Precision Measurement of the Coherent Scattering Length of n-$^{4}$He Using Neutron Interferometry*

Our recent work measured the coherent scattering length ($b_{c}$) of n-$^{4}$He to $10^{-3}$ relative precision, a factor of $10\times$ improvement over previous measurements. Neutron interferometry is used for precision measurements of scattering lengths for a variety of isotopes. Examples include the ($b_{c}$) of $^{1}$H, $^{2}$H, $^{3}$He and the incoherent scattering length of $^{3}$He. Neutron scattering lengths of light nuclei provide useful tests of nuclear potential models and can serve as inputs for nuclear effective field theories. We used a monolithic, perfect-silicon neutron interferometer which splits the wave-function of a single neutron, via Bragg diffraction, into two coherent separated paths and a phase shift, directly proportional to $b_{c}$, is introduced by the $^{4}$He sample. We will report our result and describe our method. This work was performed at the NIST Center for Neutron Research (NCNR) and is supported by the National Science Foundation.