Instead complex, multi-parameter phenomenological models have been developed to tackle nucleon-nucleon (NN) interactions. In systems with more than two nucleons poorly understood three nucleon (3N) interactions must be included with NN models to match the experimentally measured binding energies; a quantity that is known to great precision. Neutron scattering lengths, which describe a neutron's s-wave interaction with a target nucleus, are predicted by NN+3N models, and therefore provide crucial benchmarks in the testing of various theoretical approaches. Neutron scattering lengths of light nuclei also play an important role in effective field theories (EFT) since EFTs' use low-energy observables to constrain mean-field behavior. This experiment used neutron interferometry to determine the spin-dependent incoherent scattering length bi of n-3He, and was the first neutron interferometric experiment to use a polarized gas sample. Neutrons were polarized to Pn=93% using a transmission-mode supermirror. The neutron spin state could be flipped 180° with a precession coil. The neutron polarization was measured periodically during the experiment by replacing the interferometer with an optically thick 3He cell which provided analyzing powers of up to 99%.Two different techniques were used to measure Pn and the spin flipper efficiency to 0.04% relative uncertainty. This experiment used a target cell filled with 3He gas (figure 1) placed in one path of the interferometer. The NIST glass shop fabricated four boron-free glass target cells. Each cylindrical cell had outer dimensions of 25.4 mm diameter x 42 mm and was sealed with approximately 2 bar of 3He gas. The 3He gas was polarized over two days to an initial polarization of P3HE = 65-75% using spin exchange optical pumping techniques at a separate facility. The cell was transferred to the interferometer using a portable battery power solenoid with typical transport loss in P3HE of only a few percent. The largest cell lifetime at the interferometer, which had non-ideal magnetic field gradients, was 150 hours.
Over the course of 2 separate data runs taken in 2008 and 2013 (shown in figure 2), we measured bi = (-2.343 ± 0.013 (statistical) ± 0.017 (systematic)) fm. Figure 3 shows this the current state of the n-3He system. This result and the previous one are systematically limited by the small but nonzero triplet absorption cross section of 3He known only to one percent. Known NN+3N models do not match the current data on coherent and incoherent scattering lengths (including this work) for n-3He by several σ showing the need for greater experimental and theoretical work.