Attenuation of the NMR signal in a field gradient due to stochastic dynamics with memory

TL;DR

This paper derives a general expression for NMR signal attenuation in a magnetic field gradient considering stochastic particle dynamics with memory, applicable to various diffusion types and pulse sequences.

Contribution

It introduces a unified method to calculate NMR signal attenuation for non-Markovian stochastic motions, extending previous models to include memory effects and refocusing sequences.

Findings

Derived a general attenuation function S(t) for non-Markovian dynamics.

Showed the applicability to normal, anomalous diffusion, and refocusing pulse sequences.

Evaluated signal attenuation using a generalized Langevin equation with exponential memory kernel.

Abstract

The attenuation function S(t) for an ensemble of spins in a magnetic-field gradient is calculated by accumulation of the phase shifts in the rotating frame resulting from the displacements of spin-bearing particles. The found S(t), expressed through the particle mean square displacement, is applicable for any kind of stationary stochastic motion of spins, including their non-markovian dynamics with memory. The known expressions valid for normal and anomalous diffusion are obtained as special cases in the long time approximation. The method is also applicable to the NMR pulse sequences based on the refocusing principle. This is demonstrated by describing the Hahn spin echo experiment. The attenuation of the NMR signal is also evaluated providing that the random motion of particle is modeled by the generalized Langevin equation with the memory kernel exponentially decaying in time.