Precision Measurement of the Neutron Scattering Length of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>He</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:math> Using Neutron Interferometry
R. Haun, F. E. Wietfeldt, M. Arif, M. G. Huber, T. C. Black, B. Heacock, D. A. Pushin, Chandra Shahi
Abstract
We report a 0.08% measurement of the bound neutron scattering length of $^{4}\mathrm{He}$ using neutron interferometry. The result is $b=(3.0982\ifmmode\pm\else\textpm\fi{}0.0021[\mathrm{stat}]\ifmmode\pm\else\textpm\fi{}0.0014[\mathrm{syst}])\text{ }\text{ }\mathrm{fm}$. The corresponding free atomic scattering length is $a=(2.4746\ifmmode\pm\else\textpm\fi{}0.0017[\mathrm{stat}]\ifmmode\pm\else\textpm\fi{}0.0011[\mathrm{syst}])\text{ }\text{ }\mathrm{fm}$. With this result the world average becomes $b=(3.0993\ifmmode\pm\else\textpm\fi{}0.0025)\text{ }\text{ }\mathrm{fm}$, 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.