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Non-local orbital-free density functional theory knocks on nuclear shell effects

Xinhui Wu, Gianluca Colò, Kouichi Hagino, Pengwei Zhao

Abstract

Incorporating nuclear shell effects within the framework of orbital-free density functional theory (DFT) has remained a longstanding challenge in nuclear physics. While the Hohenberg-Kohn theorem formally guarantees the existence of an orbital-free density functional that is capable of describing all many-body effects, including shell effects, practical attempts since the 1970s have consistently failed to capture such effects. This persistent difficulty has even led to the misconception that the orbital-free DFT is inherently unable to describe nuclear shell effects. Here we develop a {\it non-local} orbital-free DFT approach for atomic nuclei and demonstrate that nuclear shell effects can be successfully incorporated into the orbital-free DFT through the construction of a non-local kinetic energy density functional. In particular, we show that the non-local orbital-free functional yields a nucleon localization function that, as an established indicator of shell effects, exhibits consistent behavior with the exact Kohn-Sham solution.

Non-local orbital-free density functional theory knocks on nuclear shell effects

Abstract

Incorporating nuclear shell effects within the framework of orbital-free density functional theory (DFT) has remained a longstanding challenge in nuclear physics. While the Hohenberg-Kohn theorem formally guarantees the existence of an orbital-free density functional that is capable of describing all many-body effects, including shell effects, practical attempts since the 1970s have consistently failed to capture such effects. This persistent difficulty has even led to the misconception that the orbital-free DFT is inherently unable to describe nuclear shell effects. Here we develop a {\it non-local} orbital-free DFT approach for atomic nuclei and demonstrate that nuclear shell effects can be successfully incorporated into the orbital-free DFT through the construction of a non-local kinetic energy density functional. In particular, we show that the non-local orbital-free functional yields a nucleon localization function that, as an established indicator of shell effects, exhibits consistent behavior with the exact Kohn-Sham solution.
Paper Structure (22 equations, 3 figures)

This paper contains 22 equations, 3 figures.

Figures (3)

  • Figure 1: (a) The ground-state densities of $^{16}$O and $^{40}$Ca obtained with the Kohn-Sham approach with the Skyrme SkP interaction. (b) The nucleon localization functions (NLF) of $^{16}$O and $^{40}$Ca obtained with the Kohn-Sham approach. (c) Same as (b), but for the $^{80}$Zr and $^{140}$Yb nuclei. In the panels (b) and (c), the arrows represent the intervals where the corresponding NLF function is monotonic. The circles with numbers are used to count how many times the NLF function changes its monotonic behavior.
  • Figure 2: The nucleon localization functions for (a) $^{16}$O, (b) $^{40}$Ca, (c) $^{80}$Zr, and (d) $^{140}$Yb obtained with the semi-local kinetic energy density functionals, that is, the vW, the TF, the TF1W, and the TF1/5W functionals, where $(\alpha,\beta)$ in Eq. (\ref{['Eq:TTFvW']}) is (0,1), (1,0), (1,1) and (1,1/5), respectively. For comparison, the figure also shows the nucleon localization function with $\tau(\rho)$ from the Kohn-Sham approach.
  • Figure 3: Same as Fig. \ref{['fig2']}, but obtained with the non-local functionals with a constant $k_F$ (the dotted lines) and the density-dependent $k_F$ (the dot-dashed lines). The inset in the panel (d) magnifies a specific part of the figure to better illustrate the detailed behaviors.