  We use neutron pendell\"{o}sung interferometry to produce the only precision
measures of the (220) and (400) neutron-silicon structure factors, as well as a
factor of four improvement in the (111) structure factor uncertainty. These
data provide a high-precision measure of the silicon Debye-Waller factor at
room temperature and the first competitive neutron scattering measurement of
the mean square neutron charge radius $\langle r_n^2 \rangle = -0.1100 \pm
0.0092 \, \mathrm{fm}^2$ in over twenty years. The measured structure factors
are tabulated for general use, including searches for interactions Beyond the
Standard Model of particle physics, where constraints on the strength of a
Yukawa-modification to gravity are improved by an order of magnitude over the
20 pm to 10 nm length scale range.
