Exact calculation, using angular momentum, of combined Zeeman and quadrupolar interactions in NMR
Exact calculation, using angular momentum, of combined Zeeman and quadrupolar interactions in NMR
复制标题
使用角动量精确计算 NMR 中组合塞曼和四极相互作用
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
A. D. Bain
中科院分区：
文献类型：
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作者：
A. D. Bain
自旋大于1/2的核的NMR通常受到四极相互作用的强烈影响。塞曼项和四极项的组合通常可以用微扰理论来处理，但也需要精确的计算。我们解释了一个确切的方法，消除了复杂的运营商的评价。相反，计算是基于Liouvillian的矩阵元素，与哈密顿的交换子。然后可以直接从Liouvillian的本征向量和本征值计算光谱。借助于角动量方法，可以证明自旋I的四极相互作用完全由（2 I −1）个约化矩阵元决定--对于自旋3/2，这意味着只有两个量。不需要各种基算符的确切性质，因为计算只需要角动量量子数。完整的刘维尔矩阵可以从选择规则和维格纳-埃卡特定理计算。此外，我们提出了一个表达式，这些减少矩阵元素，这是有效的任何自旋。该理论涵盖了从四极微扰NMR光谱到塞曼微扰核四极共振的整个范围。
The NMR of nuclei with spins greater than ½ is often strongly influenced by the quadrupole interaction. This combination of Zeeman and quadrupole terms can usually be treated using perturbation theory, but an exact calculation is also needed. We explain an exact approach that eliminates the evaluation of commutators of complicated operators. Instead, the calculation is based on matrix elements of the Liouvillian, the commutator with the Hamiltonian. The spectrum can then be calculated directly from the eigenvectors and eigenvalues of the Liouvillian. With the aid of angular momentum methods, it can be shown that the quadupole interaction for spin I is fully determined by only (2I −1) reduced matrix elements—for spin 3/2, this means only two quantities. The exact nature of the various basis operators is not needed, since the calculation only needs the angular momentum quantum numbers. The full Liouvillian matrix can be calculated from selection rules and the Wigner-Eckart theorem. Furthermore, we present an expression for these reduced matrix elements which is valid for any spin. This theory covers the whole range from quadrupole-perturbed NMR spectra to Zeeman-perturbed nuclear quadrupole resonance.
稀环境中半整数四极核核磁共振观察的一般策略。
DOI：
10.1006/jmre.2001.2353
发表时间：
2001
期刊：
Journal of magnetic resonance (San Diego, Calif. : 1997)
影响因子：
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作者：
Lipton,AS;Sears,JA;Ellis,PD
通讯作者：
Ellis,PD