Searching for New Physics and Determining the Neutron Charge Radius with Precision Pendellösung Interference Measurements

The Bragg-diffracted intensity of a neutron beam incident on a nearly-perfect crystal slab exhibits pendellösung oscillations, the absolute phase of which depends on the neutron wavelength, crystal thickness, and neutron-crystalline potential.  Pendellösung interference studies were used to determine the thermally-averaged coherent scattering amplitudes for the (111), (220), and (400) symmetry planes in silicon with relative precision of 5 x 10^-5.  Fitting the scattering amplitudes to a known functional form results in sensitive measures of silicon’s mean square atomic thermal displacement and the neutron charge radius.  When combined with prior determinations of these parameters, constraints on a BSM Yukawa modification to gravity are improved over the 10 nm to 20 pm length scale range.