Generalized Cumulant Expansions and Spin‐Relaxation Theory
Generalized Cumulant Expansions and Spin‐Relaxation Theory
复制标题
广义累积量展开式和自旋弛豫理论
DOI：
10.1063/1.1669833
复制
发表时间：
1968
影响因子：
4.4
通讯作者：
J. Freed
中科院分区：
文献类型：
--
作者：
J. Freed
Kubo 的广义累积量展开法应用于适合分子系统 NMR 和 ESR 研究的自旋弛豫理论分析。它导致了适当平均磁化算子（以及自旋密度矩阵）的运动方程的一般形式解。该解决方案允许在运动变窄的区域中方便地进行微扰扩展；即，当随机函数自旋扰动 H1(t) 服从 | H1(t) |τc<1，其中τc是随机过程的相关时间。它显示了这种对时间 t≫τc 有效的展开如何生成 | 中所有阶的时间无关的 R 或松弛矩阵。 1(t) |τc，通过四阶给出详细表达式。虽然 R 矩阵提供了主洛伦兹共振线的线宽和动态频移，但发现通过制定没有限制 t≫τc 的累积量方法，可以预测弱辅助洛伦兹共振线。这些辅助线表现为二阶扰动......
The generalized cumulant expansion method of Kubo is applied to an analysis of spin‐relaxation theory appropriate for NMR and ESR studies of molecular systems. It leads to a general, formal solution of the equation of motion of a suitably averaged magnetization operator (and also the spin‐density matrix). This solution permits a convenient perturbation expansion in the region of motional narrowing; i.e., when the random functional spin perturbation H1(t) obeys | H1(t) |τc<1, where τc is a correlation time for the random process. It is shown how this expansion valid for times t≫τc generates the time‐independent R or relaxation matrix to all orders in | 1(t) |τc, and detailed expressions are given through fourth order. While the R matrix supplies the linewidth and dynamic frequency shift of the main Lorentzian resonance line, it is found that by formulating the cumulant method without the restriction t≫τc, weak subsidiary Lorentzian lines are predicted. These subsidiary lines appear as second‐order perturba...