$^3$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.