Performing an accurate measurement of Δb_i of 3He using Neutron Spin Echo

We recently performed measurements of the neutron incoherent scattering lengths for 129Xe and 131Xe. As a part of those measurements the Δb_i of 3He was also measured for a short time, only 6 hours, as a calibration. The results of this measurement indicate a very precise value could be obtained for a typical length experiment on NSE. Theories which take the data from measurements in three-body nuclear systems and predict what should be seen in a 4-body system like 4He or n-3He, which is an essential step needed to check the internal consistency of the three-body force extraction from systems with only three bodies, do not quite agree with the data by amounts too large to be explained only by 4-body forces. Furthermore, in the specific case of the n-3He system, the two best measurements of the n-3He incoherent scattering length differ by 3 sigma. During the course of our test measurement we found several important experimental and theoretical factors relevant to a measurement with precision beyond the error of the current measurements. We estimate that we could obtain a 1% measurement for Δb_i of 3He in one week.