$^3$He Relaxation Time Measurements at $\sim$400mK for the neutron electric dipole moment (nEDM) experiment

In the new nEDM experiment planned to be carried out at the SNS, the measurement cell will be made of dTPB-dPS (wavelength shifting material) coated acrylic and filled with superfluid $^4$He. NMR technique will be used to measure the neutron precession frequency by comparing with that of the polarized $^3$He using the spin-dependent nuclear reaction: $\vec{n}+\vec{^{3}He} \rightarrow p + t + 764$ keV. The polarized $^3$He will be used as a comagnetometer to monitor the B field \emph{in situ} during the experiment. Understanding the relaxation mechanism of polarized $^3$He under the experimental conditions and maintaining $^3$He polarization is crucial. Following our earlier study of the $^3$He relaxation time in a dTPB-dPS coated cylindrical acrylic cell at a temperature of 1.9K in the presence of superfluid $^4$He with a magnetic holding field of 21 G, similar measurements at $\sim$400 mK (the proposed nEDM experimental temperature) have been carried out using a dilution refrigerator in TUNL at $\sim$7 G. Preliminary results will be presented.