The Nuclear Energy Density Functional: What do we really know?

We present the simplest NEDF to date, determined by only 4 significant phenomenological parameters, yet capable of fitting measured nuclear masses with better accuracy than the Bethe-Weizsacker mass formula, while also describing density structures (charge radii, neutron skins etc.) and time-dependent phenomena (induced fission, giant resonances, low energy nuclear collisions, etc.). The 4 significant parameters are necessary to describe bulk nuclear properties (binding energies and charge radii); additional 2 to 3 parameters have little influence on the bulk nuclear properties, but allow independent control of the density dependence of the symmetry energy, excitation energy of isovector excitations, and the Thomas-Reiche-Kuhn sum rule. This Hohenberg-Kohn--style of DFT successfully realizes Weizsacker's ideas and provides a computationally tractable model for a variety of static nuclear properties and dynamics, from finite nuclei to neutron stars, where it will also provide a new insight into the physics of the r-process, nucleosynthesis, neutron star crust structure, and neutron star mergers. This new NEDF clearly separates the bulk geometric properties -- volume, surface, symmetry, and Coulomb energies which amount to approximately 8 MeV per nucleon or up to about 2000 MeV per nucleus for heavy nuclei -- from finer details related to shell effects, pairing, isospin breaking, etc which contribute at most a few MeV for the entire nucleus. Thus it provides a systematic framework for organizing various contributions to the NEDF. Measured and calculated physical observables -- i.e symmetry and saturation properties, the neutron matter equation of state, and the frequency of giant dipole resonances -- lead directly to new terms, not considered in current NEDF parameterizations.