  There is an extensive literature on magnetic gradient induced spin
relaxation. Cates, Schaefer and Happer (CSH) in a seminal paper, have solved
the problem in the regime where diffusion theory (the Torrey equation is
applicable using an expansion of the density matrix in diffusion equation
eigenfunctions and angular momentum tensors. McGregor has solved the problem in
the same regime using a slightly more general formulation using Redfield theory
formulated in terms of the auto-correlation function of the fluctuating field
seen by the spins and calculating the correlation functions using the diffusion
theory Green's function. The results of both calculations were shown to agree
for a special case. In the present work we show that the eigenfunction
expansion of the Torrey equation yields the expansion of the Green's function
for the diffusion equation thus showing the identity of this approach with that
of Redfield theory. The general solution can also be obtained directly from the
Torrey equation for the density matrix. Thus the physical content of the
Redfield and Torrey approaches are identical. We then introduce a more general
expression for the position autocorrelation function of particles moving in a
closed cell, extending the range of applicability of the theory.
