We report the first results from a new approach for measuring the $^3$He neutron incoherent scattering length $b_{ i}$. $b_{ i}$ is directly proportional to the difference $\Delta b=b_{ +}-b_{ -}$ in the two low-energy s-wave neutron-nucleus scattering amplitudes $b_{ +}$ and $b_{ -}$, corresponding to the singlet $J=0$ and triplet $J=1$ states of the neutron-$^3$He interaction, respectively. An accurate measurement of $b_{ i}$ can help distinguish among different models of three-nucleon interactions by comparison to { \it ab initio} nuclear theory calculations. The neutron birefringence caused by $\Delta b$ results in neutron spin rotation around the nuclear polarization. We measured $\Delta b$ using polarized neutron spin rotation and the transmission of neutrons through a $^3$He gas target polarized in situ by spin-exchange optical pumping. This brief test measurement, conducted at the FZ-J\"ulich neutron spin echo spectrometer at the Heinz Maier Leibnitz Zentrum (MLZ), yielded $\Delta b = [-5.27 \pm 0.05$ (stat.) $- 0.05$ (syst.)] fm. We argue that this method can be improved in precision to resolve the discrepancies between two prior measurements of $b_i$ which are dependent on the polarized absorption cross section $\sigma_p$. Further with absolute $^{ 3}$He polarization via NMR (in a properly-shaped cell) concurrent with accurate neutron transmission measurements, $\sigma_p$ can be measured to obtain independent values of $b_{ +}$ and $b_{ -}$.
Categories: nucl-ex physics.atom-ph