# Localization regime in diffusion NMR: theory and experiments

## TL;DR

This paper explores the localization regime in diffusion NMR, demonstrating how high-gradient conditions lead to boundary-localized magnetization and a stretched-exponential signal decay, with theoretical and experimental validation.

## Contribution

It provides a comprehensive theoretical and experimental analysis of the localization regime in diffusion NMR across various geometries, highlighting its generic nature at high gradients.

## Key findings

- Localization regime causes boundary-localized magnetization.
- Stretched-exponential decay observed in experiments.
- Agreement between theory, simulations, and experiments.

## Abstract

In this work we investigate the emergence of the localization regime for diffusion in various geometries: inside slabs, inside cylinders and around rods arranged on a square array. At high gradients, the transverse magnetization is strongly attenuated in the bulk, whereas the macroscopic signal is formed by the remaining magnetization localized near boundaries of the sample. As a consequence, the signal is particularly sensitive to the microstructure. Our theoretical analysis relies on recent mathematical advances on the study of the Bloch-Torrey equation. Experiments were conducted with hyperpolarized xenon-129 gas in 3D-printed phantoms and show an excellent agreement with numerical simulations and theoretical predictions. Our mathematical arguments and experimental evidence indicate that the localization regime with a stretched-exponential decay of the macroscopic signal is a generic feature of diffusion NMR that can be observed at moderately high gradients in most NMR scanners.