The scattering length difference between the $b_1$ and $b_0$ states of $n$-$^3$He using a neutron interferometer*

We report a determination of the $n-$$^3$He scattering length difference $\Delta b^{\prime} = b_{1}^{\prime}-b_{0}^{\prime}= $($-5.411\pm0.051$) fm between the triplet and singlet states using a neutron interferometer. This revises our previous result $\Delta b^{\prime}=$($-5.610\pm0.042$) fm obtained using the same technique in 2008. A sample placed in one of the beam paths of the interferometer causes a phase shift that is proportional to sample's scattering length density, thickness and $n$ wavelength. For this experiment, polarized neutrons were incident on the interferometer and the relative phase shift caused by a spin-dependent interaction with a polarized $^3$He target was measured. The neutron polarization and spin flipper efficiency were determined separately using helium-3 analyzers to $<$ 0.1 \% relative uncertainty. This re-evaluation comes from new phase shift data taken in 2013 and a partial reanalysis of the 2008 data that includes a systematic correction caused by magnetic field gradients which was previously underestimated. Scattering lengths of low Z materials are important for both providing inputs into effective field theories and testing nuclear models. This result along with other measured values of $b$ for $^3$He will be compared to nucleon models.\\[4pt] In collaboration with M. Arif, W.C. Chen, T.R. Gentile, D.S. Hussey, NIST; T.C. Black, University of North Carolina-Wilmington; D.A. Pushin, University of Waterloo; C.B. Shahi, F.E. Wietfeldt, Tulane University; and L. Yang, University of Illinois at Urbana-Champaign.