Internal consistency of neutron coherent scattering length measurements from neutron interferometry and from neutron gravity reflectometry

Many theories beyond the Standard Model postulate short-range modifications to gravity which produce deviations of Newton's gravitational potential from a strict 1/r dependence. It is common to analyze experiments searching for these modifications using a potential of the form V'(r) = - GMm/r [1 + alpha exp (-r/lambda)]. The best present constraints on a for lambda < 100 nm come from neutron scattering and often employ comparisons of different measurements of the coherent neutron scattering amplitudes b. We analyze the internal consistency of existing data from two different types of measurements of low-energy neutron scattering amplitudes: neutron interferometry, which involves squared momentum transfers q(2) = 0, and neutron gravity reflectometry, which involves squared momentum transfers q(2) = 8mV(opt) where m is the neutron mass and is the neutron optical potential of the medium. We show that the fractional difference Lb averaged over the seven elements where high precision data exist on the same material from both measurement methods is [2.2 +/- 1.4] x 10(-4). We also show that Delta b/vertical bar b vertical bar for these data is insensitive both to exotic Yukawa interactions and also to the electromagnetic neutron-atom interactions proportional to the neutron-electron scattering length b(ne) and the neutron polarizability scattering amplitude b(pol). This result will be useful in any future global analyses of neutron scattering data to determine b(ne) and bound alpha and lambda. We also discuss how various neutron interferometric and scattering techniques with cold and ultracold neutrons can be used to improve the precision of b measurements and make some specific proposals.