Barskiy Danila A, Pravdivtsev Andrey N
Institut für Physik, Johannes Gutenberg Universität Mainz, 55128, Mainz, Germany.
Helmholtz Institut Mainz, 55128, Mainz, Germany.
Chemphyschem. 2025 Jul 2;26(13):e202500092. doi: 10.1002/cphc.202500092. Epub 2025 May 19.
In nuclear magnetic resonance (NMR), the bulk magnetization of a sample is commonly assumed to be proportional to spin polarization, with each spin of the same type contributing equally to the measured signal. Herein, the high-field theorem for general spin-I systems (where I is the spin quantum number): the total measurable NMR signal remains unaffected by the grouping of spins into equivalent units (e.g., molecules) is proved, provided the system is at thermodynamic equilibrium in the high field limit ( , where is the Larmor frequency and characterizes internal spin-spin interactions). The results are derived using both magnetization equations and density matrix formalism. The theorem, however, does not extend to conditions far from thermodynamic equilibrium (e.g., hyperpolarization), NMR of solids in the regime when quadrupolar or dipole-dipole interactions are not negligible, and zero- to ultralow-field NMR. Three educational problems designed to deepen understanding of the material in classroom settings are also presented. This work reinforces established principles in magnetic resonance but also highlights areas for further exploration.
在核磁共振（NMR）中，通常假定样品的体磁化强度与自旋极化成正比，同一类型的每个自旋对测量信号的贡献相同。在此，证明了一般自旋 - I 系统（其中 I 是自旋量子数）的高场定理：只要系统在高场极限下处于热力学平衡（ ，其中 是拉莫尔频率， 表征内部自旋 - 自旋相互作用），自旋分组为等效单元（例如分子）时，总可测量 NMR 信号不受影响。结果是使用磁化方程和密度矩阵形式推导出来的。然而，该定理不适用于远离热力学平衡的情况（例如超极化）、四极或偶极 - 偶极相互作用不可忽略时的固体 NMR 以及零至超低场 NMR。还提出了三个旨在加深课堂环境中对该材料理解的教学问题。这项工作强化了磁共振中的既定原理，但也突出了有待进一步探索的领域。
