Precision neutron-interferometric measurement of the coherent neutron-scattering length in silicon

The neutron-interferometry (NI) technique provides a precise and direct way to measure the bound, coherent scattering lengths $b$ of low-energy neutrons in solids, liquids, or gases. The potential accuracy of NI to measure $b$ has not been fully realized in past experiments, due to systematic sources of error. We have used a method which eliminates two of the main sources of error to measure the scattering length of silicon with a relative standard uncertainty of 0.005%. The resulting value, $b=4.1507\mathrm{}\left(2\right)\mathrm{}\mathrm{fm},$ is in agreement with the current accepted value, but has an uncertainty five times smaller.