THE DYNAMICAL THEORY OF NUCLEAR INDUCTION
THE DYNAMICAL THEORY OF NUCLEAR INDUCTION
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DOI：
10.1103/physrev.89.728
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发表时间：
1953-01-01
期刊：
影响因子：
--
通讯作者：
BLOCH, F
中科院分区：
文献类型：
--
作者：
WANGSNESS, RK;BLOCH, F
从微观角度出发，通过统计方法推导出核感应动力学。唯一本质上缺乏通用性的是假设样品中的原子核彼此独立，因此该处理没有考虑自旋-自旋相互作用产生的特征。通过考虑任意外部场和分子环境对代表性核的同时作用，导出“分布矩阵”的一阶线性微分方程组。它类似于分布函数的经典玻尔兹曼方程，并允许在积分时确定任何自旋函数随时间变化的宏观平均值。这个一般结果特别适用于宏观核极化的时间依赖性，并研究了它满足其中一位作者最初提出的唯象微分方程的条件（FB）。除了该方程不描述由相邻自旋相互作用引起的线结构这一事实之外，还发现其有效性仅对于自旋大于1的核以及另外四极弛豫至关重要的情况受到严重限制。在这些情况下，它要求分子环境是各向同性的，例如在气体和液体样品中，并且此外，它们与原子核相互作用的特征频率与拉莫尔频率相比要大，使得纵向和横向弛豫时间之间存在相等。
Starting from the microscopic viewpoint, the dynamics of nuclear induction is derived by means of statistical methods. The only essential lack of generality lies in the assumption that the nuclei in the sample are independent of each other, so that the treatment does not account for features arising from spin-spin interaction. By considering the simultaneous action of an arbitrary external field and of the molecular surroundings upon a representative nucleus a system of linear differential equations of the first order is derived for the" distribution matrix." It is analogous to the classical Boltzmann equation for the distribution function and allows, upon integration, to determine the macroscopic average value of any spin function in its dependence upon time. This general result is particularly applied to the time dependence of the macroscopic nuclear polarization, and the conditions are investigated under which it satisfies the phenomenological differential equation originally proposed by one of the authors (FB). Besides the fact that this equation does not describe line structures caused by the interaction of neighboring spins its validity is found to be seriously restricted only for nuclei having a spin larger than unity and in cases where, in addition, quadrupole relaxation is essential. It demands in these cases that the molecular surroundings are isotropic, eg, as in gaseous and liquid samples, and further, that their characteristic frequencies of interaction with the nuclei are large compared to the Larmor frequency so that there exists equality between the longitudinal and the transverse relaxation time.