oscillator Brackets
journal, May 1972


Hartree-Fock Calculations with Skyrme's Interaction. I. Spherical Nuclei
journal, March 1972


Nuclear energy density optimization
journal, August 2010


Time-dependent hartree-fock theory with Skyrme's interaction
journal, September 1975


Self-consistent mean-field models for nuclear structure
journal, January 2003

  • Bender, Michael; Heenen, Paul-Henri; Reinhard, Paul-Gerhard
  • Reviews of Modern Physics, Vol. 75, Issue 1
  • DOI: 10.1103/RevModPhys.75.121

Time-odd components in the mean field of rotating superdeformed nuclei
journal, October 1995


Energy-density functionals inspired by effective-field theories: Applications to neutron drops
journal, September 2018


The kinetic energy density in Kohn–Sham density functional theory
journal, January 2005


Microscopically based energy density functionals for nuclei using the density matrix expansion. II. Full optimization and validation
journal, May 2018


Importance truncation for large-scale configuration interaction approaches
journal, June 2009


Unitary correlation operator method and similarity renormalization group: Connections and differences
journal, June 2008


Consequences of the center–of–mass correction in nuclear mean–field models
journal, April 2000

  • Bender, M.; Rutz, K.; Reinhard, P. -G.
  • The European Physical Journal A, Vol. 7, Issue 4
  • DOI: 10.1007/PL00013645

Peripheral nucleon-nucleon scattering at fifth order of chiral perturbation theory
journal, January 2015


Local three-nucleon interaction from chiral effective field theory
journal, November 2007


Hartree-Fock Calculations with Skyrme's Interaction. II. Axially Deformed Nuclei
journal, January 1973


Flow-equations for Hamiltonians
journal, January 1994


Evolution of Nuclear Many-Body Forces with the Similarity Renormalization Group
journal, August 2009


Translationally invariant density
journal, July 2004


Ab initio translationally invariant nonlocal one-body densities from no-core shell-model theory
journal, February 2018


Microscopic optical potentials derived from ab initio translationally invariant nonlocal one-body densities
journal, March 2018


From low-momentum interactions to nuclear structure
journal, July 2010

  • Bogner, S. K.; Furnstahl, R. J.; Schwenk, A.
  • Progress in Particle and Nuclear Physics, Vol. 65, Issue 1
  • DOI: 10.1016/j.ppnp.2010.03.001

Pairing renormalization and regularization within the local density approximation
journal, April 2006


High-quality two-nucleon potentials up to fifth order of the chiral expansion
journal, August 2017


Nuclear energy density optimization: Large deformations
journal, February 2012