Spin relaxation and linear-in-electric-field frequency shift in an arbitrary, time-independent magnetic field

A method is presented to calculate the spin relaxation times T1, T2 due to a non-uniform magnetic field, and the linear-in-electric-field precession frequency shift {\delta}{\omega}E when an electric field is present, in the diffusion approximation for spins confined to a rectangular cell. It is found that the rectangular cell geometry admits of a general result for T1, T2, and {\delta}{\omega}E in terms of the spatial cosine-transform components of the magnetic field.