Transverse spin relaxation in inhomogeneous magnetic fields
Scott D. Stoller, William Happer, and Freeman J. Dyson
We discuss the transition between two limiting cases of transverse spin
relaxation due to magnetic-field inhomogeneities: very fast spatial
diffusion, when the spins relax exponentially with time, and very slow
spatial diffusion, when the spins relax exponentially with the cube of
the time. Both limiting cases as well as intermediate cases can be
described in terms of Airy functions, which are the eigenfunctions of the
time-independent Torrey equation. Branch points in the eigenvalue
spectrum and other interesting properties follow from the fact that the
Torrey equation is not self-adjoint.
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