High Precision Measurement of the Coherent Scattering length of n-$^{4}$He

Neutron interferometry provides a tool for high-precision measurement of scattering lengths for gaseous samples. Examples include measurements of the coherent scattering lengths ($b_{c}$) 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 may serve as inputs for nuclear effective field theories. Our current work is to measure $b_{c}$ of n-$^{4}$He to the $10^{-3}$ relative precision level. We use a perfect silicon neutron interferometer which splits the matter wave of a single neutron, via Bragg diffraction, into two coherent separated paths and recombines them. A relative phase shift, directly proportional to $b_{c}$, is introduced by the gas sample. The data from this experiment have been collected and we will report a preliminary result. This work is supported by the National Science Foundation.