NMR line shapes of a gas of nuclear spin-1/2 molecules in fluctuating nano-containers

Abstract

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, ${\tau }_{\mathsf{c}}\to \infty$, the overall line shape is shown to obey a logarithmic low frequency asymptotics, $I(\omega )=const\times \ln (\frac{1}{\omega })$, at $\omega \to 0$, and exponentially decaying asymptotics in a high frequency domain. For the Gaussian ensemble of the rapidly fluctuating containers of a finite ${\tau }_{\mathsf{c}}$, the overall line shape has a bell-shaped profile with $\sim {\omega }^{-4}$ 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.

14 pages, 4 figures