A Complete Approach to Determine the ${}^3$He neutron incoherent scattering length $b_i$

Abstract

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-Jülich 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 $b_{-}$.

8 pages, 3 figures. includes Supplement