Precision Measurement of the n-$^3$He Incoherent Scattering Length Using Neutron Interferometry*

The low energy neutron-$^3$He scattering lengths are important for testing nuclear potential models that include three nucleon forces, effective field theories for few-body nuclear systems,and neutron scattering measurements of quantum excitations in liquid helium. We report the first measurement of the $n$-$^3$He incoherent scattering length using neutron interferometry: $b_i' = (-2.512\pm 0.012\mbox{ statistical} \pm0.014\mbox{ systematic})$ fm.This is in good agreement with a recent calculation using the AV18+UIX potential [1], but disagrees with a previous measurement using pseudomagnetic spin rotation [2]. This work also demonstrates the first use of a polarized nuclear target in a neutron interferometer.\\[4pt] [1] H.~M.~Hofmann and G.~M.~Hale, Phys. Rev. C {\bf 68}, 021002(R) (2003).\\[0pt] [2] O. Zimmer {\em et al.}, EPJdirect C {\bf A1}, 1 (2002).