  We study the energy of an impurity (polaron) that interacts strongly in a sea
of fermions when the effective range of the impurity-fermion interaction
becomes important, thereby mapping the Fermi polaron of condensed matter
physics and ultracold atoms to strongly interacting neutrons. We present
Quantum Monte Carlo results for this neutron polaron, and compare these with
effective field theory calculations that also include contributions beyond the
effective range. We show that state-of-the-art nuclear density functionals vary
substantially and generally underestimate the neutron polaron energy. Our
results thus provide constraints for adjusting the time-odd components of
nuclear density functionals to better characterize polarized systems.
