Spin Dependent Absorption Cross Section of Neutron $^3He$

Measurement of neutron scattering lengths for light nuclei provides a good opportunity to test theories of nucleon-nucleon and three-nucleon forces. The largest systematic uncertainty for recent measurements of the neutron-$^3He$ incoherent scattering length originates from lack of precise knowledge of the spin dependent abosorption cross section (SDACS). To measure the SDACS to $\sim$0.1\%, the primary experimental challenge is to measure the $^3He$ polarization to the same precision. We are developing a new approach to measure the polarization based on the free induction decay (FID) method. The $^3He$ gas, sealed in a special T-shape cell, is polarized with the spin exchange optical pumping method. The polarized $^3He$ nuclei, which are magnetic dipoles, can induce a classical magnetic field. By using the $^3He$ itself as a magnetometer, the Larmor frequency of the $^3He$ can be measured with FID method. We have chosen a special T-shape for the cell that allows for a calculable magnetic field from the $^3He$ gas while also permitting acceptable neutron transimission. If we flip the polarized $^3He$ 1$80^{\circ}$, the magnetic field will change and therefore the Larmor frequency of $^3He$ will change also. With this method, the polarization of $^3He$, and then the SDACS of n+$^3He$ can be measured to high precision.