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 formThe best present constraints on α for λ < 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 momentum transfers q 2 = 0, and neutron gravity reflectometry, which involves momentum transfers q 2 = 8mVopt where m is the neutron mass and Vopt is the neutron optical potential of the medium. We show that the fractional difference ∆b |b| averaged over the 7 elements where high precision data exists on the same material from both measurement methods is [2.2 ± 1.4] × 10 −4 . We also show that ∆b |b| for this data is insensitive both to exotic Yukawa interactions and also to the electromagnetic neutron-atom interactions proportional to the neutron-electron scattering length bne and the neutron polarizability scattering amplitude b pol . This result will be useful in any future global analyses of neutron scattering data to determine bne and bound α and λ. 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.

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