We have performed high precision measurements of the zero-energy neutron scattering amplitudes of gas phase molecular hydrogen, deuterium, and $^{3}$He using neutron interferometry. We find $b_{mathit{np}}=(-3.7384 pm 0.0020)$ fmcite{Schoen03}, $b_{mathit{nd}}=(6.6649 pm 0.0040)$ fmcite{Black03,Schoen03}, and $b_{n^{3}textrm{He}} = (5.8572 pm 0.0072)$ fmcite{Huffman04}. When combined with the previous world data, properly corrected for small multiple scattering, radiative corrections, and local field effects from the theory of neutron optics and combined by the prescriptions of the Particle Data Group, the zero-energy scattering amplitudes are: $b_{mathit{np}}=(-3.7389 pm 0.0010)$ fm, $b_{mathit{nd}}=(6.6683 pm 0.0030)$ fm, and $b_{n^{3}textrm{He}} = (5.853 pm .007)$ fm. The precision of these measurements is now high enough to severely constrain NN few-body models. The n-d and n-$^{3}$He coherent neutron scattering amplitudes are both now in disagreement with the best current theories. The new values can be used as input for precision calculations of few body processes. This precision data is sensitive to small effects such as nuclear three-body forces, charge-symmetry breaking in the strong interaction, and residual electromagnetic effects not yet fully included in current models.
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