  Orbital-free Density Functional Theory (OF-DFT) has been used when studying
atoms, molecules and solids. In nuclear physics, there has been basically no
application of OF-DFT so far, as the Density Functional Theory (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 application of OF-DFT to nuclei. In
particular, we have implemented possible choices for an orbital-free kinetic
energy and solved the associated Schr\"odinger 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 discussing the practical applications to nuclei and
the open questions.
