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

In the new neutron electric dipole moment (nEDM) experiment which is planned to be carried out at the SNS, the neutron storage cell will be made of dTPB-dPS (a wavelength shifting material) coated acrylic and filled with superfluid $^4$He. The experiment will use the nuclear magnetic resonance technique to measure the neutron precession frequency by comparing with that of the polarized $^3$He using spin dependence of the nuclear absorption process: $\vec{n} + \vec{^{3}He} \rightarrow p + t + 764$ keV. The polarized $^3$He will be used as a co-magnetometer to monitor the magnetic field \emph{in situ} during the experiment. Understanding the relaxation mechanism of polarized $^3$He in the storage cell 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 at a magnetic holding field of 21 gauss, similar measurements at $\sim$400mK (the proposed nEDM experimental temperature) have been carried out using a dilution refrigerator at TUNL with the magnetic holding field of $\sim$7 gauss. Preliminary results will be presented.