Monte Carlo Simulation of Spin Relaxation due to v $\times$ E effect in nEDM experiment

We have simulated the precession of spin-polarized Ultra Cold Neutrons and $^{3}$He atoms in uniform and static {\it B} and {\it E} fields and calculated the spin relaxation. The spin relaxation times $T_1$ (longitudinal) and $T_2$ (transverse) of spin-polarized UCN and $^3$He atoms are important considerations in the new measurements of neutron Electric Dipole Moment in the SNS nEDM experiment. The uniform {\it E} field creates a motional magnetic field due to the {\nolinebreak$\vec{v} \times \vec{E}$} effect which combines with collisions with the walls of the holding cell to produce constant variation of the total {\it B} field and result in the spin relaxation of the neutron and $^3$He samples. Scattering of $^3$He atoms in $^4$He also results in spin relaxation and is highly temperature dependent. In the SNS nEDM experiment the {\it B} field has magnitude of 10 mGauss. The applied {\it E} field is parallel to the {\it B} field and has a magnitude of 50 kV/cm. We have found the relaxation times for the neutron due to the {\nolinebreak$\vec{v} \times \vec{E}$} effect to be long compared to holding times and neutron lifetime. On the other hand, the {\nolinebreak$\vec{v} \times \vec{E}$} effect could be important for $^3$He relaxation times.