Pendellösung Interferometry Probes the Neutron Charge Radius, Lattice Dynamics, and Fifth Forces

Abstract: Structure factors describe how incident radiation is scattered from materials such as silicon and germanium and characterize the physical interaction between the material and scattered particles. We use neutron pendell\"{o}sung interferometry to make precision measurements of the (220) and (400) neutron-silicon structure factors, and achieve a factor of four improvement in the (111) structure factor uncertainty. These data provide measurements of the silicon Debye-Waller factor at room temperature and the mean square neutron charge radius $\langle r_n^2 \rangle = -0.1101 \pm 0.0089 \, \mathrm{fm}^2$. Combined with existing measurements of the Debye-Waller factor and charge radius, the measured structure factors also improve constraints on the strength of a Yukawa-modification to gravity by an order of magnitude over the 20 pm to 10 nm length scale range.