Precision Neutron Interferometric Measurement of thendCoherent Neutron Scattering Length and Consequences for Models of Three-Nucleon Forces

We have performed the first high precision measurement of the coherent neutron scattering length of deuterium in a pure sample using neutron interferometry. We find $b_{nd}=(6.665\pm 0.004)\mathrm{f}\mathrm{m}$ in agreement with the world average of previous measurements using different techniques, $b_{nd}=(6.6730\pm 0.0045)\mathrm{f}\mathrm{m}$. We compare the new world average for the $nd$ coherent scattering length $b_{nd}=(6.669\pm 0.003)\mathrm{f}\mathrm{m}$ to calculations of the doublet and quartet scattering lengths from several modern nucleon-nucleon potential models with three-nucleon force (3NF) additions and show that almost all theories are in serious disagreement with experiment. This comparison is a more stringent test of the models than past comparisons with the less precisely determined doublet scattering length of ${}^{2}a_{nd}=(0.65\pm 0.04)\mathrm{f}\mathrm{m}$.