# Surface-Collision Analysis of Microscale-Confined 129Xe in Pyrex Vapor Cells Based on Stem-Transport and Gradient Diffusion Dynamics

## TL;DR

This paper studies how surface collisions in Pyrex vapor cells affect the spin coherence of 129Xe atoms and proposes a method to optimize cell geometry for better performance in NMR gyroscopes.

## Contribution

A new structural coupling factor and geometry correction model are introduced to predict and reduce transverse relaxation rates in Pyrex vapor cells.

## Key findings

- The model predicts transverse relaxation rates with high accuracy (R2=0.982) across eight configurations.
- Geometry optimization reduces the relaxation rate by 41.8%, from 0.225 to 0.131s−1.
- The framework enables in-situ comparison of surface depolarization effects across fabrication protocols.

## Abstract

Surface collisions at Pyrex walls limit the spin coherence in nuclear magnetic resonance gyroscopes (NMRG) vapor cells, while the cavity–stem junction introduces geometry dependent exchange that perturbs the transverse spin relaxation time T2 of 129Xe atoms. We combine T2 measurements with Monte Carlo simulations of confined diffusion and surface collisions to decompose the relaxation of Xe atoms and derive a cavity–stem geometry correction for wall relaxation. A structural coupling factor (SCF) is introduced to compress stem length and aperture diameter into a dimensionless metric for diffusion-limited mixing, enabling prediction of the transverse relaxation rate versus geometry. Across eight simulated configurations, the model yields R2=0.982 and agrees with experiments within 7–9%, comparable to the measurement uncertainty (±0.015s−1). Using the validated framework, geometry optimization reduces the relaxation rate from 0.225 to 0.131s−1 (a 41.8% improvement). This Pyrex surface-collisional analysis provides an in-situ, T2-based route to compare effective surface depolarization across fabrication and surface-treatment protocols while accounting for cavity–stem coupling.