Orbital-free density functional theory: Differences and similarities between electronic and nuclear systems

Orbital-free density functional theory (OF-DFT) has been used when studying atoms, molecules, and solids. In nuclear physics, applications of OF-DFT have been quite scarce so far, as DFT has been widely applied to the study of many nuclear properties mostly within the Kohn-Sham (KS) scheme. There are many realizations of nuclear KS-DFT, but computations become very demanding for heavy systems, such as superheavy nuclei and the inner crust of neutron stars, and it is hard to describe exotic nuclear shapes using a finite basis made with a limited number of orbitals. These bottlenecks could, in principle, be overcome by an orbital-free formulation of DFT. This work is a first step towards the realistic application of OF-DFT to nuclei. In particular, we have implemented possible choices for an orbital-free kinetic energy and solved the associated Schrödinger equation either with simple potentials or with simplified nuclear density functionals. While the former choice sheds light on the differences between electronic and nuclear systems, the latter choice allows us to discuss the practical applications to nuclei as well as open questions.