  The properties of inhomogeneous neutron matter are crucial to the physics of
neutron-rich nuclei and the crust of neutron stars. Advances in computational
techniques now allow us to accurately determine the binding energies and
densities of many neutrons interacting via realistic microscopic interactions
and confined in external fields. We perform calculations for different external
fields and across several shells to place important constraints on
inhomogeneous neutron matter, and hence the large isospin limit of the nuclear
energy density functionals that are used to predict properties of heavy nuclei
and neutron star crusts. We find important differences between microscopic
calculations and current density functionals; in particular the isovector
gradient terms are significantly more repulsive than in traditional models, and
the spin-orbit and pairing forces are comparatively weaker.
