Incorporating nuclear shell effects within the framework of orbital-free density functional theory (DFT) has remained a long-standing 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 nonlocal 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 nonlocal kinetic energy density functional. In particular, we show that the nonlocal 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.

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• Nuclear density functional theory
• Nuclear many-body theory