Dipolar relaxation in a many-body system of spins of 1/2
Dipolar relaxation in a many-body system of spins of 1/2
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DOI：
10.1063/1.480709
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发表时间：
2000-01-15
影响因子：
4.4
通讯作者：
Freed, JH
中科院分区：
文献类型：
--
作者：
Nevzorov, AA;Freed, JH
文献I[J.Chem.太棒了。112,1413(2000)][1,1413(2000)][[1]，[1,1413(2000)][1，1,1413(2000)][1，1，14，3(2)][1，1，14(2)][1，1，14(2)][1，1，14(2)][1，1，14(2)][1，1，14(2)][1，1，4(2)][1，1，4(2)]，处理存在由平移扩散随机调制的偶极相互作用的双自旋系统的密度矩阵方程，推广到具有1/2相同自旋的多体系统。在高温近似下(适用于稀溶液)，对于单个非选择性脉冲，问题的对称性使得人们可以得到与两粒子解有关的自由感应衰变信号的紧凑有序二项式表达式，并且它仍然包含两个自旋等色度分量。后者是通过求解相应的随机Liouville方程来估计的，该方程允许人们以统一的方式恢复两种极限情况，包括Anderson关于刚性晶格中统计展宽的结果和经典的Torrey-Bloembergen-Redfield运动展宽的表达式，经Hwang和Freed修正。得到了热力学极限下的线形表达式，即宏观体积中大量粒子的线形表达式。结果发现，在所研究的整个运动范围内，多体偶极线形非常接近洛伦兹线形，线宽与自旋浓度成正比，正如先前对极限情况所预测的那样。绘制的线宽与平移扩散系数值的关系图清楚地显示了固态极限、运动收缩极限和中间区域。该方法被扩展到描述固体回波序列中的多体系统的行为。这使得人们能够在整个运动范围内获得均匀的T-2‘S。T-2中极小值的平移扩散系数与论文I(C)2000美国物理研究所的双自旋情形的值大致相同。[S0021-9606(00)02903-2]。
The method utilized in Paper I [J. Chem. Phys. 112, 1413 (2000)] for treating the density matrix equation for a two-spin system in the presence of the dipolar interaction that is randomly modulated by translational diffusion, is extended to a many-body system of identical spins of 1/2. Generalized cumulant expansions are used, which allow one to take full advantage of the statistical independence of the motions of spins. In the high-temperature approximation (appropriate for dilute solutions), for a single nonselective pulse, the symmetry of the problem allows one to obtain a compact ordered binomial expression for the free-induction decay signal that is related to the two-particle solution, and it still contains the two spin-isochromat components. The latter are evaluated by solving the corresponding stochastic Liouville equation, which allows one to recover in a unified way the two limiting cases including Anderson's result for statistical broadening in a rigid lattice and the classical Torrey-Bloembergen-Redfield expression for the motional narrowing, as corrected by Hwang and Freed. The line shape expression in the thermodynamic limit, i.e., for large numbers of particles in a macroscopic volume, is obtained. It is found that the many-body dipolar line shapes are very close to Lorentzians over the entire motional range studied, with the linewidths proportional to the spin concentration, as predicted earlier for the limiting cases. Linewidths plotted versus the values of the translational diffusion coefficient clearly show the solid-state limit, the motional-narrowing limit, and the intermediate region. The method is extended to describe the behavior of the many-body system in a solid-echo sequence. This enables one to obtain the homogeneous T-2's over the whole range of motions. A minimum in T-2 is found at approximately the same value of translational diffusion coefficient as was found for the two-spin case in Paper I. (C) 2000 American Institute of Physics. [S0021-9606(00)02903-2].