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 $T_2$ of ¹²⁹Xe atoms. We combine $T_2$ 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 $R^2=0.982$ and agrees with experiments within 7–$9\%$, comparable to the measurement uncertainty ($\pm 0.015{\mathrm{s}}^{-1}$). Using the validated framework, geometry optimization reduces the relaxation rate from $0.225$ to $0.131{\mathrm{s}}^{-1}$ (a $41.8\%$ improvement). This Pyrex surface-collisional analysis provides an in-situ, $T_2$-based route to compare effective surface depolarization across fabrication and surface-treatment protocols while accounting for cavity–stem coupling.

Reliable modeling of pressure-broadened spectra is essential for maintaining physical consistency in alkali vapor-cell diagnostics. In this work, we investigate the low-power absorption spectra of isotopically enriched ⁸⁷Rb vapor cells at the D₁ and D₂ transitions, systematically comparing three fitting algorithms: single Lorentzian, hyperfine-resolved Voigt, and the doublet Lorentzian approximation. Experiments were performed across optical intensities from 40 nW to 10 mW, buffer-gas pressures from 200 Torr to 520 Torr, and temperatures between 370 K and 390 K. It is shown that when the pressure broadening dominates over Doppler broadening and the optical intensity remains below the saturation regime, the reduced doublet Lorentzian model achieves a fitting accuracy of R² > 0.996. Under the pressure conditions of 350 Torr, the fitting error for both the doublet and Voigt approximations remains below 0.3% for the D₂ line and below 0.1% for the D₁ line. At the pressures of 520 Torr and under elevated optical intensities, the spectrum evolves toward a single-peaked profile, rendering a single Lorentzian model sufficient. The quantitative applicability boundary of the doublet approximation in ⁸⁷Rb vapor cells is established, defining the operational regime where hyperfine-resolved modeling can be reduced under collision-dominated conditions in NMRG systems.

The spin relaxation rate of Xe isotopes is a key characteristic of nuclear magnetic resonance gyroscopes (NMRGs). A pump-induced biphasic relaxation (PBR) model is proposed to describe the pump dependence of the transverse relaxation rate of ¹²⁹Xe nuclear spin. The distribution of electron polarization is theoretically analyzed based on the Bloch–Torrey equations and the volume-averaged polarization is evaluated through NMR frequency shift measurements. Experimental results confirm the theoretical quadratic dependence between Γ and $P_{Rb}$ with a high fitting accuracy (R² = 0.9969). The predicted linear (R² > 0.9966) and hyperbolic (R² > 0.9942) regimes of Γ versus pump power are also observed. Validation across different pump power conditions shows agreement between the model and measurements, with an average relative deviation of 0.2169%. The multi-stage process of nuclear spin relaxation is quantified, thereby providing a robust validation for the PBR model.