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Orbital-free Density Functional Theory (OF-DFT) has been used when studyingatoms, molecules and solids. In nuclear physics, there has been basically noapplication of OF-DFT so far, as the Density Functional Theory (DFT) has beenwidely applied to the study of many nuclear properties mostly within theKohn-Sham (KS) scheme. There are many realizations of nuclear KS-DFT, butcomputations become very demanding for heavy systems, such as superheavy nucleiand the inner crust of neutron stars, and it is hard to describe exotic nuclearshapes using a finite basis made with a limited number of orbitals. Thesebottlenecks could, in principle, be overcome by an orbital-free formulation ofDFT. This work is a first step towards the application of OF-DFT to nuclei. Inparticular, we have implemented possible choices for an orbital-free kineticenergy and solved the associated Schr\"odinger equation either with simplepotentials or with simplified nuclear density functionals. While the formerchoice sheds light on the differences between electronic and nuclear systems,the latter choice allows us discussing the practical applications to nuclei andthe open questions.

Orbital-free Density Functional Theory: differences and similarities between electronic and nuclear systems