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

In the new neutron electric dipole moment (nEDM) experiment planned to be carried out at the SNS, the neutron storage cell will be made of dTPB-dPS (wavelength shifting material) coated acrylic and filled with superfluid $^4$He at $\sim$400mK. 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 the spin-dependent nuclear process: $\vec{n}+\vec{^{3}He}\rightarrow p+t+764$ keV. The polarized $^3$He will also be used as a co-magnetometer to monitor \emph{in situ} the magnetic field during the experiment. Understanding the relaxation mechanism of polarized $^3$He in the storage cell under the experimental conditions and maintaining the $^3$He polarization is crucial. Following our earlier study[1] 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, more measurements at $\sim$400mK have been carried out in cylindrical and rectangular acrylic cells using a dilution refrigerator at TUNL with the magnetic holding field of $\sim$7 G. Preliminary results will be presented. [1] Q. Ye \textit{et al.} Physical Review A, 77:053408, 2008