Precision neutron interferometric measurements and updated evaluations of the n-p and n-d coherent neutron scattering lengths

We have performed high-precision measurements of the coherent neutron scattering lengths of gas phase molecular hydrogen and deuterium using neutron interferometry. After correcting for molecular binding and multiple scattering from the molecule, we find ${b}_{\mathrm{np}}=(\ensuremath{-}3.7384\ifmmode\pm\else\textpm\fi{}0.0020)\mathrm{fm}$ and ${b}_{\mathrm{nd}}=(6.6649\ifmmode\pm\else\textpm\fi{}0.0040)\mathrm{fm}.$ Our results are in agreement with the world average of previous measurements, ${b}_{\mathrm{np}}=(\ensuremath{-}3.7410\ifmmode\pm\else\textpm\fi{}0.0010)\mathrm{fm}$ and ${b}_{\mathrm{nd}}=(6.6727\ifmmode\pm\else\textpm\fi{}0.0045)\mathrm{fm}.$ The new world averages for the $n\ensuremath{-}p$ and $n\ensuremath{-}d$ coherent scattering lengths, including our new results, are ${b}_{\mathrm{np}}=(\ensuremath{-}3.7405\ifmmode\pm\else\textpm\fi{}0.0009)\mathrm{fm}$ and ${b}_{\mathrm{nd}}=(6.6683\ifmmode\pm\else\textpm\fi{}0.0030)\mathrm{fm}.$ We compare ${b}_{\mathrm{nd}}$ with the calculations of the doublet and quartet scattering lengths of several nucleon-nucleon potential models and show that almost all known calculations are in disagreement with the precisely measured linear combination corresponding to the coherent scattering length. Combining the world data on ${b}_{\mathrm{nd}}$ with the modern high-precision theoretical calculations of the quartet $n\ensuremath{-}d$ scattering lengths recently summarized by Friar et al., we deduce a new value for the doublet scattering length of ${}^{2}{a}_{\mathrm{nd}}=[0.645\ifmmode\pm\else\textpm\fi{}0.003(\mathrm{expt})\ifmmode\pm\else\textpm\fi{}0.007(\mathrm{theory})]\mathrm{fm}.$ This value is a factor of 4, more precise than the previously accepted value of ${}^{2}{a}_{\mathrm{nd}}=[0.65\ifmmode\pm\else\textpm\fi{}0.04(\mathrm{expt})]\mathrm{fm}.$ The current state of knowledge of scattering lengths in the related $p\ensuremath{-}d$ system, ideas for improving by a factor of 5 the accuracy of the ${b}_{\mathrm{np}}$ and ${b}_{\mathrm{nd}}$ measurements using neutron interferometry, and possibilities for further improvement of our knowledge of the coherent neutron scattering lengths of ${}^{3}\mathrm{H},$ ${}^{3}\mathrm{He},$ and ${}^{4}\mathrm{He}$ are discussed.