A Precision Measurement of the Neutron Scattering Length of He-4 Using Neutron Interferometry

We report a 0.08 % measurement of the bound neutron scattering length of $^4$He using neutron interferometry. The result is $b = (3.0982 \pm 0.0021 \mbox{ [stat]} \pm 0.0014 \mbox{ [sys]}) \mbox{ fm}$. The corresponding free atomic scattering length is $a = (2.4746 \pm 0.0017 \mbox{ [stat]} \pm 0.0011 \mbox{ [sys]}) \mbox{ fm}$. With this result the world average becomes $b = (3.0993 \pm 0.0025)$ fm, a 2 % downward shift and a reduction in uncertainty by more than a factor of six. Our result is in disagreement with a previous neutron interferometric measurement but is in good agreement with earlier measurements using neutron transmission.