| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 72806 | Microporous and Mesoporous Materials | 2015 | 5 Pages |
•Commutator expansions for solving Bloch–Torrey’s equation are derived.•Moments of the echo decay are derived in terms of commutators.•The case of freely diffusing spins in a constant magnetic field is solved.•The case of diffusing spins restricted between two plates is solved in the short-gradient pulse limit.
In this paper commutator expansions for solving the Bloch–Torrey’s equation are derived. An exact solution for free diffusion in a constant magnetic field gradient is found. Furthermore the moments of the signal in the short gradient pulse limit for spins confined to a restricted geometry are derived. The moments are tested numerically against the known solution of diffusing spins between two perpendicular plates in the short gradient pulse limit.
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