Abstract
Formulas are derived for the contribution of the three-spin non-secular dipolar interactions to the characteristic time \(T_{1\rho \rho }\) of the nuclear spin–lattice relaxation in solids in the doubly rotating frame (DRF), which are convenient for practical use. Both the singly rotating frame (RF) and the DRF are in their own magic-angle conditions to select such interactions with maximal efficiency. One of the formulas is expressed in particular in terms of motionally averaged parts of the second moment of the absorption RF nuclear magnetic resonance line; another differs mainly from the first in that the second moment parameters are substituted for the corresponding RF local field ones. An analytical interrelation between the formulas is established. The formulas are self-consistent and equivalent, and each of them individually well describes the three-spin dipolar contribution of protons of polycrystalline benzene to their spin–lattice relaxation in the DRF at ultraslow rotary and diffusive motions of its molecules.
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Acknowledgements
The author thanks Dr. V.E. Zobov for clarification of the distinctive features of the terms of Eq. (4) and Professor V.A. Atsarkin for critical remarks. The work is performed on the program of the state task for Fryazino branch of Kotel’nikov IRE RAS.
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Mefed, A.E. Three-Spin Dipolar Contribution to Nuclear Spin–Lattice Relaxation in Solids in the Doubly Rotating Frame: Practical Formulas. Appl Magn Reson 52, 759–768 (2021). https://doi.org/10.1007/s00723-021-01327-0
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DOI: https://doi.org/10.1007/s00723-021-01327-0