涨落纳米容器中自旋为1/2的核分子气体的NMR线型
NMR line shapes of a gas of nuclear spin-1/2 molecules in fluctuating nano-containers
摘要：
本文研究了介质中纳米气体容器几何形状的起伏对纳米容器内气体核磁共振谱线形状的影响。对于纳米容器体积和相对于外部磁场的取向的两种典型动力学，我们精确计算了自旋为1/2的携带分子的气体的核磁共振线形状：（i）高斯随机动力学，和（ii）对于规则的谐波振动。对于高斯系综的静态无序容器具有无限的相关时间，$τ_{\sf c} \to \infty $，整体线的形状被证明服从对数低频渐近，$ I(ω) = {const} \times \ln (\frac{1}ω)$，在$ω\to 0$，和指数衰减的渐近在高频域。对于有限$τ_{\sf c}$的快速波动容器的高斯系综，整个线型具有钟形轮廓，并具有$\sim ω^{-4}$远翼特性。此外，我们精确地计算了当液体中的纳米气泡受到由于声波的谐波变形的影响时，NMR线形状的卫星结构。
英文摘要：
Reported in this paper is the impact of the fluctuations of the geometry of the nano-meter gas containers in the medium on the NMR line shape of the gas inside of the nano-containers. We calculate exactly the NMR line shape of the gas of spin-1/2 carrying molecules for two typical dynamics of the nano-container volume and the orientation with respect to the external magnetic field: (i) for a Gaussian stochastic dynamics, and (ii) for the regular harmonic vibrations. For the Gaussian ensemble of static disordered containers having an infinite correlation time, $τ_{\sf c} \to \infty $, the overall line shape is shown to obey a logarithmic low frequency asymptotics, $ I(ω) = {const} \times \ln (\frac{1}ω)$, at $ω\to 0$, and exponentially decaying asymptotics in a high frequency domain. For the Gaussian ensemble of the rapidly fluctuating containers of a finite $τ_{\sf c}$, the overall line shape has a bell-shaped profile with $\sim ω^{-4}$ far wing behaviour. In addition, we calculate exactly a satellite structure of the NMR line shape when the nano-bubbles in a liquid are affected by the harmonic deformations due to the acoustic waves.
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