  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 $b_{\mathit{np}}=(-3.7384 \pm 0.0020)$
fm\cite{Schoen03}, $b_{\mathit{nd}}=(6.6649 \pm 0.0040)$
fm\cite{Black03,Schoen03}, and $b_{n^{3}\textrm{He}} = (5.8572 \pm 0.0072)$
fm\cite{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.
