  Significant effort has been devoted to searching for new fundamental forces
of nature. At short length scales (below approximately 10 nm), the strongest
experimental constraints come from neutron scattering from individual nuclei in
gases. The leading experiments at longer length scales instead measure forces
between macroscopic test masses. We propose a hybrid of these two approaches:
scattering neutrons off of a target that has spatial structure at nanoscopic
length scales. Such structures will give a coherent enhancement to small-angle
scattering, where the new force is most significant. This can considerably
improve the sensitivity of neutron scattering experiments for new forces in the
0.1 - 100 nm range. We discuss the backgrounds due to Standard Model
interactions and a variety of potential target structures that could be used,
estimating the resulting sensitivities. We show that, using only one day of
beam time at a modern neutron scattering facility, our proposal has the
potential to detect new forces as much as two orders of magnitude beyond
current laboratory constraints at the appropriate length scales.
