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Spin-Lattice Relaxation

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NMR

Abstract

Consider an ensemble of systems consisting of two arbitrary spins I and S. The interaction mechanism is assumed to be dipolar interaction. Spin-lattice relaxation refers to the z components of the magnetizations. The stationary part of the Hamiltonian is given as the Zeeman expression

$$ \mathcal{H}_{0}= \hbar\omega_{I} I_{z}-\hbar\omega_{s} S_{z} $$
((12.1))

where ωI = γIB0 and ωs = γsB0. No assumption is yet made concerning the gyromagnetic ratios of the spin-bearing particles, γI and γs. The spin-interaction Hamiltonian Hi is identified with that for dipolar coupling Hd.

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Notes

  1. This holds true for samples with powder geometry. Deviations are only expected with ordered systems permitting only very few orientations of the interdipole vectors.

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  2. Besides, the modulus of this term is small compared with that of the first term, because, in the period in which the correlation function retains non-vanishing values, i.e., τ ≲ τc, the sine function either remains minor if ωl(k)τC≲ 1, or oscillates

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  3. Because of the even character of the autocorrelation function, the sign of τ may be reversed in order to conform to the usual convention of the Fourier transformation (see Sect. 42.3).

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  4. Exceptions are found in cubic-or tetrahedral structure-like molecular environments where the electric-field gradient may even vanish.

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  5. In [335] an interesting NMR experiment is described that permits the direct observation of the resonance in the effective field acting as the quantization field in the rotating frame.

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Author information

Authors and Affiliations

  1. Sektion Kernresonanzspektroskopie, Universität Ulm, Albert-Einstein-Allee 11, D-89069, Ulm, Germany

    Prof. Dr. Rainer Kimmich

Authors
  1. Prof. Dr. Rainer Kimmich
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© 1997 Springer-Verlag Berlin Heidelberg

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Kimmich, R. (1997). Spin-Lattice Relaxation. In: NMR. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60582-6_12

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  • DOI: https://doi.org/10.1007/978-3-642-60582-6_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64465-8

  • Online ISBN: 978-3-642-60582-6

  • eBook Packages: Springer Book Archive

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