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

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 (Formula presented.) of ¹²⁹Xe atoms. We combine (Formula presented.) 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 (Formula presented.) and agrees with experiments within 7– (Formula presented.), comparable to the measurement uncertainty ((Formula presented.)). Using the validated framework, geometry optimization reduces the relaxation rate from (Formula presented.) to (Formula presented.) (a (Formula presented.) improvement). This Pyrex surface-collisional analysis provides an in-situ, (Formula presented.) -based route to compare effective surface depolarization across fabrication and surface-treatment protocols while accounting for cavity–stem coupling.