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Nuclear magnetization relaxation by diffusion in a parabolic magnetic field

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  • Le Doussal, Pierre
  • Sen, Pabitra N.

Abstract

An exact expressions for the transverse magnetization of spins diffusing in a filed (B0 + g1z +_g2z2ẑ reveals that a natural length scale lc = (8D/γg2)14, and a frequency associated with it Ω0 = 4D/l2c govern the decay. Here D is the diffusion constant and γ is the gyromagnetic ratio. lc is the size of the packet of magnetization at long times, i.e., Ω0t ⪢ 1. In the short time, the magnetization density |M(z,t)| ∼ exp[ − Dγ2 (g1 + 2g2z)2t3/3], i.e., it is permissible to use an effective local gradient. The magnetization decays rapidly where the magnetic field varies rapidly - thus the magnetization accumulates at the extremum of the field. At long times, the magnetization decays as exp(-Ω0t/2), as opposed to exp(-t3) in a uniform gradient. The phase distribution is not a Gaussian which leads the decay rate Ω0 ≈ √g2 to be a non-analytic function of g2.

Suggested Citation

  • Le Doussal, Pierre & Sen, Pabitra N., 1992. "Nuclear magnetization relaxation by diffusion in a parabolic magnetic field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 186(1), pages 115-120.
    • Handle: RePEc:eee:phsmap:v:186:y:1992:i:1:p:115-120
    DOI: 10.1016/0378-4371(92)90370-6
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    Cited by:

    1. Mitra, P.P., 1997. "Diffusion in porous materials as probed by pulsed gradient NMR measurements," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 241(1), pages 122-127.

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