$^3$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