High-Precision Determination of the Neutron Coherent Scattering Length

The neutron coherent scattering length b(c) has been determined interferometrically to an uncertainty of about 5 × 10(−5) by measuring the nondispersive phase. We propose improving the uncertainty to about 10(−6) by optimizing various parameters of the interferometric experiment. Any uncertainty in the b(c) determination arising from possible variations in the constitution of the ambient air can be eliminated by performing the experiment in vacuum. When such uncertainty is attained, it becomes necessary to account for the neutron beam refraction at the sample-ambient interfaces, to infer the correct b(c) from the observed phase. The formula for the phase used hitherto is approximate and would significantly overestimate b(c). The refractive index for neutrons can thus be determined to a phenomenal uncertainty of about 10(−12).