2026/07/25 by Fumihiro Imoto
#physics.comp-ph
Nonlocal kinetic-energy density functionals (KEDFs) can encode nuclear shell structure in orbital-free density functional theory (OFDFT), but self-consistency requires accurate functional derivatives and a stable solution of the Euler equation. We construct a density-dependent-kernel KEDF whose correction is learned from Kohn-Sham (KS) reference data. Linearity in the kernel shape yields analytic Euler--Lagrange (EL) responses. The fit uses exact energy-matching equalities and soft quadratic inequality penalties for violations of prescribed tail-response and selected-path energy-rise margins, evaluated by an active-set repeated penalized least-squares iteration. We formulate the radial EL equation as the rearranged one-orbital eigenproblem. In a constant-kF 16O benchmark it converges without density mixing and agrees with imaginary-time evolution (ITE) to sub-keV energy. Adaptive-step ITE gives final species EL residuals of at most 0.07 MeV in the reported calculations, and rearranged diagonalization reaches the same stationary densities. For spherical N=Z systems without spin--orbit or Coulomb terms, nucleus-specific fits for A=16 to 140 reproduce shell patterns and radii. A correction trained on three nuclei transfers the shell pattern and radius, but not the absolute energy, to a previously unseen A=140 system.